Comparing magnetic fluctuation dynamics in nonlinear MHD simulations of low-aspect-ratio RFPs to RELAX experiments

NASA Astrophysics Data System (ADS)

McCollam, K. J.; den Hartog, D. J.; Jacobson, C. M.; Sovinec, C. R.; Masamune, S.; Sanpei, A.

2017-10-01

We present comparisons of magnetic tearing fluctuation activity between RFP experiments on the low-aspect-ratio RELAX device (R / a 2) and nonlinear simulations of zero-beta, single-fluid MHD using the NIMROD code in both cylindrical and toroidal geometries at a Lundquist number of S =104 , nearly as high as experimental values. Time-average fluctuation amplitudes observed in the simulations are similar to those from the experiments, but more rigorous comparisons versus spectral mode numbers are in progress. We also focus on how the spatiotemporal dynamics of the fluctuations vary with RFP equilibrium parameters. Interestingly, at shallow reversal, cylindrical simulations show a relatively uncoupled spectrum of nearly quiescent modes periodically varying in time, whereas the corresponding toroidal cases show a fully chaotic spectrum of strongly nonlinearly interacting modes. We ascribe this to the geometric m = 1 coupling present in the toroidal but not the cylindrical case. We present initial results from convergence studies with increased spatial resolution for both geometries. Simulations at higher S are planned. This work is supported by the U.S. DOE and by the Japan Society for the Promotion of Science.

Separation of Evans and Hiro currents in VDE of tokamak plasma

NASA Astrophysics Data System (ADS)

Galkin, Sergei A.; Svidzinski, V. A.; Zakharov, L. E.

2014-10-01

Progress on the Disruption Simulation Code (DSC-3D) development and benchmarking will be presented. The DSC-3D is one-fluid nonlinear time-dependent MHD code, which utilizes fully 3D toroidal geometry for the first wall, pure vacuum and plasma itself, with adaptation to the moving plasma boundary and accurate resolution of the plasma surface current. Suppression of fast magnetosonic scale by the plasma inertia neglecting will be demonstrated. Due to code adaptive nature, self-consistent plasma surface current modeling during non-linear dynamics of the Vertical Displacement Event (VDE) is accurately provided. Separation of the plasma surface current on Evans and Hiro currents during simulation of fully developed VDE, then the plasma touches in-vessel tiles, will be discussed. Work is supported by the US DOE SBIR Grant # DE-SC0004487.

Experimental identification of nonlinear coupling between (intermediate, small)-scale microturbulence and an MHD mode in the core of a superconducting tokamak

NASA Astrophysics Data System (ADS)

Sun, P. J.; Li, Y. D.; Ren, Y.; Zhang, X. D.; Wu, G. J.; Xu, L. Q.; Chen, R.; Li, Q.; Zhao, H. L.; Zhang, J. Z.; Shi, T. H.; Wang, Y. M.; Lyu, B.; Hu, L. Q.; Li, J.; The EAST Team

2018-01-01

In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence (k\\perpρi˜2{-}5.2 ) and the MHD mode (toroidal mode number m = -1 , poloidal mode number n = 1 ) are measured simultaneously, using a four-channel tangential CO2 laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.

Global MHD simulation of magnetosphere using HPF

NASA Astrophysics Data System (ADS)

Ogino, T.

We have translated a 3-dimensional magnetohydrodynamic (MHD) simulation code of the Earth's magnetosphere from VPP Fortran to HPF/JA on the Fujitsu VPP5000/56 vector-parallel supercomputer and the MHD code was fully vectorized and fully parallelized in VPP Fortran. The entire performance and capability of the HPF MHD code could be shown to be almost comparable to that of VPP Fortran. A 3-dimensional global MHD simulation of the earth's magnetosphere was performed at a speed of over 400 Gflops with an efficiency of 76.5% using 56 PEs of Fujitsu VPP5000/56 in vector and parallel computation that permitted comparison with catalog values. We have concluded that fluid and MHD codes that are fully vectorized and fully parallelized in VPP Fortran can be translated with relative ease to HPF/JA, and a code in HPF/JA may be expected to perform comparably to the same code written in VPP Fortran.

Simulation of Alfvén eigenmode bursts using a hybrid code for nonlinear magnetohydrodynamics and energetic particles

NASA Astrophysics Data System (ADS)

Todo, Y.; Berk, H. L.; Breizman, B. N.

2012-03-01

A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δBm/n/B ~ 5 × 10-3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δBm/n/B ~ 2 × 10-3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Dynamics of tokamak plasma surface current in 3D ideal MHD model

NASA Astrophysics Data System (ADS)

Galkin, Sergei A.; Svidzinski, V. A.; Zakharov, L. E.

2013-10-01

Interest in the surface current which can arise on perturbed sharp plasma vacuum interface in tokamaks was recently generated by a few papers (see and references therein). In dangerous disruption events with plasma-touching-wall scenarios, the surface current can be shared with the wall leading to the strong, damaging forces acting on the wall A relatively simple analytic definition of δ-function surface current proportional to a jump of tangential component of magnetic field nevertheless leads to a complex computational problem on the moving plasma-vacuum interface, requiring the incorporation of non-linear 3D plasma dynamics even in one-fluid ideal MHD. The Disruption Simulation Code (DSC), which had recently been developed in a fully 3D toroidal geometry with adaptation to the moving plasma boundary, is an appropriate tool for accurate self-consistent δfunction surface current calculation. Progress on the DSC-3D development will be presented. Self-consistent surface current calculation under non-linear dynamics of low m kink mode and VDE will be discussed. Work is supported by the US DOE SBIR grant #DE-SC0004487.

Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kavitha, L., E-mail: louiskavitha@yahoo.co.in; The Abdus Salam International Centre for Theoretical Physics, Trieste; Lavanya, C.

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales muchmore » shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.« less

MHD retrofit of steam power plants. Feasibility study. Summary and conclusions, Part I

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1979-07-01

The US Department of Energy Division of Magnetohydrodynamics (DOE/MHD) initiated this study to evaluate the feasibility of a retrofit option to reduce the time and cost of commercializing MHD. The MHD retrofit option will integrate a nominal 260 megawatt thermal (MWt) MHD topping cycle into an existing or scheduled private utility steam plant; this facility will test both the MHD system and the combined operation of the MHD/steam plant. The 260 MWt input level was determined to be the size which could most effectively demonstrate and verify the engineering design and operational characteristics of a coal-fired, open-cycle, MHD power plant.more » Details are presented. A goal of the MHD program is to have operational by the year 2003 a commercial size, fully integrated MHD plant. This would be accomplished by demonstrating commercial scale, baseload performance of a fully integrated, MHD/steam power plant. (WHK)« less

SAC: Sheffield Advanced Code

NASA Astrophysics Data System (ADS)

Griffiths, Mike; Fedun, Viktor; Mumford, Stuart; Gent, Frederick

2013-06-01

The Sheffield Advanced Code (SAC) is a fully non-linear MHD code designed for simulations of linear and non-linear wave propagation in gravitationally strongly stratified magnetized plasma. It was developed primarily for the forward modelling of helioseismological processes and for the coupling processes in the solar interior, photosphere, and corona; it is built on the well-known VAC platform that allows robust simulation of the macroscopic processes in gravitationally stratified (non-)magnetized plasmas. The code has no limitations of simulation length in time imposed by complications originating from the upper boundary, nor does it require implementation of special procedures to treat the upper boundaries. SAC inherited its modular structure from VAC, thereby allowing modification to easily add new physics.

Feedback and Control of Linear and Nonlinear Global MHD Modes in Rotating Plasmas

NASA Astrophysics Data System (ADS)

Finn, J. M.; Chacon, L.

2002-11-01

We present studies of feedback applied to resistive wall modes in the presence of plasma rotation. The main tool used is a Newton-Krylov nonlinear reduced resistive MHD code with completely implicit time stepping[1]. The effects of proportional and derivative gain and toroidal phase shift are investigated. In addition to studying the complete stabilization of the resistive wall mode, we present results on controlling the amplitude of nonlinear modes locked to the wall but propagating slowly; we also show results on reducing the hysteresis in the locking-unlocking bifurcation diagram. [1] L. Chacon, D. A. Knoll and J. M. Finn, "An implicit, nonlinear reduced resistive MHD solver", J. Comp. Phys. v. 178, pp 15-36 (2002).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Stabilization of the SIESTA MHD Equilibrium Code Using Rapid Cholesky Factorization

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; D'Azevedo, E. A.; Seal, S. K.

2016-10-01

The SIESTA MHD equilibrium code solves the discretized nonlinear MHD force F ≡ J X B - ∇p for a 3D plasma which may contain islands and stochastic regions. At each nonlinear evolution step, it solves a set of linearized MHD equations which can be written r ≡ Ax - b = 0, where A is the linearized MHD Hessian matrix. When the solution norm | x| is small enough, the nonlinear force norm will be close to the linearized force norm | r| 0 obtained using preconditioned GMRES. In many cases, this procedure works well and leads to a vanishing nonlinear residual (equilibrium) after several iterations in SIESTA. In some cases, however, | x|>1 results and the SIESTA code has to be restarted to obtain nonlinear convergence. In order to make SIESTA more robust and avoid such restarts, we have implemented a new rapid QR factorization of the Hessian which allows us to rapidly and accurately solve the least-squares problem AT r = 0, subject to the condition | x|<1. This avoids large contributions to the nonlinear force terms and in general makes the convergence sequence of SIESTA much more stable. The innovative rapid QR method is based on a pairwise row factorization of the tri-diagonal Hessian. It provides a complete Cholesky factorization while preserving the memory allocation of A. This work was supported by the U.S. D.O.E. contract DE-AC05-00OR22725.

Global Magnetohydrodynamic Simulation Using High Performance FORTRAN on Parallel Computers

NASA Astrophysics Data System (ADS)

Ogino, T.

High Performance Fortran (HPF) is one of modern and common techniques to achieve high performance parallel computation. We have translated a 3-dimensional magnetohydrodynamic (MHD) simulation code of the Earth's magnetosphere from VPP Fortran to HPF/JA on the Fujitsu VPP5000/56 vector-parallel supercomputer and the MHD code was fully vectorized and fully parallelized in VPP Fortran. The entire performance and capability of the HPF MHD code could be shown to be almost comparable to that of VPP Fortran. A 3-dimensional global MHD simulation of the earth's magnetosphere was performed at a speed of over 400 Gflops with an efficiency of 76.5 VPP5000/56 in vector and parallel computation that permitted comparison with catalog values. We have concluded that fluid and MHD codes that are fully vectorized and fully parallelized in VPP Fortran can be translated with relative ease to HPF/JA, and a code in HPF/JA may be expected to perform comparably to the same code written in VPP Fortran.

Impact of chemical reaction in fully developed radiated mixed convective flow between two rotating disk

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Waqas, M.; Alsaedi, A.

2018-06-01

Flow of magnetohydrodynamic (MHD) viscous fluid between two rotating disks is modeled. Angular velocities of two disks are different. Flow is investigated for nonlinear mixed convection. Heat transfer is analyzed for nonlinear thermal radiation and heat generation/absorption. Chemical reaction is also implemented. Convective conditions of heat and mass transfer are studied. Transformations used lead to reduction of PDEs into the ODEs. The impacts of important physical variables like Prandtl number, Reynold number, Hartman number, mixed convection parameter, chemical reaction and Schmidt number on velocities, temperature and concentration are elaborated. In addition velocity and temperature gradients are physically interpreted. Our obtained results indicate that radial, axial and tangential velocities decrease for higher estimation of Hartman number.

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.

2004-01-01

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

Fully Implicit, Nonlinear 3D Extended Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chacon, Luis; Knoll, Dana

2003-10-01

Extended magnetohydrodynamics (XMHD) includes nonideal effects such as nonlinear, anisotropic transport and two-fluid (Hall) effects. XMHD supports multiple, separate time scales that make explicit time differencing approaches extremely inefficient. While a fully implicit implementation promises efficiency without sacrificing numerical accuracy,(D. A. Knoll et al., phJ. Comput. Phys.) 185 (2), 583-611 (2003) the nonlinear nature of the XMHD system and the numerical stiffness associated with the fast waves make this endeavor difficult. Newton-Krylov methods are, however, ideally suited for such a task. These synergistically combine Newton's method for nonlinear convergence, and Krylov techniques to solve the associated Jacobian (linear) systems. Krylov methods can be implemented Jacobian-free and can be preconditioned for efficiency. Successful preconditioning strategies have been developed for 2D incompressible resistive(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002) and Hall(L. Chacón and D. A. Knoll, phJ. Comput. Phys.), 188 (2), 573-592 (2003) MHD models. These are based on ``physics-based'' ideas, in which knowledge of the physics is exploited to derive well-conditioned (diagonally-dominant) approximations to the original system that are amenable to optimal solver technologies (multigrid). In this work, we will describe the status of the extension of the 2D preconditioning ideas for a 3D compressible, single-fluid XMHD model.

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

NASA Astrophysics Data System (ADS)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

On the local well-posedness and a Prodi-Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion

NASA Astrophysics Data System (ADS)

Larios, Adam; Pei, Yuan

2017-07-01

We prove a Prodi-Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of only two velocity and two magnetic components. To the best of our knowledge, this is the first Prodi-Serrin-type criterion for such a 3D hydrodynamic system which is not fully dissipative, and indicates that such an approach may be successful on other systems. In addition, we provide a constructive proof of the local well-posedness of solutions to the fully dissipative 3D MHD-Boussinesq system, and also the fully inviscid, irresistive, non-diffusive MHD-Boussinesq equations. We note that, as a special case, these results include the 3D non-diffusive Boussinesq system and the 3D MHD equations. Moreover, they can be extended without difficulty to include the case of a Coriolis rotational term.

Fully 3D modeling of tokamak vertical displacement events with realistic parameters

NASA Astrophysics Data System (ADS)

Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

2016-10-01

In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

MHD shocks in coronal mass ejections

NASA Technical Reports Server (NTRS)

Steinolfson, R. S.

1991-01-01

The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Local properties of magnetic reconnection in nonlinear resistive- and extended-magnetohydrodynamic toroidal simulations of the sawtooth crash

DOE PAGES

Beidler, M. T.; Cassak, P. A.; Jardin, S. C.; ...

2016-12-15

We diagnose local properties of magnetic reconnection during a sawtooth crash employing the three-dimensional toroidal, extended-magnetohydrodynamic (MHD) code M3D-C 1. To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical (m, n) = (1, 1) mode at the q = 1 surface, where m and n are the poloidal and toroidal mode numbers and q is the safety factor. We study the nonlinear evolution of a particular test equilibrium in a non-reduced field representation using both resistive-MHD and extended-MHD models. We find growth rates for the extended-MHD reconnection process exhibitmore » a nonlinear acceleration and greatly exceed that of the resistive-MHD model, as is expected from previous experimental, theoretical, and computational work. We compare the properties of reconnection in the two simulations, revealing the reconnecting current sheets are locally different in the two models and we present the first observation of the quadrupole out-of-plane Hall magnetic field that appears during extended-MHD reconnection in a 3D toroidal simulation (but not in resistive-MHD). We also explore the dependence on toroidal angle of the properties of reconnection as viewed in the plane perpendicular to the helical magnetic field, finding qualitative and quantitative effects due to changes in the symmetry of the reconnection process. Furthermore, this study is potentially important for a wide range of magnetically confined fusion applications, from confirming simulations with extended-MHD effects are sufficiently resolved to describe reconnection, to quantifying local reconnection rates for purposes of understanding and predicting transport, not only at the q = 1 rational surface for sawteeth, but also at higher order rational surfaces that play a role in disruptions and edge-confinement degradation.« less

Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D

DOE PAGES

Liu, Feng; Huijsmans, G. T. A.; Loarte, A.; ...

2015-09-04

In the Quiescent H-mode (QH-mode) regime, the edge harmonic oscillation (EHO), thought to be a saturated kink-peeling mode (KPM) driven unstable by current and rotation, is found in experiment to provide sufficient stationary edge particle transport to avoid the periodic expulsion of particles and energy by edge localized modes (ELMs). In this article, both linear and nonlinear MHD modelling of QH-mode plasmas from the DIII-D tokamak have been investigated to understand the mechanism leading to the appearance of the EHO in QH-mode plasmas. For the first time nonlinear MHD simulations with low-n modes both with ideal wall and resistive wallmore » boundary conditions have been carried out with 3-D non-linear MHD code JOREK. The results show, in agreement with the original conjectures, that in the nonlinear phase, kink peeling modes are the main unstable modes in QH-mode plasmas of DIIID and that the kink-peeling modes saturate non-linearly leading to a 3-D stationary state. The characteristics of the kink-peeling modes, in terms of mode structure and associated decrease of the edge plasma density associated with them, are in good agreement with experimental measurements of the EHO in DIII-D. Finally, the effect of plasma resistivity, the role of plasma parallel rotation as well as the effect of the conductivity of the vacuum vessel wall on the destabilization and saturation of kink-peeling modes have been evaluated for experimental QH-mode plasma conditions in DIII-D.« less

The method of projected characteristics for the evolution of magnetic arches

NASA Technical Reports Server (NTRS)

Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

1987-01-01

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacón, L.; Cappello, S.

2010-08-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacón, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code in cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonfiglio, Daniele; Chacon, Luis; Cappello, Susanna

2010-01-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacon, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code inmore » cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.« less

Frequency chirpings in Alfven continuum

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

2017-10-01

We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

Nonlinear simulation of the fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, Malik; Faganello, Matteo; Berk, Herbert; Garbet, Xavier; Benkadda, Sadruddin; PIIM Team; IFS Team; IRFM Team

2014-10-01

We propose to extend the Odblom-Breizman precessional fishbone model to account for both the MagnetoHydroDynamic (MHD) nonlinearity at the q = 1 surface and the nonlinear response of the energetic particles contained within the q = 1 surface. This electromagnetic mode, whose excitation, damping and frequency chirping are determined by the self-consistent interaction between an energetic trapped particle population and the bulk plasma evolution, can induce effective transport and losses for the energetic particles, being them alpha-particles in next-future fusion devices or heated particles in present Tokamaks. The model is reduced to its simplest form, assuming a reduced MHD description for the bulk plasma and a two-dimensional phase-space evolution (gyro and bounce averaged) for deeply trapped energetic particles. Numerical simulations have been performed in order to characterize the mode chirping and saturation, in particular looking at the interplay between the development of phase-space structures and the system dissipation associated to the MHD non-linearities at the resonance locations.

Comparing nonlinear MHD simulations of low-aspect-ratio RFPs to RELAX experiments

NASA Astrophysics Data System (ADS)

McCollam, K. J.; den Hartog, D. J.; Jacobson, C. M.; Sovinec, C. R.; Masamune, S.; Sanpei, A.

2016-10-01

Standard reversed-field pinch (RFP) plasmas provide a nonlinear dynamical system as a validation domain for numerical MHD simulation codes, with applications in general toroidal confinement scenarios including tokamaks. Using the NIMROD code, we simulate the nonlinear evolution of RFP plasmas similar to those in the RELAX experiment. The experiment's modest Lundquist numbers S (as low as a few times 104) make closely matching MHD simulations tractable given present computing resources. Its low aspect ratio ( 2) motivates a comparison study using cylindrical and toroidal geometries in NIMROD. We present initial results from nonlinear single-fluid runs at S =104 for both geometries and a range of equilibrium parameters, which preliminarily show that the magnetic fluctuations are roughly similar between the two geometries and between simulation and experiment, though there appear to be some qualitative differences in their temporal evolution. Runs at higher S are planned. This work is supported by the U.S. DOE and by the Japan Society for the Promotion of Science.

Fully implicit adaptive mesh refinement solver for 2D MHD

NASA Astrophysics Data System (ADS)

Philip, B.; Chacon, L.; Pernice, M.

2008-11-01

Application of implicit adaptive mesh refinement (AMR) to simulate resistive magnetohydrodynamics is described. Solving this challenging multi-scale, multi-physics problem can improve understanding of reconnection in magnetically-confined plasmas. AMR is employed to resolve extremely thin current sheets, essential for an accurate macroscopic description. Implicit time stepping allows us to accurately follow the dynamical time scale of the developing magnetic field, without being restricted by fast Alfven time scales. At each time step, the large-scale system of nonlinear equations is solved by a Jacobian-free Newton-Krylov method together with a physics-based preconditioner. Each block within the preconditioner is solved optimally using the Fast Adaptive Composite grid method, which can be considered as a multiplicative Schwarz method on AMR grids. We will demonstrate the excellent accuracy and efficiency properties of the method with several challenging reduced MHD applications, including tearing, island coalescence, and tilt instabilities. B. Philip, L. Chac'on, M. Pernice, J. Comput. Phys., in press (2008)

Extended MHD Turbulence and Its Applications to the Solar Wind

NASA Astrophysics Data System (ADS)

Abdelhamid, Hamdi M.; Lingam, Manasvi; Mahajan, Swadesh M.

2016-10-01

Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k\\lt 1/{λ }I), Hall (1/{λ }I\\lt k\\lt 1/{λ }e), and electron inertia (k\\gt 1/{λ }e) regimes; k is the wavenumber and {λ }s=c/{ω }{ps} is the skin depth of species “s.” In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of -11/3 and -13/3 are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately -4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard “dissipation” range paradigm.

Modeling of Nonlinear Beat Signals of TAE's

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-03-01

Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core

Magnetotail dynamics under isobaric constraints

NASA Technical Reports Server (NTRS)

Birn, Joachim; Schindler, Karl; Janicke, Lutz; Hesse, Michael

1994-01-01

Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

The modulational instability for the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we study the modulational instability for the TDNLS equations derived by Hada (1993) and Brio, Hunter, and Johnson to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.

On MHD nonlinear stretching flow of Powell-Eyring nanomaterial

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Sajjad, Rai; Muhammad, Taseer; Alsaedi, Ahmed; Ellahi, Rahmat

This communication addresses the magnetohydrodynamic (MHD) flow of Powell-Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell-Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted.

Liquid-metal flows: Magnetohydrodynamics and applications; Proceedings of the Fifth Beersheba International Seminar on Magnetohydrodynamic Flows and Turbulence, University of the Negev, Beersheba, Israel, Mar. 2-6, 1987

DOE Office of Scientific and Technical Information (OSTI.GOV)

Branover, H.; Mond, M.; Unger, Y.

The present collection of papers on MHD-related uses of liquid metal flows and their applications discusses topics in laminar MHD flows, MHD power generation, metallurgical MHD applications, and two-phase MHD flows. Attention is given to MHD flows with closed streamlines, nonlinear waves in liquid metals under a transverse magnetic field, liquid-metal MHD conversion of nuclear energy to electricity, the testing of optimized MHD conversion (OMACON) systems, and aspects of a liquid-metal induction generator. Also discussed are MHD effects in liquid-metal breeder reactors, a plasma-driven MHD powerplant, modeling the recirculating flows in channel-induction surfaces, the hydrodynamics of aluminum reduction cells, free-surfacemore » determination in a levitation-melting process, the parametric interactions of waves in bubbly liquid metals, and the occurrence of cavitation in water jets.« less

Experimental evidence of phase coherence of magnetohydrodynamic turbulence in the solar wind: GEOTAIL satellite data.

PubMed

Koga, D; Chian, A C-L; Hada, T; Rempel, E L

2008-02-13

Magnetohydrodynamic (MHD) turbulence is commonly observed in the solar wind. Nonlinear interactions among MHD waves are likely to produce finite correlation of the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in the quasi-linear theory) or have a finite coherence. Using a method based on the surrogate data technique, we analysed the GEOTAIL magnetic field data to evaluate the phase coherence in MHD turbulence in the Earth's foreshock region. The results demonstrate the existence of finite phase correlation, indicating that nonlinear wave-wave interactions are in progress.

Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D [Connection between plasma response and RMP ELM suppression in DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wingen, Andreas; Ferraro, Nathaniel M.; Shafer, Morgan W.

Calculations of the plasma response to applied non-axisymmetric fields in several DIII-D discharges show that predicted displacements depend strongly on the edge current density. This result is found using both a linear two-fluid-MHD model (M3D-C1) and a nonlinear ideal-MHD model (VMEC). Furthermore, it is observed that the probability of a discharge being edge localized mode (ELM)-suppressed is most closely related to the edge current density, as opposed to the pressure gradient. It is found that discharges with a stronger kink response are closer to the peeling–ballooning stability limit in ELITE simulations and eventually cross into the unstable region, causing ELMsmore » to reappear. Thus for effective ELM suppression, the RMP has to prevent the plasma from generating a large kink response, associated with ELM instability. Experimental observations are in agreement with the finding; discharges which have a strong kink response in the MHD simulations show ELMs or ELM mitigation during the RMP phase of the experiment, while discharges with a small kink response in the MHD simulations are fully ELM suppressed in the experiment by the applied resonant magnetic perturbation. The results are cross-checked against modeled 3D ideal MHD equilibria using the VMEC code. The procedure of constructing optimal 3D equilibria for diverted H-mode discharges using VMEC is presented. As a result, kink displacements in VMEC are found to scale with the edge current density, similar to M3D-C1, but the displacements are smaller. A direct correlation in the flux surface displacements to the bootstrap current is shown.« less

Computational Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Norman, M. L.

1994-05-01

Cosmic magnetic fields have intrigued and vexed astrophysicists seeking to understand their complex dynamics in a wide variety of astronomical settings. Magnetic fields are believed to play an important role in regulating star formation in molecular clouds, providing an effective viscosity in accretion disks, accelerating astrophysical jets, and influencing the large scale structure of the ISM of disk galaxies. Radio observations of supernova remnants and extragalactic radio jets prove that magnetic fields are are fundamentally linked to astrophysical particle acceleration. Magnetic fields exist on cosmological scales as shown by the existence of radio halos in clusters of galaxies. Theoretical investigation of these and other phenomena require numerical simulations due to the inherent complexity of MHD, but until now neither the computer power nor the numerical algorithms existed to mount a serious attack on the most important problems. That has now changed. Advances in parallel computing and numerical algorithms now permit the simulation of fully nonlinear, time-dependent astrophysical MHD in 2D and 3D. In this talk, I will describe the ZEUS codes for astrophysical MHD developed at the Laboratory for Computational Astrophysics (LCA) at the University of Illinois. These codes are now available to the national community. The numerical algorithms and test suite used to validate them are briefly discussed. Several applications of ZEUS to topics listed above are presented. An extension of ZEUS to model ambipolar diffusion in weakly ionized plasmas is illustrated. I discuss how continuing exponential growth in computer power and new numerical algorithms under development will allow us to tackle two grand challenges: compressible MHD turbulence and relativistic MHD. This work is partially supported by grants NSF AST-9201113 and NASA NAG 5-2493.

Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D [Connection between plasma response and RMP ELM suppression in DIII-D

DOE PAGES

Wingen, Andreas; Ferraro, Nathaniel M.; Shafer, Morgan W.; ...

2015-09-03

Calculations of the plasma response to applied non-axisymmetric fields in several DIII-D discharges show that predicted displacements depend strongly on the edge current density. This result is found using both a linear two-fluid-MHD model (M3D-C1) and a nonlinear ideal-MHD model (VMEC). Furthermore, it is observed that the probability of a discharge being edge localized mode (ELM)-suppressed is most closely related to the edge current density, as opposed to the pressure gradient. It is found that discharges with a stronger kink response are closer to the peeling–ballooning stability limit in ELITE simulations and eventually cross into the unstable region, causing ELMsmore » to reappear. Thus for effective ELM suppression, the RMP has to prevent the plasma from generating a large kink response, associated with ELM instability. Experimental observations are in agreement with the finding; discharges which have a strong kink response in the MHD simulations show ELMs or ELM mitigation during the RMP phase of the experiment, while discharges with a small kink response in the MHD simulations are fully ELM suppressed in the experiment by the applied resonant magnetic perturbation. The results are cross-checked against modeled 3D ideal MHD equilibria using the VMEC code. The procedure of constructing optimal 3D equilibria for diverted H-mode discharges using VMEC is presented. As a result, kink displacements in VMEC are found to scale with the edge current density, similar to M3D-C1, but the displacements are smaller. A direct correlation in the flux surface displacements to the bootstrap current is shown.« less

Chemical reaction and heat generation/absorption aspects in MHD nonlinear convective flow of third grade nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Alsaedi, Ahmed

Nonlinear thermal radiation and chemical reaction in magnetohydrodynamic (MHD) flow of third grade nanofluid over a stretching sheet with variable thickness are addressed. Heat generation/absorption and nonlinear convection are considered. The sheet moves with nonlinear velocity. Sheet is convectively heated. In addition zero mass flux condition for nanoparticle concentration is imposed. Results for velocity, temperature, concentration, skin friction and local Nusselt number are presented and examined. It is found that velocity and boundary layer thickness are increasing for Reynolds number. Temperature is a increasing function of the heat generation/absorption parameter while it causes a decrease in the heat transfer rate. Moreover effect of Brownian motion and chemical reaction on the concentration are quite reverse.

Nonlinearly driven harmonics of Alfvén modes

NASA Astrophysics Data System (ADS)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

NASA Astrophysics Data System (ADS)

Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

2018-01-01

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

Test particles dynamics in the JOREK 3D non-linear MHD code and application to electron transport in a disruption simulation

NASA Astrophysics Data System (ADS)

Sommariva, C.; Nardon, E.; Beyer, P.; Hoelzl, M.; Huijsmans, G. T. A.; van Vugt, D.; Contributors, JET

2018-01-01

In order to contribute to the understanding of runaway electron generation mechanisms during tokamak disruptions, a test particle tracker is introduced in the JOREK 3D non-linear MHD code, able to compute both full and guiding center relativistic orbits. Tests of the module show good conservation of the invariants of motion and consistency between full orbit and guiding center solutions. A first application is presented where test electron confinement properties are investigated in a massive gas injection-triggered disruption simulation in JET-like geometry. It is found that electron populations initialised before the thermal quench (TQ) are typically not fully deconfined in spite of the global stochasticity of the magnetic field during the TQ. The fraction of ‘survivors’ decreases from a few tens down to a few tenths of percent as the electron energy varies from 1 keV to 10 MeV. The underlying mechanism for electron ‘survival’ is the prompt reformation of closed magnetic surfaces at the plasma core and, to a smaller extent, the subsequent reappearance of a magnetic surface at the edge. It is also found that electrons are less deconfined at 10 MeV than at 1 MeV, which appears consistent with a phase averaging effect due to orbit shifts at high energy.

Fundamentals of Plasma Physics

NASA Astrophysics Data System (ADS)

Bellan, Paul M.

2008-07-01

Preface; 1. Basic concepts; 2. The Vlasov, two-fluid, and MHD models of plasma dynamics; 3. Motion of a single plasma particle; 4. Elementary plasma waves; 5. Streaming instabilities and the Landau problem; 6. Cold plasma waves in a magnetized plasma; 7. Waves in inhomogeneous plasmas and wave energy relations; 8. Vlasov theory of warm electrostatic waves in a magnetized plasma; 9. MHD equilibria; 10. Stability of static MHD equilibria; 11. Magnetic helicity interpreted and Woltjer-Taylor relaxation; 12. Magnetic reconnection; 13. Fokker-Planck theory of collisions; 14. Wave-particle nonlinearities; 15. Wave-wave nonlinearities; 16. Non-neutral plasmas; 17. Dusty plasmas; Appendix A. Intuitive method for vector calculus identities; Appendix B. Vector calculus in orthogonal curvilinear coordinates; Appendix C. Frequently used physical constants and formulae; Bibliography; References; Index.

Linear and nonlinear regimes of the 2-D Kelvin-Helmholtz/Tearing instability in Hall MHD.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.; Finn, J. M.

2002-11-01

The study to date of the magnetic field effects on the Kelvin-Helmholtz instability (KHI) within the framework of Hall MHD has been limited to configurations with uniform magnetic fields and/or with the magnetic field perpendicular to the sheared ion flow (( B_0⊥ v0 )).(E. N. Opp et al., Phys. Fluids B), 3, 885 (1990)^,(M. Fujimoto et al., J. Geophys. Res.), 96, 15725 (1991)^,(J. D. Huba, Phys. Rev. Lett.), 72, 2033 (1994) Here, we are concerned with the effects of Hall physics in configurations in which (B_0allel v0 ) and both are sheared.(L. Chacon et al, Phys. Lett. A), submitted (2002) In resistive MHD, and for this configuration, either the tearing mode instability (TMI) or the KHI instability dominates depending upon their relative strength.( R. B. Dahlburg et al., Phys. Plasmas), 4, 1213 (1997) In Hall MHD, however, Hall physics decouples the ion and electron flows in a boundary layer of thickness (d_i=c/ω_pi) (ion skin depth), within which electrons are the only magnetized species. Hence, while KHI essentially remains an ion instability, TMI becomes an electron instability. As a result, both KHI and TMI can be unstable simultaneously and interact, creating a very rich linear and nonlinear behavior. This is confirmed by a linear study of the Hall MHD equations. Nonlinearly, both saturated regimes and highly dynamic regimes (with vortex and magnetic island merging) are observed.

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

NASA Astrophysics Data System (ADS)

Sjögreen, Björn; Yee, H. C.

2018-07-01

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] - MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5]. Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9], and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21,22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

Self-Consistent and Time-Dependent Solar Wind Models

NASA Technical Reports Server (NTRS)

Ong, K. K.; Musielak, Z. E.; Rosner, R.; Suess, S. T.; Sulkanen, M. E.

1997-01-01

We describe the first results from a self-consistent study of Alfven waves for the time-dependent, single-fluid magnetohydrodynamic (MHD) solar wind equations, using a modified version of the ZEUS MHD code. The wind models we examine are radially symmetrical and magnetized; the initial outflow is described by the standard Parker wind solution. Our study focuses on the effects of Alfven waves on the outflow and is based on solving the full set of the ideal nonlinear MHD equations. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; thus, the models naturally account for the back-reaction of the wind on the waves, as well as for the nonlinear interaction between different types of MHD waves. Our results clearly demonstrate when momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast streams in solar coronal holes; we discuss the range of wave amplitudes required to obtained such fast stream solutions.

Enhanced Spectral Anisotropies Near the Proton-Cyclotron Scale: Possible Two-Component Structure in Hall-FLR MHD Turbulence Simulations

NASA Technical Reports Server (NTRS)

Ghosh, Sanjoy; Goldstein, Melvyn L.

2011-01-01

Recent analysis of the magnetic correlation function of solar wind fluctuations at 1 AU suggests the existence of two-component structure near the proton-cyclotron scale. Here we use two-and-one-half dimensional and three-dimensional compressible MHD models to look for two-component structure adjacent the proton-cyclotron scale. Our MHD system incorporates both Hall and Finite Larmor Radius (FLR) terms. We find that strong spectral anisotropies appear adjacent the proton-cyclotron scales depending on selections of initial condition and plasma beta. These anisotropies are enhancements on top of related anisotropies that appear in standard MHD turbulence in the presence of a mean magnetic field and are suggestive of one turbulence component along the inertial scales and another component adjacent the dissipative scales. We compute the relative strengths of linear and nonlinear accelerations on the velocity and magnetic fields to gauge the relative influence of terms that drive the system with wave-like (linear) versus turbulent (nonlinear) dynamics.

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Tsuji, Paul H.

Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered inmore » an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.« less

Progress report on PIXIE3D, a fully implicit 3D extended MHD solver

NASA Astrophysics Data System (ADS)

Chacon, Luis

2008-11-01

Recently, invited talk at DPP07 an optimal, massively parallel implicit algorithm for 3D resistive magnetohydrodynamics (PIXIE3D) was demonstrated. Excellent algorithmic and parallel results were obtained with up to 4096 processors and 138 million unknowns. While this is a remarkable result, further developments are still needed for PIXIE3D to become a 3D extended MHD production code in general geometries. In this poster, we present an update on the status of PIXIE3D on several fronts. On the physics side, we will describe our progress towards the full Braginskii model, including: electron Hall terms, anisotropic heat conduction, and gyroviscous corrections. Algorithmically, we will discuss progress towards a robust, optimal, nonlinear solver for arbitrary geometries, including preconditioning for the new physical effects described, the implementation of a coarse processor-grid solver (to maintain optimal algorithmic performance for an arbitrarily large number of processors in massively parallel computations), and of a multiblock capability to deal with complicated geometries. L. Chac'on, Phys. Plasmas 15, 056103 (2008);

Validation of Extended MHD Models using MST RFP Plasmas

NASA Astrophysics Data System (ADS)

Jacobson, C. M.; Chapman, B. E.; Craig, D.; McCollam, K. J.; Sovinec, C. R.

2016-10-01

Significant effort has been devoted to improvement of computational models used in fusion energy sciences. Rigorous validation of these models is necessary in order to increase confidence in their ability to predict the performance of future devices. MST is a well diagnosed reversed-field pinch (RFP) capable of operation over a wide range of parameters. In particular, the Lundquist number S, a key parameter in resistive magnetohydrodynamics (MHD), can be varied over a wide range and provide substantial overlap with MHD RFP simulations. MST RFP plasmas are simulated using both DEBS, a nonlinear single-fluid visco-resistive MHD code, and NIMROD, a nonlinear extended MHD code, with S ranging from 104 to 5 ×104 for single-fluid runs, with the magnetic Prandtl number Pm = 1 . Experiments with plasma current IP ranging from 60 kA to 500 kA result in S from 4 ×104 to 8 ×106 . Validation metric comparisons are presented, focusing on how magnetic fluctuations b scale with S. Single-fluid NIMROD results give S b - 0.21 , and experiments give S b - 0.28 for the dominant m = 1 , n = 6 mode. Preliminary two-fluid NIMROD results are also presented. Work supported by US DOE.

Extended-MHD Studies of Flow-Profile Effects on Edge Harmonic Oscillations in QH-mode Discharges

NASA Astrophysics Data System (ADS)

King, J. R.; Burrell, K. H.; Garofalo, A. M.; Jenkins, T. G.; Kruger, S. E.; Snyder, P. B.

2012-10-01

It is desirable to have an ITER H-mode regime that is quiescent to edge-localized modes (ELMs). ELMs deposit large, localized, impulsive, surface heat loads that can damage the divertor. One such quiescent regime with edge harmonic oscillations (EHO) is observed on DIII-D, JET, JT-60U, and ASDEX-U [1]. The physical mechanisms of EHO are not fully understood, but linear MHD calculations suggest EHO may be a saturated kink-peeling mode partially driven by flow-profile shear [2]. We present preliminary EHO computations using the extended-MHD NIMROD code. The model incorporates first-order FLR effects and parallel heat flows. Using reconstructed DIII-D profiles from discharges with EHO, we scan the ExB and polodial flow profiles and compute linear stability. The aim is to ascertain the role of the ExB flow shear, as motivated by experimental results [3], and to compare with theoretical predictions where the growth rate is enhanced at intermediate wavenumbers and cut-off at large wavenumbers by diamagnetic effects [4]. Initial nonlinear computations exploring the EHO saturation mechanism are presented.[4pt] [1] Phys. Plasmas, v19, p056117, 2012 (and refs. within).[0pt] [2] Nucl. Fusion, v47, p961, 2007.[0pt] [3] Nucl. Fusion, v51, p083018, 2011.[0pt] [4] Phys. Plasmas v10, p4405, 2003.

New analysis of magnetic tornadoes

NASA Astrophysics Data System (ADS)

Arter, Wayne

2017-04-01

The recent work[1] showed how the equations of ideal, compressible magnetohydrodynamics (MHD) may be elegantly formulated in terms of Lie derivatives, building on the work of Helmholtz, Walen and Arnold. The ``linear" fields approach reduces ideal MHD to a low order set of non-linear ordinary differential equations capable of further simplification, so has the potential to enrich understanding of this difficult subject, which has application both to laboratory and geophysical/astrophysical plasmas. The just published work [2] extends the linear fields' solution of compressible nonlinear MHD to the case where the magnetic field depends on superlinear powers of position vector, usually but not always, expressed in Cartesian components. Implications of the resulting Lie-Taylor series expansion for physical applicability of the Dolzhansky-Kirchhoff (D-K) ``linear field" equations are found to be positive. It is demonstrated how resistivity may be included in the D-K model. Arguments are put forward that the D-K equations may be regarded as illustrating properties of nonlinear MHD in the same sense that the Lorenz equations inform about the onset of convective turbulence. It is thereby suggested that the Lie-Taylor series approach may lead to valuable insights into MHD turbulence, especially fast timescale transients and the role of plasmoids. This work has been part-funded by the RCUK Energy Programme. 1. Arter, W. 2013 ``Potential vorticity formulation of compressible magnetohydrodynamics. Phys. Rev. Lett. 110, 015004." (doi:10.1103/PhysRevLett.110.015004) 2. Arter, W. 2017 ``Beyond linear fields: the Lie-Taylor expansion", Proc. R. Soc. A473, 20160525; http://dx.doi.org/10.1098/rspa.2016.0525

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beidler, M. T.; Cassak, P. A.; Jardin, S. C.

We diagnose local properties of magnetic reconnection during a sawtooth crash employing the three-dimensional toroidal, extended-magnetohydrodynamic (MHD) code M3D-C 1. To do so, we sample simulation data in the plane in which reconnection occurs, the plane perpendicular to the helical (m, n) = (1, 1) mode at the q = 1 surface, where m and n are the poloidal and toroidal mode numbers and q is the safety factor. We study the nonlinear evolution of a particular test equilibrium in a non-reduced field representation using both resistive-MHD and extended-MHD models. We find growth rates for the extended-MHD reconnection process exhibitmore » a nonlinear acceleration and greatly exceed that of the resistive-MHD model, as is expected from previous experimental, theoretical, and computational work. We compare the properties of reconnection in the two simulations, revealing the reconnecting current sheets are locally different in the two models and we present the first observation of the quadrupole out-of-plane Hall magnetic field that appears during extended-MHD reconnection in a 3D toroidal simulation (but not in resistive-MHD). We also explore the dependence on toroidal angle of the properties of reconnection as viewed in the plane perpendicular to the helical magnetic field, finding qualitative and quantitative effects due to changes in the symmetry of the reconnection process. Furthermore, this study is potentially important for a wide range of magnetically confined fusion applications, from confirming simulations with extended-MHD effects are sufficiently resolved to describe reconnection, to quantifying local reconnection rates for purposes of understanding and predicting transport, not only at the q = 1 rational surface for sawteeth, but also at higher order rational surfaces that play a role in disruptions and edge-confinement degradation.« less

Nonlinear MHD Waves in a Prominence Foot

NASA Astrophysics Data System (ADS)

Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.

2015-11-01

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.

Modeling TAE Response To Nonlinear Drives

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-10-01

Experiment has detected the Toroidal Alfven Eigenmodes (TAE) with signals at twice the eigenfrequency.These harmonic modes arise from the second order perturbation in amplitude of the MHD equation for the linear modes that are driven the energetic particle free energy. The structure of TAE in realistic geometry can be calculated by generalizing the linear numerical solver (AEGIS package). We have have inserted all the nonlinear MHD source terms, where are quadratic in the linear amplitudes, into AEGIS code. We then invert the linear MHD equation at the second harmonic frequency. The ratio of amplitudes of the first and second harmonic terms are used to determine the internal field amplitude. The spatial structure of energy and density distribution are investigated. The results can be directly employed to compare with experiments and determine the Alfven wave amplitude in the plasma region.

Nonlinear helicons bearing multi-scale structures

NASA Astrophysics Data System (ADS)

Abdelhamid, Hamdi M.; Yoshida, Zensho

2017-02-01

The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing a wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution, which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

Nonlinear Two Fluid and Kinetic ELM Simulations

NASA Astrophysics Data System (ADS)

Strauss, H. R.; Sugiyama, L.; Chang, C. S.; Ku, S.; Hientzsch, B.; Breslau, J.; Park, W.; Samtaney, R.; Adams, M.; Jardin, S.

2006-04-01

Simulations of ELMs using dissipative MHD, two fluid MHD, and neoclassical kinetic physics models are being carried out using the M3D code [1]. Resistive MHD simulations of nonlinear edge pressure and current driven instabilities have been performed, initialized with realistic DIIID equilibria. Simulations show the saturation of the modes and relaxation of equilbrium profiles. Linear simulations including two fluid effects show the stabilization of toroidal mode number n = 10 modes, when the Hall parameter H, the ratio of ion skin depth to major radius, exceeds a threshhold. Nonlinear simulations are being done including gyroviscous stabilization. Kinetic effects are incorporated by coupling with the XGC code [2], which is able to simulate the edge plasma density and pressure pedestal buildup. These profiles are being used to initialize M3D simulations of an ELM crash and pedestal relaxation. The goal is to simulate an ELM cycle. [1] Park, W., Belova, E.V., Fu, G.Y., Tang, X.Z., Strauss, H.R., Sugiyama, L.E., Phys. Plas. 6, 1796 (1999).[2] Chang, C.S., Ku, S., and Weitzner, H., Phys. Plas. 11, 2649 (2004)

Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations

NASA Astrophysics Data System (ADS)

Beidler, Matthew T.; Callen, James D.; Hegna, Chris C.; Sovinec, Carl R.

2017-10-01

Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extended-MHD code NIMROD, building on previous work by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. Supported by DOE OFES Grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664.

Fully Implict Magneto-hydrodynamics Simulations of Coaxial Plasma Accelerators

DOE PAGES

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-01-05

The resistive Magneto-Hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. We developed a fully implicit MHD simulation tool to solve the resistive MHD governing equations in the context of a cell-centered finite-volume scheme. The primary objective of this study is to use the fully-implicit algorithm to obtain insights into the plasma acceleration and jet formation processes in Coaxial Plasma accelerators; electromagnetic acceleration devices that utilize self-induced magnetic fields to accelerate thermal plasmas to large velocities. We also carry out plasma-surface simulations in order to study the impact interactionsmore » when these high velocity plasma jets impinge on target material surfaces. Scaling studies are carried out to establish some basic functional relationships between the target-stagnation conditions and the current discharged between the coaxial electrodes.« less

Data-driven Modeling of the Solar Corona by a New Three-dimensional Path-conservative Osher-Solomon MHD Model

NASA Astrophysics Data System (ADS)

Feng, Xueshang; Li, Caixia; Xiang, Changqing; Zhang, Man; Li, HuiChao; Wei, Fengsi

2017-11-01

A second-order path-conservative scheme with a Godunov-type finite-volume method has been implemented to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time. This code operates on the six-component composite grid system in three-dimensional spherical coordinates with hexahedral cells of quadrilateral frustum type. The generalized Osher-Solomon Riemann solver is employed based on a numerical integration of the path-dependent dissipation matrix. For simplicity, the straight line segment path is used, and the path integral is evaluated in a fully numerical way by a high-order numerical Gauss-Legendre quadrature. Besides its very close similarity to Godunov type, the resulting scheme retains the attractive features of the original solver: it is nonlinear, free of entropy-fix, differentiable, and complete, in that each characteristic field results in a different numerical viscosity, due to the full use of the MHD eigenstructure. By using a minmod limiter for spatial oscillation control, the path-conservative scheme is realized for the generalized Lagrange multiplier and the extended generalized Lagrange multiplier formulation of solar wind MHD systems. This new model that is second order in space and time is written in the FORTRAN language with Message Passing Interface parallelization and validated in modeling the time-dependent large-scale structure of the solar corona, driven continuously by Global Oscillation Network Group data. To demonstrate the suitability of our code for the simulation of solar wind, we present selected results from 2009 October 9 to 2009 December 29 show its capability of producing a structured solar corona in agreement with solar coronal observations.

Data-Driven Modeling of Solar Corona by a New 3d Path-Conservative Osher-Solomon MHD Odel

NASA Astrophysics Data System (ADS)

Feng, X. S.; Li, C.

2017-12-01

A second-order path-conservative scheme with Godunov-type finite volume method (FVM) has been implemented to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time. This code operates on the six-component composite grid system in 3D spherical coordinates with hexahedral cells of quadrilateral frustum type. The generalized Osher-Solomon Riemann solver is employed based on a numerical integration of the path-dependentdissipation matrix. For simplicity, the straight line segment path is used and the path-integral is evaluated in a fully numerical way by high-order numerical Gauss-Legendre quadrature. Besides its closest similarity to Godunov, the resulting scheme retains the attractive features of the original solver: it is nonlinear, free of entropy-fix, differentiable and complete in that each characteristic field results in a different numerical viscosity, due to the full use of the MHD eigenstructure. By using a minmod limiter for spatial oscillation control, the pathconservative scheme is realized for the generalized Lagrange multiplier (GLM) and the extended generalized Lagrange multiplier (EGLM) formulation of solar wind MHD systems. This new model of second-order in space and time is written in FORTRAN language with Message Passing Interface (MPI) parallelization, and validated in modeling time-dependent large-scale structure of solar corona, driven continuously by the Global Oscillation Network Group (GONG) data. To demonstrate the suitability of our code for the simulation of solar wind, we present selected results from October 9th, 2009 to December 29th, 2009 , & Year 2008 to show its capability of producing structured solar wind in agreement with the observations.

Acceleration of the Fast Solar Wind by Solitary Waves in Coronal Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

2001-01-01

The purpose of this investigation is to develop a new model for the acceleration of the fast solar wind by nonlinear. time-dependent multidimensional MHD simulations of waves in solar coronal holes. Preliminary computational studies indicate that nonlinear waves are generated in coronal holes by torsional Alfv\\'{e}n waves. These waves in addition to thermal conduction may contribute considerably to the accelerate the solar wind. Specific goals of this proposal are to investigate the generation of nonlinear solitary-like waves and their effect on solar wind acceleration by numerical 2.5D MHD simulation of coronal holes with a broad range of plasma and wave parameters; to study the effect of random disturbances at the base of a solar coronal hole on the fast solar wind acceleration with a more advanced 2.5D MHD model and to compare the results with the available observations; to extend the study to a full 3D MHD simulation of fast solar wind acceleration with a more realistic model of a coronal hole and solar boundary conditions. The ultimate goal of the three year study is to model the, fast solar wind in a coronal hole, based on realistic boundary conditions in a coronal hole near the Sun, and the coronal hole structure (i.e., density, temperature. and magnetic field geometry,) that will become available from the recently launched SOHO spacecraft.

Acceleration of the Fast Solar Wind by Solitary Waves in Coronal Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

2000-01-01

The purpose of this investigation is to develop a new model for the acceleration of the fast solar wind by nonlinear, time-dependent multidimensional MHD simulations of waves in solar coronal holes. Preliminary computational studies indicate that solitary-like waves are generated in coronal holes nonlinearly by torsional Alfven waves. These waves in addition to thermal conduction may contribute considerably to the accelerate the solar wind. Specific goals of this proposal are to investigate the generation of nonlinear solitary-like waves and their effect on solar wind acceleration by numerical 2.5D MHD simulation of coronal holes with a broad range of plasma and wave parameters; to study the effect of random disturbances at the base of a solar coronal hole on the fast solar wind acceleration with a more advanced 2.5D MHD model and to compare the results with the available observations; to extend the study to a full 3D MHD simulation of fast solar wind acceleration with a more realistic model of a coronal hole and solar boundary conditions. The ultimate goal of the three year study is to model the fast solar wind in a coronal hole, based on realistic boundary conditions in a coronal hole near the Sun, and the coronal hole structure (i.e., density, temperature, and magnetic field geometry) that will become available from the recently launched SOHO spacecraft.

Validation of MHD Models using MST RFP Plasmas

NASA Astrophysics Data System (ADS)

Jacobson, C. M.; Chapman, B. E.; den Hartog, D. J.; McCollam, K. J.; Sarff, J. S.; Sovinec, C. R.

2017-10-01

Rigorous validation of computational models used in fusion energy sciences over a large parameter space and across multiple magnetic configurations can increase confidence in their ability to predict the performance of future devices. MST is a well diagnosed reversed-field pinch (RFP) capable of operation with plasma current ranging from 60 kA to 500 kA. The resulting Lundquist number S, a key parameter in resistive magnetohydrodynamics (MHD), ranges from 4 ×104 to 8 ×106 for standard RFP plasmas and provides substantial overlap with MHD RFP simulations. MST RFP plasmas are simulated using both DEBS, a nonlinear single-fluid visco-resistive MHD code, and NIMROD, a nonlinear extended MHD code, with S ranging from 104 to 105 for single-fluid runs, and the magnetic Prandtl number Pm = 1 . Validation metric comparisons are presented, focusing on how normalized magnetic fluctuations at the edge b scale with S. Preliminary results for the dominant n = 6 mode are b S - 0 . 20 +/- 0 . 02 for single-fluid NIMROD, b S - 0 . 25 +/- 0 . 05 for DEBS, and b S - 0 . 20 +/- 0 . 02 for experimental measurements, however there is a significant discrepancy in mode amplitudes. Preliminary two-fluid NIMROD results are also presented. Work supported by US DOE.

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD

NASA Astrophysics Data System (ADS)

Beidler, M. T.; Callen, J. D.; Hegna, C. C.; Sovinec, C. R.

2017-05-01

The nonlinear, extended-magnetohydrodynamic (MHD) code NIMROD is benchmarked with the theory of time-dependent forced magnetic reconnection induced by small resonant fields in slab geometry in the context of visco-resistive MHD modeling. Linear computations agree with time-asymptotic, linear theory of flow screening of externally applied fields. The inclusion of flow in nonlinear computations can result in mode penetration due to the balance between electromagnetic and viscous forces in the time-asymptotic state, which produces bifurcations from a high-slip state to a low-slip state as the external field is slowly increased. We reproduce mode penetration and unlocking transitions by employing time-dependent externally applied magnetic fields. Mode penetration and unlocking exhibit hysteresis and occur at different magnitudes of applied field. We also establish how nonlinearly determined flow screening of the resonant field is affected by the square of the magnitude of the externally applied field. These results emphasize that the inclusion of nonlinear physics is essential for accurate prediction of the reconnected field in a flowing plasma.

Electric Current Filamentation Induced by 3D Plasma Flows in the Solar Corona

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nickeler, Dieter H.; Karlický, Marian; Kraus, Michaela

Many magnetic structures in the solar atmosphere evolve rather slowly, so they can be assumed as (quasi-)static or (quasi-)stationary and represented via magnetohydrostatic (MHS) or stationary magnetohydrodynamic (MHD) equilibria, respectively. While exact 3D solutions would be desired, they are extremely difficult to find in stationary MHD. We construct solutions with magnetic and flow vector fields that have three components depending on all three coordinates. We show that the noncanonical transformation method produces quasi-3D solutions of stationary MHD by mapping 2D or 2.5D MHS equilibria to corresponding stationary MHD states, that is, states that display the same field-line structure as themore » original MHS equilibria. These stationary MHD states exist on magnetic flux surfaces of the original 2D MHS states. Although the flux surfaces and therefore also the equilibria have a 2D character, these stationary MHD states depend on all three coordinates and display highly complex currents. The existence of geometrically complex 3D currents within symmetric field-line structures provides the basis for efficient dissipation of the magnetic energy in the solar corona by ohmic heating. We also discuss the possibility of maintaining an important subset of nonlinear MHS states, namely force-free fields, by stationary flows. We find that force-free fields with nonlinear flows only arise under severe restrictions of the field-line geometry and of the magnetic flux density distribution.« less

The variety of MHD shock waves interactions in the solar wind flow

NASA Technical Reports Server (NTRS)

Grib, S. A.

1995-01-01

Different types of nonlinear shock wave interactions in some regions of the solar wind flow are considered. It is shown, that the solar flare or nonflare CME fast shock wave may disappear as the result of the collision with the rotational discontinuity. By the way the appearance of the slow shock waves as the consequence of the collision with other directional discontinuity namely tangential is indicated. Thus the nonlinear oblique and normal MHD shock waves interactions with different solar wind discontinuities (tangential, rotational, contact, shock and plasmoidal) both in the free flow and close to the gradient regions like the terrestrial magnetopause and the heliopause are described. The change of the plasma pressure across the solar wind fast shock waves is also evaluated. The sketch of the classification of the MHD discontinuities interactions, connected with the solar wind evolution is given.

Nonlinear MHD study on the influence of E×B flow in QH-mode plasma of DIII-D

NASA Astrophysics Data System (ADS)

Liu, Feng; Huijsmans, Guido; Loarte, Alberto; Garofalo, Andrea; Solomon, Wayne; Nkonga, Boniface; Hoelzl, Matthias

2017-10-01

In QH-mode experiments with zero-net NBI torque show that there remains a finite E×B rotation in the pedestal region implying that a minimum E×B flow or flow shear is required for the plasma to develop the Edge Harmonic Oscillation (EHO), which is a saturated KPM (kink-peeling mode) characteristic of the QH-mode. To understand the roles of E×B flow and its shear in the saturation of KPMs, non-linear MHD simulations of DIII-D QH-mode plasmas including toroidal mode numbers n = 0 to 10 with different E×B rotation speed have been performed. These simulation show that ExB rotation strongly stabilizes high-n modes but destabilizes low-n modes (particularly the n =2 mode) in the linear growth phase, which is consistent experimental observations and previous linear MHD modelling. US DOE under DE-FC02-04ER54698.

High-beta extended MHD simulations of stellarators

NASA Astrophysics Data System (ADS)

Bechtel, T. A.; Hegna, C. C.; Sovinec, C. R.; Roberds, N. A.

2016-10-01

The high beta properties of stellarator plasmas are studied using the nonlinear, extended MHD code NIMROD. In this work, we describe recent developments to the semi-implicit operator which allow the code to model 3D plasma evolution with better accuracy and efficiency. The configurations under investigation are an l=2, M=5 torsatron with geometry modeled after the Compact Toroidal Hybrid (CTH) experiment and an l=2, M=10 torsatron capable of having vacuum rotational transform profiles near unity. High-beta plasmas are created using a volumetric heating source and temperature dependent anisotropic thermal conduction and resistivity. To reduce computation expenses, simulations are initialized from stellarator symmetric pseudo-equilibria by turning on symmetry breaking modes at finite beta. The onset of MHD instabilities and nonlinear consequences are monitored as a function of beta as well as the fragility of the magnetic surfaces. Research supported by US DOE under Grant No. DE-FG02-99ER54546.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

NASA Astrophysics Data System (ADS)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

A Numerical Approach to Solving the Hall MHD Equations Including Diamagnetic Drift (Preprint)

DTIC Science & Technology

2008-02-19

SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Dr. Jean-Luc Cambier a. REPORT...1997. [3] L. Chacon and D.A. Knoll. A 2d high-beta hall mhd implicit nonlinear solver. Journal of Computational Physics, 188:573–592, 2003. [4] Tony F

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

Modeling MHD Stagnation Point Flow of Thixotropic Fluid with Non-uniform Heat Absorption/Generation

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Shah, Faisal; Khan, Muhammad Ijaz; Alsaedi, Ahmed; Yasmeen, Tabassum

2017-12-01

Here magnetohydrodynamic (MHD) stagnation point flow by nonlinear stretching sheet is discussed. Variable thickness of sheet is accounted. In addition non-uniform heat generation/absorption concept is retained. Numerical treatment to arising nonlinear system is presented. Shooting procedure is adopted for numerical treatment. Graphs and tables lead to physical description of results. It is observed that skin friction enhances for ( H a) and it decays for different rising values of ( K 1), ( K 2) and ( n). Further temperature gradient increases for higher estimation of (Pr) and decreases for larger ( H a). Major findings of present analysis are presented.

Visco-Resistive MHD Modeling Benchmark of Forced Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Beidler, M. T.; Hegna, C. C.; Sovinec, C. R.; Callen, J. D.; Ferraro, N. M.

2016-10-01

The presence of externally-applied 3D magnetic fields can affect important phenomena in tokamaks, including mode locking, disruptions, and edge localized modes. External fields penetrate into the plasma and can lead to forced magnetic reconnection (FMR), and hence magnetic islands, on resonant surfaces if the local plasma rotation relative to the external field is slow. Preliminary visco-resistive MHD simulations of FMR in a slab geometry are consistent with theory. Specifically, linear simulations exhibit proper scaling of the penetrated field with resistivity, viscosity, and flow, and nonlinear simulations exhibit a bifurcation from a flow-screened to a field-penetrated, magnetic island state as the external field is increased, due to the 3D electromagnetic force. These results will be compared to simulations of FMR in a circular cross-section, cylindrical geometry by way of a benchmark between the NIMROD and M3D-C1 extended-MHD codes. Because neither this geometry nor the MHD model has the physics of poloidal flow damping, the theory of will be expanded to include poloidal flow effects. The resulting theory will be tested with linear and nonlinear simulations that vary the resistivity, viscosity, flow, and external field. Supported by OFES DoE Grants DE-FG02-92ER54139, DE-FG02-86ER53218, DE-AC02-09CH11466, and the SciDAC Center for Extended MHD Modeling.

Final Technical Report: Collaborative Research Center for Nonlinear Simulation of Energetic Particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berk, Herbert L.

2018-02-15

The study of this project focused on developing a reduced nonlinear model to describe chirping processes in a fusion plasma. A successful method was developed with results clear enough to allow an analytic theory to be developed that replicates the long term response of a nonlinear phase space structure immersed in the MHD continnuum.

Fully implicit adaptive mesh refinement MHD algorithm

NASA Astrophysics Data System (ADS)

Philip, Bobby

2005-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former results in stiffness due to the presence of very fast waves. The latter requires one to resolve the localized features that the system develops. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. To our knowledge, a scalable, fully implicit AMR algorithm has not been accomplished before for MHD. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technologyootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite --FAC-- algorithms) for scalability. We will demonstrate that the concept is indeed feasible, featuring optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations will be presented on a variety of problems.

An Analysis of Processes in the Solar Wind in a Thin Layer Adjacent to the Front of the Shock Wave

NASA Astrophysics Data System (ADS)

Molotkov, I. A.; Atamaniuk, B.

2018-05-01

A two-dimensional stationary system of nonlinear magnetohydrodynamics (MHD) equations in a thin layer adjoining the front of the interplanetary shock wave has been solved. Previously, any available publications relied on linear transport equations. But the presence of high-energy particles in the solar wind (SW) requires taking into account the processes of self-interaction. Our analysis examines the nonlinear terms in the MHD equations. A solution has been constructed for three cases: (1) in the absence of magnetic reconnections; (2) for magnetic reconnections; and (3) with the simultaneous action of reconnections and junction of magnetic islands. In all three cases, expressions were found for the main parameters of the SW. The results obtained on the basis of the solution of the MHD equations are consistent with the conclusions based on the investigation of the particle velocity distribution functions. This makes it possible to confirm the previously established fraction of particles excited to energies above 1 MeV.

Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D

DOE PAGES

King, Josh D.; Strait, Edward J.; Lazerson, Samuel A.; ...

2015-07-01

DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics (MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidal mode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. Moreover, these tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. We determine scans of the applied poloidal spectrum and edge safety factors which confirm thatmore » low-pressure, n = 1 non-axisymmetric tokamak equilibria are a single, dominant, stable eigenmode. But, at higher beta, near the ideal kink mode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.« less

Multi-megawatt, gigajoule plasma operation in Tore Supra

NASA Astrophysics Data System (ADS)

Dumont, R. J.; Goniche, M.; Ekedahl, A.; Saoutic, B.; Artaud, J.-F.; Basiuk, V.; Bourdelle, C.; Corre, Y.; Decker, J.; Elbèze, D.; Giruzzi, G.; Hoang, G.-T.; Imbeaux, F.; Joffrin, E.; Litaudon, X.; Lotte, Ph; Maget, P.; Mazon, D.; Nilsson, E.; The Tore Supra Team

2014-07-01

Integrating several important technological elements required for long pulse operation in magnetic fusion devices, the Tore Supra tokamak routinely addresses the physics and technology issues related to this endeavor and, as a result, contributes essential information on critical issues for ITER. During the last experimental campaign, components of the radiofrequency system including an ITER relevant launcher (passive active multijunction (PAM)) and continuous wave/3.7 GHz klystrons, have been extensively qualified, and then used to develop steady state scenarios in which the lower hybrid (LH), ion cyclotron (IC) and electron cyclotron (EC) systems have been combined in fully stationary shots (duration ˜150 s, injected power up to ˜8 MW, injected/extracted energy up to ˜1 GJ). Injection of LH power in the 5.0-6.0 MW range has extended the domain of accessible plasma parameters to higher densities and non-inductive currents. These discharges exhibit steady electron internal transport barriers (ITBs). We report here on various issues relevant to the steady state operation of future devices, ranging from operational aspects and limitations related to the achievement of long pulses in a fully actively cooled fusion device (e.g. overheating due to fast particle losses), to more fundamental plasma physics topics. The latter include a beneficial influence of IC resonance heating on the magnetohydrodynamic (MHD) stability in these discharges, which has been studied in detail. Another interesting observation is the appearance of oscillations of the central temperature with typical periods of the order of one to several seconds, caused by a nonlinear interplay between LH deposition, MHD activity and bootstrap current in the presence of an ITB.

Stratified Simulations of Collisionless Accretion Disks

NASA Astrophysics Data System (ADS)

Hirabayashi, Kota; Hoshino, Masahiro

2017-06-01

This paper presents a series of stratified-shearing-box simulations of collisionless accretion disks in the recently developed framework of kinetic magnetohydrodynamics (MHD), which can handle finite non-gyrotropy of a pressure tensor. Although a fully kinetic simulation predicted a more efficient angular-momentum transport in collisionless disks than in the standard MHD regime, the enhanced transport has not been observed in past kinetic-MHD approaches to gyrotropic pressure anisotropy. For the purpose of investigating this missing link between the fully kinetic and MHD treatments, this paper explores the role of non-gyrotropic pressure and makes the first attempt to incorporate certain collisionless effects into disk-scale, stratified disk simulations. When the timescale of gyrotropization was longer than, or comparable to, the disk-rotation frequency of the orbit, we found that the finite non-gyrotropy selectively remaining in the vicinity of current sheets contributes to suppressing magnetic reconnection in the shearing-box system. This leads to increases both in the saturated amplitude of the MHD turbulence driven by magnetorotational instabilities and in the resultant efficiency of angular-momentum transport. Our results seem to favor the fast advection of magnetic fields toward the rotation axis of a central object, which is required to launch an ultra-relativistic jet from a black hole accretion system in, for example, a magnetically arrested disk state.

Implementation of the full viscoresistive magnetohydrodynamic equations in a nonlinear finite element code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haverkort, J.W.; Dutch Institute for Fundamental Energy Research, P.O. Box 6336, 5600 HH Eindhoven; Blank, H.J. de

Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. Amore » rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.« less

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, H. C.

2003-01-01

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

MHD modeling of DIII-D QH-mode discharges and comparison to observations

NASA Astrophysics Data System (ADS)

King, Jacob

2016-10-01

MHD modeling of DIII-D QH-mode discharges and comparison to observations Nonlinear NIMROD simulations, initialized from a reconstruction of a DIII-D QH-mode discharge with broadband MHD, saturate into a turbulent state, but do not saturate when flow is not included. This is consistent with the experimental results of the quiescent regime observed on DIII-D with broadband MHD activity [Garofalo et al., PoP (2015) and refs. within]. These ELM-free discharges have the normalized pedestal-plasma confinement necessary for burning-plasma operation on ITER. Relative to QH-mode operation with more coherent MHD activity, operation with broadband MHD tends to occur at higher densities and lower rotation and thus may be more relevant to ITER. The nonlinear NIMROD simulations require highly accurate equilibrium reconstructions. Our equilibrium reconstructions include the scrape-off-layer profiles and the measured toroidal and poloidal rotation profiles. The simulation develops into a saturated turbulent state and the n=1 and 2 modes become dominant through an inverse cascade. Each toroidal mode in the range of n=1-5 is dominant at a different time. The perturbations are advected and sheared apart in the counter-clockwise direction consistent with the direction of the poloidal flow inside the LCFS. Work towards validation through comparison to magnetic coil and Doppler reflectometry measurements is presented. Consistent with experimental observations during QH-mode, the simulated state leads to large particle transport relative to the thermal transport. Analysis shows that the phase of the density and temperature perturbations differ resulting in greater convective particle transport relative to the convective thermal transport. This work supported by the U.S. Department of Energy Office of Science and the SciDAC Center for Extended MHD Modeling under Contract Numbers DE-FC02-06ER54875, DE-FC02-08ER54972 and DE-FC02-04ER54698.

Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

NASA Technical Reports Server (NTRS)

Lee, Nam C.; Parks, George K.

1992-01-01

A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

Hall-MHD simulations of the magnetosphere-northward solar wind interface : the Kelvin-Helmholtz instability as an entry mechanism for the solar wind through mixing and reconnections

NASA Astrophysics Data System (ADS)

Leroy, Matthieu; Keppens, Rony

2016-04-01

The transfer of matter from the solar-wind to the Earth's magnetosphere during southward solar wind is mostly well understood but the processes governing the same phenomenon during northward solar wind remains to be fully apprehended. Numerous numerical studies have investigated the topic with many interesting results but most of these were considering two-dimensional situations with simplified magnetic configuration and often neglecting the inhomogeneities for the sake of clarity. Given the typical parameters at the magnetosphere-solar wind interface, the situation must be considered in the frame of Hall-MHD, due to the fact that the current layers widths and the gradient lengths can be in the order of the ion inertial length. As a consequence of Hall-MHD creating a third vector component from two planar ones, and also because magnetic perturbations can affect the field configuration at a distance in all directions and not only locally, three-dimensional treatment is necessary. In this spirit three-dimensional simulations of a configuration approaching the conditions leading to the development of Kelvin-Helmholtz instabilities at the flank of the magnetosphere during northward oriented solar-wind are performed as means to study the entry of solar-wind matter into Earth's magnetic field. In the scope of assessing the effect of the Hall-term in the physical processes, the simulations are also performed in the MHD frame. Furthermore the influence of the density and velocity jump through the shear layer on the rate of mass entering the magnetosphere is explored. Indeed, depending on the exact values of the physical quantities, the Kelvin-Helmholtz instability may have to compete with secondary instabilities and the non-linear phase may exhibit vortex merging and large-scale structures reorganisation, creating very different mixing layers, or generate different reconnection sites, locally and at a distance. These different configurations may have discernible signatures that can be identified by spacecraft diagnostics.

Infiltration of MHD liquid into a deformable porous material

NASA Astrophysics Data System (ADS)

Naseem, Anum; Mahmood, Asif; Siddique, J. I.; Zhao, Lifeng

2018-03-01

We analyze the capillary rise dynamics for magnetohydrodynamics (MHD) fluid flow through deformable porous material in the presence of gravity effects. The modeling is performed using mixture theory approach and mathematical manipulation yields a nonlinear free boundary problem. Due to the capillary rise action, the pressure gradient in the liquid generates a stress gradient that results in the deformation of porous substrate. The capillary rise process for MHD fluid slows down as compared to Newtonian fluid case. Numerical solutions are obtained using a method of lines approach. The graphical results are presented for important physical parameters, and comparison is presented with Newtonian fluid case.

Beyond linear fields: the Lie–Taylor expansion

PubMed Central

2017-01-01

The work extends the linear fields’ solution of compressible nonlinear magnetohydrodynamics (MHD) to the case where the magnetic field depends on superlinear powers of position vector, usually, but not always, expressed in Cartesian components. Implications of the resulting Lie–Taylor series expansion for physical applicability of the Dolzhansky–Kirchhoff (D–K) equations are found to be positive. It is demonstrated how resistivity may be included in the D–K model. Arguments are put forward that the D–K equations may be regarded as illustrating properties of nonlinear MHD in the same sense that the Lorenz equations inform about the onset of convective turbulence. It is suggested that the Lie–Taylor series approach may lead to valuable insights into other fluid models. PMID:28265187

MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.

2017-09-01

This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.

Measuring the equations of state in a relaxed magnetohydrodynamic plasma.

PubMed

Kaur, M; Barbano, L J; Suen-Lewis, E M; Shrock, J E; Light, A D; Brown, M R; Schaffner, D A

2018-01-01

We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

Measuring the equations of state in a relaxed magnetohydrodynamic plasma

NASA Astrophysics Data System (ADS)

Kaur, M.; Barbano, L. J.; Suen-Lewis, E. M.; Shrock, J. E.; Light, A. D.; Brown, M. R.; Schaffner, D. A.

2018-01-01

We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

Inverse energy cascades in three-dimensional turbulence

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1991-01-01

Fully three-dimensional magnetohydrodynamic (MHD) turbulence at large kinetic and low magnetic Reynolds numbers is considered in the presence of a strong uniform magnetic field. It is shown by numerical simulation of a model of MHD that the energy inverse cascades to longer length scales when the interaction parameter is large. While the steady-state dynamics of the driven problem is three-dimensional in character, the behavior has resemblance to two-dimensional hydrodynamics. These results have implications in turbulence theory, MHD power generator, planetary dynamos, and fusion reactor blanket design.

Large eddy simulations of compressible magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Grete, Philipp

2017-02-01

Supersonic, magnetohydrodynamic (MHD) turbulence is thought to play an important role in many processes - especially in astrophysics, where detailed three-dimensional observations are scarce. Simulations can partially fill this gap and help to understand these processes. However, direct simulations with realistic parameters are often not feasible. Consequently, large eddy simulations (LES) have emerged as a viable alternative. In LES the overall complexity is reduced by simulating only large and intermediate scales directly. The smallest scales, usually referred to as subgrid-scales (SGS), are introduced to the simulation by means of an SGS model. Thus, the overall quality of an LES with respect to properly accounting for small-scale physics crucially depends on the quality of the SGS model. While there has been a lot of successful research on SGS models in the hydrodynamic regime for decades, SGS modeling in MHD is a rather recent topic, in particular, in the compressible regime. In this thesis, we derive and validate a new nonlinear MHD SGS model that explicitly takes compressibility effects into account. A filter is used to separate the large and intermediate scales, and it is thought to mimic finite resolution effects. In the derivation, we use a deconvolution approach on the filter kernel. With this approach, we are able to derive nonlinear closures for all SGS terms in MHD: the turbulent Reynolds and Maxwell stresses, and the turbulent electromotive force (EMF). We validate the new closures both a priori and a posteriori. In the a priori tests, we use high-resolution reference data of stationary, homogeneous, isotropic MHD turbulence to compare exact SGS quantities against predictions by the closures. The comparison includes, for example, correlations of turbulent fluxes, the average dissipative behavior, and alignment of SGS vectors such as the EMF. In order to quantify the performance of the new nonlinear closure, this comparison is conducted from the subsonic (sonic Mach number M s ≈ 0.2) to the highly supersonic (M s ≈ 20) regime, and against other SGS closures. The latter include established closures of eddy-viscosity and scale-similarity type. In all tests and over the entire parameter space, we find that the proposed closures are (significantly) closer to the reference data than the other closures. In the a posteriori tests, we perform large eddy simulations of decaying, supersonic MHD turbulence with initial M s ≈ 3. We implemented closures of all types, i.e. of eddy-viscosity, scale-similarity and nonlinear type, as an SGS model and evaluated their performance in comparison to simulations without a model (and at higher resolution). We find that the models need to be calculated on a scale larger than the grid scale, e.g. by an explicit filter, to have an influence on the dynamics at all. Furthermore, we show that only the proposed nonlinear closure improves higher-order statistics.

Nonlinear Alfvén wave propagating in ideal MHD plasmas

NASA Astrophysics Data System (ADS)

Zheng, Jugao; Chen, Yinhua; Yu, Mingyang

2016-01-01

The behavior of nonlinear Alfvén waves propagating in ideal MHD plasmas is investigated numerically. It is found that in a one-dimensional weakly nonlinear system an Alfvén wave train can excite two longitudinal disturbances, namely an acoustic wave and a ponderomotively driven disturbance, which behave differently for β \\gt 1 and β \\lt 1, where β is the ratio of plasma-to-magnetic pressures. In a strongly nonlinear system, the Alfvén wave train is modulated and can steepen to form shocks, leading to significant dissipation due to appearance of current sheets at magnetic-pressure minima. For periodic boundary condition, we find that the Alfvén wave transfers its energy to the plasma and heats it during the shock formation. In two-dimensional systems, fast magneto-acoustic wave generation due to Alfvén wave phase mixing is considered. It is found that the process depends on the amplitude and frequency of the Alfvén waves, as well as their speed gradients and the pressure of the background plasma.

Nonlinear Fluid Model Of 3-D Field Effects In Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Callen, J. D.; Hegna, C. C.; Beidler, M. T.

2017-10-01

Extended MHD codes (e.g., NIMROD, M3D-C1) are beginning to explore nonlinear effects of small 3-D magnetic fields on tokamak plasmas. To facilitate development of analogous physically understandable reduced models, a fluid-based dynamic nonlinear model of these added 3-D field effects in the base axisymmetric tokamak magnetic field geometry is being developed. The model incorporates kinetic-based closures within an extended MHD framework. Key 3-D field effects models that have been developed include: 1) a comprehensive modified Rutherford equation for the growth of a magnetic island that includes the classical tearing and NTM perturbed bootstrap current drives, externally applied magnetic field and current drives, and classical and neoclassical polarization current effects, and 2) dynamic nonlinear evolution of the plasma toroidal flow (radial electric field) in response to the 3-D fields. An application of this model to RMP ELM suppression precipitated by an ELM crash will be discussed. Supported by Office of Fusion Energy Sciences, Office of Science, Dept. of Energy Grants DE-FG02-86ER53218 and DE-FG02-92ER54139.

Computational simulations of supersonic magnetohydrodynamic flow control, power and propulsion systems

NASA Astrophysics Data System (ADS)

Wan, Tian

This work is motivated by the lack of fully coupled computational tool that solves successfully the turbulent chemically reacting Navier-Stokes equation, the electron energy conservation equation and the electric current Poisson equation. In the present work, the abovementioned equations are solved in a fully coupled manner using fully implicit parallel GMRES methods. The system of Navier-Stokes equations are solved using a GMRES method with combined Schwarz and ILU(0) preconditioners. The electron energy equation and the electric current Poisson equation are solved using a GMRES method with combined SOR and Jacobi preconditioners. The fully coupled method has also been implemented successfully in an unstructured solver, US3D, and convergence test results were presented. This new method is shown two to five times faster than the original DPLR method. The Poisson solver is validated with analytic test problems. Then, four problems are selected; two of them are computed to explore the possibility of onboard MHD control and power generation, and the other two are simulation of experiments. First, the possibility of onboard reentry shock control by a magnetic field is explored. As part of a previous project, MHD power generation onboard a re-entry vehicle is also simulated. Then, the MHD acceleration experiments conducted at NASA Ames research center are simulated. Lastly, the MHD power generation experiments known as the HVEPS project are simulated. For code validation, the scramjet experiments at University of Queensland are simulated first. The generator section of the HVEPS test facility is computed then. The main conclusion is that the computational tool is accurate for different types of problems and flow conditions, and its accuracy and efficiency are necessary when the flow complexity increases.

On the maximum energy achievable in the first order Fermi acceleration at shocks

NASA Astrophysics Data System (ADS)

Grozny, I.; Diamond, P.; Malkov, M.

2002-11-01

Astrophysical shocks are considered as the sites of cosmic ray (CR) production. The primary mechanism is the diffusive shock (Fermi) acceleration which operates via multiple shock recrossing by a particle. Its efficiency, the rate of energy gain, and the maximum energy are thus determined by the transport mechanisms (confinement to the shock) of these particles in a turbulent shock environment. The turbulence is believed to be generated by accelerated particles themselves. Moreover, in the most interesting case of efficient acceleration the entire MHD shock structure is dominated by their pressure. This makes this problem one of the challenging strongly nonlinear problems of astrophysics. We suggest a physical model that describes particle acceleration, shock structure and the CR driven turbulence on an equal footing. The key new element in this scheme is nonlinear cascading of the MHD turbulence on self-excited (via modulational and Drury instability) sound-like perturbations which gives rise to a significant enrichment of the long wave part of the MHD spectrum. This is critical for the calculation of the maximum energy.

Stratified Simulations of Collisionless Accretion Disks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirabayashi, Kota; Hoshino, Masahiro, E-mail: hirabayashi-k@eps.s.u-tokyo.ac.jp

This paper presents a series of stratified-shearing-box simulations of collisionless accretion disks in the recently developed framework of kinetic magnetohydrodynamics (MHD), which can handle finite non-gyrotropy of a pressure tensor. Although a fully kinetic simulation predicted a more efficient angular-momentum transport in collisionless disks than in the standard MHD regime, the enhanced transport has not been observed in past kinetic-MHD approaches to gyrotropic pressure anisotropy. For the purpose of investigating this missing link between the fully kinetic and MHD treatments, this paper explores the role of non-gyrotropic pressure and makes the first attempt to incorporate certain collisionless effects into disk-scale,more » stratified disk simulations. When the timescale of gyrotropization was longer than, or comparable to, the disk-rotation frequency of the orbit, we found that the finite non-gyrotropy selectively remaining in the vicinity of current sheets contributes to suppressing magnetic reconnection in the shearing-box system. This leads to increases both in the saturated amplitude of the MHD turbulence driven by magnetorotational instabilities and in the resultant efficiency of angular-momentum transport. Our results seem to favor the fast advection of magnetic fields toward the rotation axis of a central object, which is required to launch an ultra-relativistic jet from a black hole accretion system in, for example, a magnetically arrested disk state.« less

Hybrid-PIC modeling of laser-plasma interactions and hot electron generation in gold hohlraum walls

NASA Astrophysics Data System (ADS)

Thoma, C.; Welch, D. R.; Clark, R. E.; Rose, D. V.; Golovkin, I. E.

2017-06-01

The walls of the hohlraum used in experiments at the national ignition facility are heated by laser beams with intensities ˜ 10 15 W/cm2, a wavelength of ˜ 1 / 3 μm, and pulse lengths on the order of a ns, with collisional absorption believed to be the primary heating mechanism. X-rays generated by the hot ablated plasma at the gold walls are then used to implode a target in the hohlraum interior. In addition to the collisional absorption of laser energy at the walls, non-linear laser-plasma interactions (LPI), such as stimulated Raman scattering and two plasmon decay, are believed to generate a population of supra-thermal electrons which, if present in the hohlraum, can have a deleterious effect on target implosion. We describe results of hohlraum modeling using a hybrid particle-in-cell code. To enable this work, new particle-based algorithms for a multiple-ion magneto-hydrodynamic (MHD) treatment, and a particle-based ray-tracing model were developed. The use of such hybrid methods relaxes the requirement to resolve the laser wavelength, and allows for relatively large-scale hohlraum simulations with a reasonable number of cells. But the non-linear effects which are believed to be the cause of hot electron generation can only be captured by fully kinetic simulations with good resolution of the laser wavelength. For this reason, we employ a two-tiered approach to hohlraum modeling. Large-scale simulations of the collisional absorption process can be conducted using the fast quasi-neutral MHD algorithm with fluid particle species. From these simulations, we can observe the time evolution of the hohlraum walls and characterize the density and temperature profiles. From these results, we can transition to smaller-scale highly resolved simulations using traditional kinetic particle-in-cell methods, from which we can fully model all of the non-linear laser-plasma interactions, as well as assess the details of the electron distribution function. We find that vacuum hohlraums should be stable to both two plasmon decay and stimulated Raman scattering instabilities for intensities ≤ 10 15 W/cm2. In gas-filled hohlraums, shocks may be induced in the blowoff gold plasma, which leads to more complex density and temperatures profiles. The resulting effect on LPI stability depends strongly on the details of the profile, and it is possible for the gas-filled hohlraum to become unstable to two plasmon decay at 1015 W/cm2 if the quarter-critical surface reaches temperatures exceeding 1 keV.

Lattice Boltzmann model for simulation of magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William

1991-01-01

A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.

Population pharmacokinetic analysis for 10-monohydroxy derivative of oxcarbazepine in pediatric epileptic patients shows no difference between Japanese and other ethnicities.

PubMed

Sugiyama, Ikuo; Bouillon, Thomas; Yamaguchi, Masayuki; Suzuki, Hikoe; Hirota, Takashi; Fink, Martin

2015-04-01

Oxcarbazepine is an anti-epileptic drug, which is almost completely metabolized by cytosolic enzymes in the liver to the active 10-monohyroxy metabolite (MHD) following oral administration. The pharmacokinetic (PK) profiles of MHD were evaluated in pediatric epileptic patients and a possible ethnic difference in PK of MHD between Japanese and non-Japanese pediatric patients was assessed. A non-linear mixed effect modeling approach was used to determine the PK of MHD. A one-compartment population model with first-order absorption appropriately described the PK of MHD. No clinically relevant differences were found for using body surface area or weight to explain between-patient variability, therefore the final model included the effects of body weight on apparent clearance (CL/F) and apparent volume of distribution (V/F) of MHD, and in addition, the effect of 3 concomitant anti-epileptic drugs (carbamazepine, phenobarbital and phenytoin) on CL/F of MHD. Inclusion of ethnicity as a covariate in the final model, concluded no ethnic difference with respect to CL/F of MHD between Japanese and non-Japanese patients. Hence, oxcarbazepine can be generally applied using the same dosage and administration for the treatment of partial onset seizures in pediatric patients, regardless of ethnicity. Copyright © 2014 The Japanese Society for the Study of Xenobiotics. Published by Elsevier Ltd. All rights reserved.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

NASA Astrophysics Data System (ADS)

Guo, W.; Ma, J.; Yu, Z.

2017-03-01

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field B z 0 , short half-distance y 0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field B z 0 , decreasing half-distance y 0 , and increasing Lundquist number of the flow driven current sheet S L although the dependence may be non-monotonic. The reconnection rate dependence on S L , B z 0 , and y 0 is also investigated.

A New Global Multi-fluid MHD Model of the Solar Corona

NASA Astrophysics Data System (ADS)

van der Holst, B.; Chandran, B. D. G.; Alterman, B. L.; Kasper, J. C.; Toth, G.

2017-12-01

We present a multi-fluid generalization of the AWSoM model, a global magnetohydrodynamic (MHD) solar corona model with low-frequency Alfven wave turbulence (van der Holst et al., 2014). This new extended model includes electron and multi-ion temperatures and velocities (protons and alpha particles). The coronal heating and acceleration is addressed via outward propagating low-frequency Alfven waves that are partially reflected by Alfven speed gradients. The nonlinear interaction of these counter-propagating waves results in turbulent energy cascade. To apportion the wave dissipation to the electron and ion temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. (2011, 2013). This heat partitioning results in a more than mass proportional heating among ions.

COSMIC-RAY PITCH-ANGLE SCATTERING IN IMBALANCED MHD TURBULENCE SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weidl, Martin S.; Jenko, Frank; Teaca, Bogdan

2015-09-20

Pitch-angle scattering rates for cosmic-ray particles in MHD simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfvén waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.

Fully Kinetic Large-scale Simulations of the Collisionless Magnetorotational Instability

NASA Astrophysics Data System (ADS)

Inchingolo, Giannandrea; Grismayer, Thomas; Loureiro, Nuno F.; Fonseca, Ricardo A.; Silva, Luis O.

2018-06-01

We present two-dimensional particle-in-cell simulations of the fully kinetic collisionless magnetorotational instability (MRI) in weakly magnetized (high β) pair plasma. The central result of this numerical analysis is the emergence of a self-induced turbulent regime in the saturation state of the collisionless MRI, which can only be captured for large enough simulation domains. One of the underlying mechanisms for the development of this turbulent state is the drift-kink instability (DKI) of the current sheets resulting from the nonlinear evolution of the channel modes. The onset of the DKI can only be observed for simulation domain sizes exceeding several linear MRI wavelengths. The DKI and ensuing magnetic reconnection activate the turbulent motion of the plasma in the late stage of the nonlinear evolution of the MRI. At steady-state, the magnetic energy has an MHD-like spectrum with a slope of k ‑5/3 for kρ < 1 and k ‑3 for sub-Larmor scale (kρ > 1). We also examine the role of the collisionless MRI and associated magnetic reconnection in the development of pressure anisotropy. We study the stability of the system due to this pressure anisotropy, observing the development of mirror instability during the early-stage of the MRI. We further discuss the importance of magnetic reconnection for particle acceleration during the turbulence regime. In particular, consistent with reconnection studies, we show that at late times the kinetic energy presents a characteristic slope of ɛ ‑2 in the high-energy region.

Newtonian CAFE: a new ideal MHD code to study the solar atmosphere

NASA Astrophysics Data System (ADS)

González, J. J.; Guzmán, F.

2015-12-01

In this work we present a new independent code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centers on the analysis of solar phenomena within the photosphere-corona region. In special the code is capable to simulate the propagation of impulsively generated linear and non-linear MHD waves in the non-isothermal solar atmosphere. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As 3D tests we present the propagation of MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the HLLE flux formula combined with Minmod, MC and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.; Klein, K. G.

2018-02-01

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

On accelerated flow of MHD powell-eyring fluid via homotopy analysis method

NASA Astrophysics Data System (ADS)

Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul

2017-09-01

The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.

Towards full-Braginskii implicit extended MHD

NASA Astrophysics Data System (ADS)

Chacon, Luis

2009-05-01

Recently, viable algorithms have been proposed for the scalable, fully-implicit temporal integration of 3D resistive MHD and cold-ion extended MHD models. While significant, these achievements must be tempered by the fact that such models lack predictive capabilities in regimes of interest for magnetic fusion. Short of including kinetic closures, a natural evolution path towards predictability starts by considering additional terms as described in Braginskii's fluid closures in the collisional regime. Here, we focus on the inclusion of two fundamental elements of relevance for fusion plasmas: anisotropic parallel electron transport, and warm-ion physics (i.e., ion finite Larmor radius effects, included via gyroviscosity). Both these elements introduce significant numerical difficulties, due to the strong anisotropy in the former, and the presence of dispersive waves in the latter. In this presentation, we will discuss progress in our fully implicit algorithmic formulation towards the inclusion of both these elements. L. Chac'on, Phys. Plasmas, 15, 056103 (2008) L. Chac'on, J. Physics: Conf. Series, 125, 012041 (2008)

Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Wang, Ya-Guang

2008-03-01

Compressible vortex sheets are fundamental waves, along with shocks and rarefaction waves, in entropy solutions to multidimensional hyperbolic systems of conservation laws. Understanding the behavior of compressible vortex sheets is an important step towards our full understanding of fluid motions and the behavior of entropy solutions. For the Euler equations in two-dimensional gas dynamics, the classical linearized stability analysis on compressible vortex sheets predicts stability when the Mach number M > sqrt{2} and instability when M < sqrt{2} ; and Artola and Majda’s analysis reveals that the nonlinear instability may occur if planar vortex sheets are perturbed by highly oscillatory waves even when M > sqrt{2} . For the Euler equations in three dimensions, every compressible vortex sheet is violently unstable and this instability is the analogue of the Kelvin Helmholtz instability for incompressible fluids. The purpose of this paper is to understand whether compressible vortex sheets in three dimensions, which are unstable in the regime of pure gas dynamics, become stable under the magnetic effect in three-dimensional magnetohydrodynamics (MHD). One of the main features is that the stability problem is equivalent to a free-boundary problem whose free boundary is a characteristic surface, which is more delicate than noncharacteristic free-boundary problems. Another feature is that the linearized problem for current-vortex sheets in MHD does not meet the uniform Kreiss Lopatinskii condition. These features cause additional analytical difficulties and especially prevent a direct use of the standard Picard iteration to the nonlinear problem. In this paper, we develop a nonlinear approach to deal with these difficulties in three-dimensional MHD. We first carefully formulate the linearized problem for the current-vortex sheets to show rigorously that the magnetic effect makes the problem weakly stable and establish energy estimates, especially high-order energy estimates, in terms of the nonhomogeneous terms and variable coefficients. Then we exploit these results to develop a suitable iteration scheme of the Nash Moser Hörmander type to deal with the loss of the order of derivative in the nonlinear level and establish its convergence, which leads to the existence and stability of compressible current-vortex sheets, locally in time, in three-dimensional MHD.

Coarse-grained incompressible magnetohydrodynamics: Analyzing the turbulent cascades

DOE PAGES

Aluie, Hussein

2017-02-21

Here, we formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarse-graining length-scales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) ismore » shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we show that the forward cascade of magnetic helicity to asymptotically small scales is impossible unless 3rd-order moments of either velocity or magnetic field become infinite.« less

Nonlinear asymmetric tearing mode evolution in cylindrical geometry

DOE PAGES

Teng, Qian; Ferraro, N.; Gates, David A.; ...

2016-10-27

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ' ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ' ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ' 0, w, wlnw, and w2.more » Δ' A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ' ql and Δ' A is consistent with the more accurate expression calculated perturbatively. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. Lastly, it is also confirmed by the simulation that the Δ' A has to be considered in calculating island saturation.« less

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

NASA Technical Reports Server (NTRS)

Moder, Jeffrey P.; Myrabo, Leik N.; Kaminski, Deborah A.

1993-01-01

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

Nonlinear generation of kinetic-scale waves by magnetohydrodynamic Alfvén waves and nonlocal spectral transport in the solar wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, J. S.; Wu, D. J.; Voitenko, Y.

We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigatemore » two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.« less

Seed islands driven by turbulence and NTM dynamics

NASA Astrophysics Data System (ADS)

Muraglia, M.; Agullo, O.; Poye, A.; Benkadda, S.; Horton, W.; Dubuit, N.; Garbet, X.; Sen, A.

2014-10-01

Magnetic reconnection is an issue for tokamak plasmas. Growing magnetic islands expel energetic particles from the plasma core leading to high energy fluxes in the SOL and may cause damage to the plasma facing components. The islands grow from seeds from the bootstrap current effects that oppose the negative delta-prime producing nonlinear island growth. Experimentally, the onset of NTM is quantified in terms of the beta parameter and the sawtooth period. Indeed, in experiments, (3;2) NTM magnetic islands are often triggered by sawtooth precursors. However (2;1) magnetic islands can appear without noticeable MHD event and the seed islands origin for the NTM growth is still an open question. Macroscale MHD instabilities (magnetic islands) coexist with micro-scale turbulent fluctuations and zonal flows which impact island dynamics. Nonlinear simulations show that the nonlinear beating of the fastest growing small-scale ballooning interchange modes on a low order rational surface drive a magnetic islands located on the same surface. The island size is found to be controlled by the turbulence level and modifies the NTM threshold and dynamics.

Coherent current-carrying filaments during nonlinear reconnecting ELMs and VDEs

NASA Astrophysics Data System (ADS)

Ebrahimi, Fatima

2017-10-01

We have examined plasmoid-mediated reconnection in a spherical tokamak using global nonlinear three-dimensional resistive MHD simulations with NIMROD. We have shown that physical current sheets/layers develop near the edge as a peeling component of ELMs or during vertical displacement events (associated with the scrape-off layer currents - halo currents), can become unstable to nonaxisymmetric 3-D current-sheet instabilities (peeling- or tearing-like) and nonlinearly form edge coherent current-carrying filaments. Time-evolving edge current sheets with reconnecting nature in NSTX and NSTX-U configurations are identified. In the case of peeling-like edge localized modes, the longstanding problem of quasiperiodic ELMs cycles is explained through the relaxation of edge current via direct numerical calculations of reconnecting emf terms. For the VDEs during disruption, we show that as the plasma is vertically displaced, edge halo current sheet becomes MHD unstable and forms coherent edge current filament structures, which would eventually bleed into the walls. Our model explains some essential asymmetric physics relevant to the experimental observations. Supported by DOE Grants DE-SC0010565, DE-AC02-09CH11466.

Thermal responses in a coronal loop maintained by wave heating mechanisms

NASA Astrophysics Data System (ADS)

Matsumoto, Takuma

2018-05-01

A full 3-dimensional compressible magnetohydrodynamic (MHD) simulation is conducted to investigate the thermal responses of a coronal loop to the dynamic dissipation processes of MHD waves. When the foot points of the loop are randomly and continuously forced, the MHD waves become excited and propagate upward. Then, 1-MK temperature corona is produced naturally as the wave energy dissipates. The excited wave packets become non-linear just above the magnetic canopy, and the wave energy cascades into smaller spatial scales. Moreover, collisions between counter-propagating Alfvén wave packets increase the heating rate, resulting in impulsive temperature increases. Our model demonstrates that the heating events in the wave-heated loops can be nanoflare-like in the sense that they are spatially localized and temporally intermittent.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boldyrev, Stanislav; Perez, Jean Carlos

The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracymore » the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectral properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the experiment.« less

MHD stagnation point flow and heat transfer of a nanofluid over a permeable nonlinear stretching/shrinking sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Jusoh, Rahimah; Nazar, Roslinda

2018-04-01

The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment

NASA Astrophysics Data System (ADS)

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-01

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Anisotropic Magnetohydrodynamic Turbulence Driven by Parametric Decay Instability: The Onset of Phase Mixing and Alfvén Wave Turbulence

NASA Astrophysics Data System (ADS)

Shoda, Munehito; Yokoyama, Takaaki

2018-06-01

We conduct a 3D magnetohydrodynamic (MHD) simulation of the parametric decay instability of Alfvén waves and resultant compressible MHD turbulence, which is likely to develop in the solar wind acceleration region. Because of the presence of the mean magnetic field, the nonlinear stage is characterized by filament-like structuring and anisotropic cascading. By calculating the timescales of phase mixing and the evolution of Alfvén wave turbulence, we have found that the early nonlinear stage is dominated by phase mixing, while the later phase is dominated by imbalanced Alfvén wave turbulence. Our results indicate that the regions in the solar atmosphere with large density fluctuation, such as the coronal bottom and wind acceleration region, are heated by phase-mixed Alfvén waves, while the other regions are heated by Alfvén wave turbulence.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment.

PubMed

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-27

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

DOE PAGES

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...

2016-01-06

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less

The Magnetic Reconnection Code: an AMR-based fully implicit simulation suite

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Bhattacharjee, A.; Ng, C.-S.

2006-12-01

Extended MHD models, which incorporate two-fluid effects, are promising candidates to enhance understanding of collisionless reconnection phenomena in laboratory, space and astrophysical plasma physics. In this paper, we introduce two simulation codes in the Magnetic Reconnection Code suite which integrate reduced and full extended MHD models. Numerical integration of these models comes with two challenges: Small-scale spatial structures, e.g. thin current sheets, develop and must be well resolved by the code. Adaptive mesh refinement (AMR) is employed to provide high resolution where needed while maintaining good performance. Secondly, the two-fluid effects in extended MHD give rise to dispersive waves, which lead to a very stringent CFL condition for explicit codes, while reconnection happens on a much slower time scale. We use a fully implicit Crank--Nicholson time stepping algorithm. Since no efficient preconditioners are available for our system of equations, we instead use a direct solver to handle the inner linear solves. This requires us to actually compute the Jacobian matrix, which is handled by a code generator that calculates the derivative symbolically and then outputs code to calculate it.

Engineering test facility design definition

NASA Technical Reports Server (NTRS)

Bercaw, R. W.; Seikel, G. R.

1980-01-01

The Engineering Test Facility (ETF) is the major focus of the Department of Energy (DOE) Magnetohydrodynamics (MHD) Program to facilitate commercialization and to demonstrate the commercial operability of MHD/steam electric power. The ETF will be a fully integrated commercial prototype MHD power plant with a nominal output of 200 MW sub e. Performance of this plant is expected to meet or surpass existing utility standards for fuel, maintenance, and operating costs; plant availability; load following; safety; and durability. It is expected to meet all applicable environmental regulations. The current design concept conforming to the general definition, the basis for its selection, and the process which will be followed in further defining and updating the conceptual design.

Energy structure of MHD flow coupling with outer resistance circuit

NASA Astrophysics Data System (ADS)

Huang, Z. Y.; Liu, Y. J.; Chen, Y. Q.; Peng, Z. L.

2015-08-01

Energy structure of MHD flow coupling with outer resistance circuit is studied to illuminate qualitatively and quantitatively the energy relation of this basic MHD flow system with energy input and output. Energy structure are analytically derived based on the Navier-Stocks equations for two-dimensional fully-developed flow and generalized Ohm's Law. The influences of applied magnetic field, Hall parameter and conductivity on energy structure are discussed based on the analytical results. Associated energies in MHD flow are deduced and validated by energy conservation. These results reveal that energy structure consists of two sub structures: electrical energy structure and internal energy structure. Energy structure and its sub structures provide an integrated theoretical energy path of the MHD system. Applied magnetic field and conductivity decrease the input energy, dissipation by fluid viscosity and internal energy but increase the ratio of electrical energy to input energy, while Hall parameter has the opposite effects. These are caused by their different effects on Bulk velocity, velocity profiles, voltage and current in outer circuit. Understanding energy structure helps MHD application designers to actively adjust the allocation of different parts of energy so that it is more reasonable and desirable.

Magnetohydrodynamics with GAMER

NASA Astrophysics Data System (ADS)

Zhang, Ui-Han; Schive, Hsi-Yu; Chiueh, Tzihong

2018-06-01

GAMER, a parallel Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement (AMR) hydrodynamic code, has been extended to support magnetohydrodynamics (MHD) with both the corner-transport-upwind and MUSCL-Hancock schemes and the constraint transport technique. The divergent preserving operator for AMR has been applied to reinforce the divergence-free constraint on the magnetic field. GAMER-MHD has fully exploited the concurrent executions between the graphic process unit (GPU) MHD solver and other central processing unit computation pertinent to AMR. We perform various standard tests to demonstrate that GAMER-MHD is both second-order accurate and robust, producing results as accurate as those given by high-resolution uniform-grid runs. We also explore a new 3D MHD test, where the magnetic field assumes the Arnold–Beltrami–Childress configuration, temporarily becomes turbulent with current sheets, and finally settles to a lowest-energy equilibrium state. This 3D problem is adopted for the performance test of GAMER-MHD. The single-GPU performance reaches 1.2 × 108 and 5.5 × 107 cell updates per second for the single- and double-precision calculations, respectively, on Tesla P100. We also demonstrate a parallel efficiency of ∼70% for both weak and strong scaling using 1024 XK nodes on the Blue Waters supercomputers.

Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario

NASA Astrophysics Data System (ADS)

Chen, Junjie; Li, Guoqiang; Qian, Jinping; Liu, Zixi

2012-11-01

The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta βN limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power Pt increases as the toroidal magnetic field BT or the normalized beta βN is increased.

Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops

NASA Technical Reports Server (NTRS)

Parhi, S.; DeBruyne, P.; Goossens, M.; Zhelyazkov, I.

1995-01-01

The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ofman, L.; Knizhnik, K.; Kucera, T.

We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evidentmore » as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.« less

Nonlinear MHD simulation of current drive by multi-pulsed coaxial helicity injection in spherical torus

NASA Astrophysics Data System (ADS)

Kanki, Takashi; Nagata, Masayoshi; Kagei, Yasuhiro

2011-10-01

The dynamics of structures of magnetic field, current density, and plasma flow generated during multi-pulsed coaxial helicity injection in spherical torus is investigated by 3-D nonlinear MHD simulations. During the driven phase, the flux and current amplifications occur due to the merging and magnetic reconnection between the preexisting plasma in the confinement region and the ejected plasma from the gun region involving the n = 1 helical kink distortion of the central open flux column (COFC). Interestingly, the diamagnetic poloidal flow which tends toward the gun region is then observed due to the steep pressure gradients of the COFC generated by ohmic heating through an injection current winding around the inboard field lines, resulting in the formation of the strong poloidal flow shear at the interface between the COFC and the core region. This result is consistent with the flow shear observed in the HIST. During the decay phase, the configuration approaches the axisymmetric MHD equilibrium state without flow because of the dissipation of magnetic fluctuation energy to increase the closed flux surfaces, suggesting the generation of ordered magnetic field structure. The parallel current density λ concentrated in the COFC then diffuses to the core region so as to reduce the gradient in λ, relaxing in the direction of the Taylor state.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zank, G. P.; Adhikari, L.; Hunana, P.

2017-02-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuationsmore » in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.« less

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2014-10-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Initial results of the code parallelization will be reported. Work is supported by the U.S. DOE SBIR program.

On MHD rotational transport, instabilities and dynamo action in stellar radiation zones

NASA Astrophysics Data System (ADS)

Mathis, Stéphane; Brun, A.-S.; Zahn, J.-P.

2009-04-01

Magnetic field and their related dynamical effects are thought to be important in stellar radiation zones. For instance, it has been suggested that a dynamo, sustained by a m = 1 MHD instability of toroidal magnetic fields (discovered by Tayler in 1973), could lead to a strong transport of angular momentum and of chemicals in such stable regions. We wish here to recall the different magnetic transport processes present in radiative zone and show how the dynamo can operate by recalling the conditions required to close the dynamo loop (BPol → BTor → BPol). Helped by high-resolution 3D MHD simulations using the ASH code in the solar case, we confirm the existence of the m = 1 instability, study its non-linear saturation, but we do not detect, up to a magnetic Reylnods number of 105, any dynamo action.

MHD stagnation-point flow over a nonlinearly shrinking sheet with suction effect

NASA Astrophysics Data System (ADS)

Awaludin, Izyan Syazana; Ahmad, Rokiah; Ishak, Anuar

2018-04-01

The stagnation point flow over a shrinking permeable sheet in the existence of magnetic field is numerically investigated in this paper. The system of partial differential equations are transformed to a nonlinear ordinary differential equation using similarity transformation and is solved numerically using the boundary value problem solver, bvp4c, in Matlab software. It is found that dual solutions exist for a certain range of the shrinking strength.

Relativistic self-similar dynamic gravitational collapses of a quasi-spherical general polytropic magnetofluid

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Xia, Yu-Kai

2017-05-01

We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.

Slip Effects On MHD Three Dimensional Flow Of Casson Fluid Over An Exponentially Stretching Surface

NASA Astrophysics Data System (ADS)

Madhusudhana Rao, B.; Krishna Murthy, M.; Sivakumar, N.; Rushi Kumar, B.; Raju, C. S. K.

2018-04-01

Heat and mass transfer effects on MHD three dimensional flow of Casson fluid over an exponentially stretching surface with slip conditions is examined. The similarity transformations are used to convert the governing equations into a set of nonlinear ordinary differential equations and are solved numerically using fourth order Runge-Kutta method along with shooting technique. The effects of Casson parameter, Hartmann number, heat source/sink,chemical reaction and slip factors on velocity, temperature and concentration are shown graphically. The skin friction coefficient and the Nusselt number are examined numerically.

Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak

NASA Astrophysics Data System (ADS)

Bicheng, LI; Zhonghe, JIANG; Jian, LV; Xiang, LI; Bo, RAO; Yonghua, DING

2018-05-01

Nonlinear magnetohydrodynamic (MHD) simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations (RMPs) are performed with NIMROD (non-ideal MHD with rotation, open discussion). Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology, plasma density and rotation profile. The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling, and finally change density profile by particle transport. At the same time, plasma rotation plays an important role during the entire evolution process.

Numerical analysis of MHD Carreau fluid flow over a stretching cylinder with homogenous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif

2018-06-01

The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.

Numerical MHD codes for modeling astrophysical flows

NASA Astrophysics Data System (ADS)

Koldoba, A. V.; Ustyugova, G. V.; Lii, P. S.; Comins, M. L.; Dyda, S.; Romanova, M. M.; Lovelace, R. V. E.

2016-05-01

We describe a Godunov-type magnetohydrodynamic (MHD) code based on the Miyoshi and Kusano (2005) solver which can be used to solve various astrophysical hydrodynamic and MHD problems. The energy equation is in the form of entropy conservation. The code has been implemented on several different coordinate systems: 2.5D axisymmetric cylindrical coordinates, 2D Cartesian coordinates, 2D plane polar coordinates, and fully 3D cylindrical coordinates. Viscosity and diffusivity are implemented in the code to control the accretion rate in the disk and the rate of penetration of the disk matter through the magnetic field lines. The code has been utilized for the numerical investigations of a number of different astrophysical problems, several examples of which are shown.

Severe overdosage with the antiepileptic drug oxcarbazepine

PubMed Central

van Opstal, J M; Janknegt, R; Cilissen, J; L’Ortije, W H V M; Nel, J E; De Heer, F

2004-01-01

Few published human data are available concerning the acute toxicity of the new antiepileptic drug oxcarbazepine of which the metabolite 10- monohydroxy derivate (MHD) is the pharmacologically effective compound. Two hours after a documented overdosage of more than 100 tablets oxcarbazepine, the serum level of the parent compound was 10-fold higher than the therapeutic dosage (31.6 mg l−1). However, the concentration of MHD, which peaked 7 h after intake, was only twofold higher (59.0 mg l−1). No life-threatening situations occurred and the patient fully recovered. The fact that oxcarbazepine is a prodrug and that the formation of the active MHD metabolite is a rate-limiting process may contribute to the relative low toxicity of the drug in overdose. PMID:15327594

Fractional calculus phenomenology in two-dimensional plasma models

NASA Astrophysics Data System (ADS)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Double-layer optical fiber coating analysis in MHD flow of an elastico-viscous fluid using wet-on-wet coating process

NASA Astrophysics Data System (ADS)

Khan, Zeeshan; Islam, Saeed; Shah, Rehan Ali; Khan, Muhammad Altaf; Bonyah, Ebenezer; Jan, Bilal; Khan, Aurangzeb

Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC) and low and high density polyethylene (LDPE/HDPE), nylon and Polysulfone. One of the most important things which affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying Oldroyd 8-constant fluid model in a pressure type die with the effect of magneto-hydrodynamic (MHD). Wet-on-wet coating process is applied for double-layer optical fiber coating. The coating process in the coating die is modeled as a simple two-layer Couette flow of two immiscible fluids in an annulus with an assigned pressure gradient. Based on the assumptions of fully developed laminar and MHD flow, the Oldroyd 8-constant model of non-Newtonian fluid of two immiscible resin layers is modeled. The governing nonlinear equations are solved analytically by the new technique of Optimal Homotopy Asymptotic Method (OHAM). The convergence of the series solution is established. The results are also verified by the Adomian Decomposition Method (ADM). The effect of important parameters such as magnetic parameter Mi , the dilatant constant α , the Pseodoplastic constant β , the radii ratio δ , the pressure gradient Ω , the speed of fiber optics V , and the viscosity ratio κ on the velocity profiles, thickness of coated fiber optics, volume flow rate, and shear stress on the fiber optics are investigated. At the end the result of the present work is also compared with the experimental results already available in the literature by taking non-Newtonian parameters tends to zero.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

Magnetic flux pumping mechanism prevents sawtoothing in 3D nonlinear MHD simulations of tokamak plasmas

NASA Astrophysics Data System (ADS)

Krebs, Isabel; Jardin, Stephen C.; Guenter, Sibylle; Lackner, Karl; Hoelzl, Matthias; Strumberger, Erika; Ferraro, Nate

2017-10-01

3D nonlinear MHD simulations of tokamak plasmas have been performed in toroidal geometry by means of the high-order finite element code M3D-C1. The simulations are set up such that the safety factor on axis (q0) is driven towards values below unity. As reported in and the resulting asymptotic states either exhibit sawtooth-like reconnection cycling or they are sawtooth-free. In the latter cases, a self-regulating magnetic flux pumping mechanism, mainly provided by a saturated quasi-interchange instability via a dynamo effect, redistributes the central current density so that the central safety factor profile is flat and q0 1 . Sawtoothing is prevented if β is sufficiently high to allow for the necessary amount of flux pumping to counterbalance the tendency of the current density profile to centrally peak. We present the results of 3D nonlinear simulations based on specific types of experimental discharges and analyze their asymptotic behavior. A set of cases is presented where aspects of the current ramp-up phase of Hybrid ASDEX Upgrade discharges are mimicked. Another set of simulations is based on low-qedge discharges in DIII-D.

Role of Interaction between Magnetic Rossby Waves and Tachocline Differential Rotation in Producing Solar Seasons

NASA Astrophysics Data System (ADS)

Dikpati, Mausumi; McIntosh, Scott W.; Bothun, Gregory; Cally, Paul S.; Ghosh, Siddhartha S.; Gilman, Peter A.; Umurhan, Orkan M.

2018-02-01

We present a nonlinear magnetohydrodynamic shallow-water model for the solar tachocline (MHD-SWT) that generates quasi-periodic tachocline nonlinear oscillations (TNOs) that can be identified with the recently discovered solar “seasons.” We discuss the properties of the hydrodynamic and magnetohydrodynamic Rossby waves that interact with the differential rotation and toroidal fields to sustain these oscillations, which occur due to back-and-forth energy exchanges among potential, kinetic, and magnetic energies. We perform model simulations for a few years, for selected example cases, in both hydrodynamic and magnetohydrodynamic regimes and show that the TNOs are robust features of the MHD-SWT model, occurring with periods of 2–20 months. We find that in certain cases multiple unstable shallow-water modes govern the dynamics, and TNO periods vary with time. In hydrodynamically governed TNOs, the energy exchange mechanism is simple, occurring between the Rossby waves and differential rotation. But in MHD cases, energy exchange becomes much more complex, involving energy flow among six energy reservoirs by means of eight different energy conversion processes. For toroidal magnetic bands of 5 and 35 kG peak amplitudes, both placed at 45° latitude and oppositely directed in north and south hemispheres, we show that the energy transfers responsible for TNO, as well as westward phase propagation, are evident in synoptic maps of the flow, magnetic field, and tachocline top-surface deformations. Nonlinear mode–mode interaction is particularly dramatic in the strong-field case. We also find that the TNO period increases with a decrease in rotation rate, implying that the younger Sun had more frequent seasons.

Alpha particle effects in burning tokamak plasmas: overview and specific examples

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sigmar, D.J.

1986-07-01

Using the total power balance of an ignited tokamak plasma as a guideline, a range of alpha driven effects is surveyed regarding their impact on achieving and maintaining fusion burn. Specific examples of MHD and kinetic modes and multi species transport dynamics are discussed, including the possible interaction of these categories of effects. This power balance approach rather than a straightforward enumeration of possible effects serves to reveal their non-linear dependence and the ensuing fragility of our understanding of the approach to and maintenance of ignition. Specific examples are given of the interaction between ..cap alpha..-power driven sawtoothing and idealmore » MHD stability, and direct ..cap alpha..-effects on MHD modes including kinetic corrections. Anomalous ion heat transport and central impurity peaking mechanisms and anomalous and collisional ..cap alpha..-transport including the ambipolar electric field are discussed.« less

Vorticity equation for MHD fast waves in geospace environment

NASA Technical Reports Server (NTRS)

Yamauchi, M.; Lundin, R.; Lui, A. T. Y.

1993-01-01

The MHD vorticity equation is modified in order to apply it to nonlinear MHD fast waves or shocks when their extent along the magnetic field is limited. Field-aligned current (FAC) generation is also discussed on the basis of this modified vorticity equation. When the wave normal is not aligned to the finite velocity convection and the source region is spatially limited, a longitudinal polarization causes a pair of plus and minus charges inside the compressional plane waves or shocks, generating a pair of FACs. This polarization is not related to the separation between the electrons and ions caused by their difference in mass, a separation which is inherent to compressional waves. The resultant double field-aligned current structure exists both with and without the contributions from curvature drift, which is questionable in terms of its contribution to vorticity change from the viewpoint of single-particle motion.

The effect of mass loading on the temperature of a flowing plasma. [in vicinity of Io

NASA Technical Reports Server (NTRS)

Linker, Jon A.; Kivelson, Margaret G.; Walker, Raymond J.

1989-01-01

How the addition of ions at rest (mass loading) affects the temperature of a flowing plasma in a MHD approximation is investigated, using analytic theory and time dependent, three-dimensional MHD simulations of plasma flow past Io. The MHD equations show that the temperature can increase or decrease relative to the background, depending on the local sonic Mach number M(S), of the flow. For flows with M(S) of greater than sq rt 9/5 (when gamma = 5/3), mass loading increases the plasma temperature. However, the simulations show a nonlinear response to the addition of mass. If the mass loading rate is large enough, the temperature increase may be smaller than expected, or the temperature may actually decrease, because a large mass loading rate slows the flow and decreases the thermal energy of the newly created plasma.

MHD boundary layer slip flow and heat transfer of ferrofluid along a stretching cylinder with prescribed heat flux.

PubMed

Qasim, Muhammad; Khan, Zafar Hayat; Khan, Waqar Ahmad; Ali Shah, Inayat

2014-01-01

This study investigates the magnetohydrodynamic (MHD) flow of ferrofluid along a stretching cylinder. The velocity slip and prescribed surface heat flux boundary conditions are employed on the cylinder surface. Water as conventional base fluid containing nanoparticles of magnetite (Fe3O4) is used. Comparison between magnetic (Fe3O4) and non-magnetic (Al2O3) nanoparticles is also made. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations and then solved numerically using shooting method. Present results are compared with the available data in the limiting cases. The present results are found to be in an excellent agreement. It is observed that with an increase in the magnetic field strength, the percent difference in the heat transfer rate of magnetic nanoparticles with Al2O3 decreases. Surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases, i.e curvature helps to enhance the heat transfer.

Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Shateyi, Stanford; Marewo, Gerald T.

2018-05-01

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Mehmood, Zaffar; Ahmad, Bilal

2018-05-01

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.

On Hydromagnetic Waves in Atmospheres with Application to the Sun

NASA Astrophysics Data System (ADS)

Campos, L. M. B. C.

Sir James Lighthill has an exceptionally wide range of research interests; one of them is magnetohydrodynamics (MHD). In a major paper (Lighthill, 1959), he considers MHD waves in general, and in particular Alfvén waves with the Hall effect. He analyzes the radiation field using a method of asymptotic estimation of Fourier integrals, which was further developed in subsequent papers (Lighthill, 1964). This method is applied to internal or acoustic-gravity waves in his book on waves in fluids (Lighthill, 1978), which includes an appendix on MHD waves. As an applied mathematician, Sir James was always aware of the applications of his theories; in the case of MHD waves he considered their role in the heating of the solar atmosphere (Lighthill, 1967). In this presentation in honor of Sir James Lighthill, I choose to address the subject of hydromagnetic waves, with application to the solar atmosphere and wind, for two reasons: first it is less likely to be covered by other authors than, say, his better known work on aerodynamics, aeroacoustics, or biofluiddynamics; and I feel a volume in honor of Sir James should reflect his significant contributions to MHD. The second motivation is that about two decades ago, Sir James suggested that I consider magneto-atmospheric waves and their role in the solar atmosphere, and this may be an appropriate occasion to report on what was made of this suggestion. Sir James has a rare ability not only to initiate new areas of research but also to pinpoint subjects ripe for significant development, and this is also substantiated in the field of atmospheric waves. In the present communication paper I consider all three MHD modes (Alfvén, slow, and fast), including viscous and resistive dissipation, cases with external magnetic fields of varying strength and direction (spherical and spiral waves), and the Hall effect and some instances of nonlinear effects; application to the solar atmosphere and wind shows that MHD waves play a major role in energy and mass balance in the solar system. The case of weakly dissipative nonlinear magnetosonic waves relates to another celebrated paper on viscous effects on large amplitude sound waves (Lighthill, 1956). Although I have research interests influenced by, or in common with, Sir James, in other areas, such as aeroacoustics (e.g., Campos, 1986), aeronautics (Campos et al., 1995), and applied mathematics (Campos, 1984a, 1994a), I chose to concentrate on magneto-atmospheric waves and the Sun, as an expression of gratitude for Sir James's inspiring suggestion.

A non-linear study of fluctuating fluid flow on MHD mixed convection through a vertical permeable plate

NASA Astrophysics Data System (ADS)

Babu, R. Suresh; Rushi Kumar, B.

2017-11-01

In this paper, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions:(i) the suction velocity (which is normal to the plate)and the free stream velocity both fluctuate with respect to time with a fixed mean; (ii) the wall temperature is constant;(iii) difference between the temperature of the plate and the free stream is moderately large due to the free convection currents. Based on the physical configuration of the model, the governing equations are derived and are non-dimensionalize using dimensionless parameters. The resultant nonlinear partial differential equations are solved using double regular perturbation technique analytically. The results are computed numerically to understand the behaviour of the fluid (i.e., effects of MHD, viscosity, body force etc.) for various non-dimensional parameters involving like Grashof number Gr, Prandtl number Pr, Hartmann number M, Eckert number E, the Viscous ratio λ and so on for velocity and temperature. These results are found to be in good agreement with known results available in the literature in the absence of few physical parameters. The numerical values of the above said flow is discussed through graphs on velocity and temperature.

Study of the Transition from MRI to Magnetic Turbulence via Parasitic Instability by a High-order MHD Simulation Code

NASA Astrophysics Data System (ADS)

Hirai, Kenichiro; Katoh, Yuto; Terada, Naoki; Kawai, Soshi

2018-02-01

Magnetic turbulence in accretion disks under ideal magnetohydrodynamic (MHD) conditions is expected to be driven by the magneto-rotational instability (MRI) followed by secondary parasitic instabilities. We develop a three-dimensional ideal MHD code that can accurately resolve turbulent structures, and carry out simulations with a net vertical magnetic field in a local shearing box disk model to investigate the role of parasitic instabilities in the formation process of magnetic turbulence. Our simulations reveal that a highly anisotropic Kelvin–Helmholtz (K–H) mode parasitic instability evolves just before the first peak in turbulent stress and then breaks large-scale shear flows created by MRI. The wavenumber of the enhanced parasitic instability is larger than the theoretical estimate, because the shear flow layers sometimes become thinner than those assumed in the linear analysis. We also find that interaction between antiparallel vortices caused by the K–H mode parasitic instability induces small-scale waves that break the shear flows. On the other hand, at repeated peaks in the nonlinear phase, anisotropic wavenumber spectra are observed only in the small wavenumber region and isotropic waves dominate at large wavenumbers unlike for the first peak. Restructured channel flows due to MRI at the peaks in nonlinear phase seem to be collapsed by the advection of small-scale shear structures into the restructured flow and resultant mixing.

Center for Extended Magnetohydrodynamics Modeling - Final Technical Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, Scott

This project funding supported approximately 74 percent of a Ph.D. graduate student, not including costs of travel and supplies. We had a highly successful research project including the development of a second-order implicit electromagnetic kinetic ion hybrid model [Cheng 2013, Sturdevant 2016], direct comparisons with the extended MHD NIMROD code and kinetic simulation [Schnack 2013], modeling of slab tearing modes using the fully kinetic ion hybrid model and finally, modeling global tearing modes in cylindrical geometry using gyrokinetic simulation [Chen 2015, Chen 2016]. We developed an electromagnetic second-order implicit kinetic ion fluid electron hybrid model [Cheng 2013]. As a firstmore » step, we assumed isothermal electrons, but have included drift-kinetic electrons in similar models [Chen 2011]. We used this simulation to study the nonlinear evolution of the tearing mode in slab geometry, including nonlinear evolution and saturation [Cheng 2013]. Later, we compared this model directly to extended MHD calculations using the NIMROD code [Schnack 2013]. In this study, we investigated the ion-temperature-gradient instability with an extended MHD code for the first time and got reasonable agreement with the kinetic calculation in terms of linear frequency, growth rate and mode structure. We then extended this model to include orbit averaging and sub-cycling of the ions and compared directly to gyrokinetic theory [Sturdevant 2016]. This work was highlighted in an Invited Talk at the International Conference on the Numerical Simulation of Plasmas in 2015. The orbit averaging sub-cycling multi-scale algorithm is amenable to hybrid architectures with GPUS or math co-processors. Additionally, our participation in the Center for Extend Magnetohydrodynamics motivated our research on developing the capability for gyrokinetic simulation to model a global tearing mode. We did this in cylindrical geometry where the results could be benchmarked with existing eigenmode calculations. First, we developed a gyrokinetic code capable of simulating long wavelengths using a fluid electron model [Chen 2015]. We benchmarked this code with an eigenmode calculation. Besides having to rewrite the field solver due to the breakdown in the gyrokinetic ordering for long wavelengths, very high radial resolution was required. We developed a technique where we used the solution from the eigenmode solver to specify radial boundary conditions allowing for a very high radial resolution of the inner solution. Using this technique enabled us to use our direct algorithm with gyrokinetic ions and drift kinetic electrons [Chen 2016]. This work was highlighted in an Invited Talk at the American Physical Society - Division of Plasma Physics in 2015.« less

Fully Parallel MHD Stability Analysis Tool

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2015-11-01

Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.

The MHD Kelvin-Helmholtz Instability. II. The Roles of Weak and Oblique Fields in Planar Flows

NASA Astrophysics Data System (ADS)

Jones, T. W.; Gaalaas, Joseph B.; Ryu, Dongsu; Frank, Adam

1997-06-01

We have carried out high-resolution MHD simulations of the nonlinear evolution of Kelvin-Helmholtz unstable flows in 21/2 dimensions. The modeled flows and fields were initially uniform except for a thin shear layer with a hyperbolic tangent velocity profile and a small, normal mode perturbation. These simulations extend work by Frank et al. and Malagoli, Bodo, & Rosner. They consider periodic sections of flows containing magnetic fields parallel to the shear layer, but projecting over a full range of angles with respect to the flow vectors. They are intended as preparation for fully three-dimensional calculations and to address two specific questions raised in earlier work: (1) What role, if any, does the orientation of the field play in nonlinear evolution of the MHD Kelvin-Helmholtz instability in 21/2 dimensions? (2) Given that the field is too weak to stabilize against a linear perturbation of the flow, how does the nonlinear evolution of the instability depend on strength of the field? The magnetic field component in the third direction contributes only through minor pressure contributions, so the flows are essentially two-dimensional. In Frank et al. we found that fields too weak to stabilize a linear perturbation may still be able to alter fundamentally the flow so that it evolves from the classical ``Cat's Eye'' vortex expected in gasdynamics into a marginally stable, broad laminar shear layer. In that process the magnetic field plays the role of a catalyst, briefly storing energy and then returning it to the plasma during reconnection events that lead to dynamical alignment between magnetic field and flow vectors. In our new work we identify another transformation in the flow evolution for fields below a critical strength. That we found to be ~10% of the critical field needed for linear stabilization in the cases we studied. In this ``very weak field'' regime, the role of the magnetic field is to enhance the rate of energy dissipation within and around the Cat's Eye vortex, not to disrupt it. The presence of even a very weak field can add substantially to the rate at which flow kinetic energy is dissipated. In all of the cases we studied magnetic field amplification by stretching in the vortex is limited by tearing mode, ``fast'' reconnection events that isolate and then destroy magnetic flux islands within the vortex and relax the fields outside the vortex. If the magnetic tension developed prior to reconnection is comparable to Reynolds stresses in the flow, that flow is reorganized during reconnection. Otherwise, the primary influence on the plasma is generation of entropy. The effective expulsion of flux from the vortex is very similar to that shown by Weiss for passive fields in idealized vortices with large magnetic Reynolds numbers. We demonstrated that this expulsion cannot be interpreted as a direct consequence of steady, resistive diffusion, but must be seen as a consequence of unsteady fast reconnection.

Determining the Importance of Energy Transfer between Magnetospheric Regions via MHD Waves using Constellations of Spacecraft

NASA Technical Reports Server (NTRS)

Cattell, Cynthia A.

2004-01-01

This grant was focused on research in two specific areas: (1) development of new techniques and software for assimilation, analysis and visualization of data from multiple satellites making in-situ measurements; and (2) determination of the role of MHD waves in energy transport during storms and substorms. Results were obtained in both areas and presented at national meetings and in publications. The talks and papers that were supported in part or fully by this grant are listed in this paper.

Numerical Simulation for the Unsteady MHD Flow and Heat Transfer of Couple Stress Fluid over a Rotating Disk

PubMed Central

2014-01-01

The present work is devoted to study the numerical simulation for unsteady MHD flow and heat transfer of a couple stress fluid over a rotating disk. A similarity transformation is employed to reduce the time dependent system of nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs). The Runge-Kutta method and shooting technique are employed for finding the numerical solution of the governing system. The influences of governing parameters viz. unsteadiness parameter, couple stress and various physical parameters on velocity, temperature and pressure profiles are analyzed graphically and discussed in detail. PMID:24835274

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

NASA Astrophysics Data System (ADS)

Fang, Tiegang

2014-05-01

In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

NASA Astrophysics Data System (ADS)

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; Luce, T. C.; Taylor, N. Z.; Terranova, D.; Turco, F.; Wilcox, R. S.; Wingen, A.; Cappello, S.; Chrystal, C.; Escande, D. F.; Holcomb, C. T.; Marrelli, L.; Paz-Soldan, C.; Piron, L.; Predebon, I.; Zaniol, B.; DIII-D, The; RFX-Mod Teams

2017-07-01

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. In this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8-1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.

Population pharmacokinetics of oxcarbazepine and its metabolite 10-hydroxycarbazepine in healthy subjects.

PubMed

Antunes, Natalicia de Jesus; van Dijkman, Sven C; Lanchote, Vera Lucia; Wichert-Ana, Lauro; Coelho, Eduardo Barbosa; Alexandre Junior, Veriano; Takayanagui, Osvaldo Massaiti; Tozatto, Eduardo; van Hasselt, J G Coen; Della Pasqua, Oscar

2017-11-15

Oxcarbazepine is indicated for the treatment of partial or generalised tonic-clonic seizures. Most of the absorbed oxcarbazepine is converted into its active metabolite, 10-hydroxycarbazepine (MHD), which can exist as R-(-)- and S-(+)-MHD enantiomers. Here we describe the influence of the P-glycoprotein (P-gp) inhibitor verapamil, on the disposition of oxcarbazepine and MHD enantiomers, both of which are P-gp substrates. Healthy subjects (n=12) were randomised to oxcarbazepine or oxcarbazepine combined with verapamil at doses of 300mg b.i.d. and 80mg t.i.d., respectively. Blood samples (n=185) were collected over a period of 12h post oxcarbazepine dose. An integrated PK model was developed using nonlinear mixed effects modelling using a meta-analytical approach. The pharmacokinetics of oxcarbazepine was described by a two-compartment model with absorption transit compartments and first-order elimination. The concentration-time profiles of both MHD enantiomers were characterised by a one-compartment distribution model. Clearance estimates (95% CI) were 84.9L/h (69.5-100.3) for oxcarbazepine and 2.0L/h (1.9-2.1) for both MHD enantiomers. The volume of distribution was much larger for oxcarbazepine (131L (97-165)) as compared to R-(-)- and S-(+)-MHD (23.6L (14.4-32.8) vs. 31.7L (22.5-40.9), respectively). Co-administration of verapamil resulted in a modest increase of the apparent bioavailability of oxcarbazepine by 12% (10-28), but did not affect parent or metabolite clearances. Despite the evidence of comparable systemic levels of OXC and MHD following administration of verapamil, differences in brain exposure to both moieties cannot be excluded after P-glycoprotein inhibition. Copyright © 2017. Published by Elsevier B.V.

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. Inmore » this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8–1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.« less

Role of a continuous MHD dynamo in the formation of 3D equilibria in fusion plasmas

DOE PAGES

Piovesan, P.; Bonfiglio, D.; Cianciosa, M.; ...

2017-04-28

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum safety factor above unity and thus removing sawteeth. It also enables steady-state hybrid operation, by redistributing non-inductive current driven near the center by electron cyclotron waves. A validated flux pumping model is not yet available, but it would be necessary to extrapolate hybrid operation to future devices. Inmore » this work flux pumping physics is investigated for helical core equilibria stimulated by external 3D fields in DIII-D hybrid plasmas. We show that flux pumping can be produced in a continuous way by an MHD dynamo emf. The same effect maintains helical equilibria in reversed-field pinch (RFP) plasmas. The effective MHD dynamo loop voltage is calculated for experimental 3D equilibrium reconstructions, by balancing Ohm’s law over helical flux surfaces, and is consistent with the expected current redistribution. Similar results are also obtained with more sophisticated nonlinear MHD simulations. The same modelling approach is applied to helical RFP states forming spontaneously in RFX-mod as the plasma current is raised above 0.8–1 MA. This comparison allows to identify the underlying physics common to tokamak and RFP: a helical core displacement modulates parallel current density along flux tubes, which requires a helical electrostatic potential to build up, giving rise to a helical MHD dynamo flow.« less

Alfvénic wave packets collision in a kinetic plasma

NASA Astrophysics Data System (ADS)

Pezzi, Oreste; Parashar, Tulasi N.; Servidio, Sergio; Valentini, Francesco; Malara, Francesco; Matthaeus, William H.; Veltri, Pierluigi

2016-04-01

The problem of two colliding and counter-propagating Alfvénic wave packets has been investigated in detail since the late Seventies. In particular Moffatt [1] and Parker [2] showed that, in the framework of the incompressible magnetohydrodynamics (MHD), nonlinear interactions can develop only during the overlapping of the two packets. Here we describe a similar problem in the framework of the kinetic physics. The collision of two quasi-Alfvénic packets has been analyzed by means of MHD, Hall-MHD and kinetic simulations performed with two different hybrid codes: a PIC code [3] and a Vlasov-Maxwell code [4]. Due to the huge computational cost, only a 2D-3V phase space is allowed (two dimensions in the physical space, three dimensions in the velocity space). Preliminary results suggest that, as well as in the MHD case, the most relevant nonlinear effects occur during the overlapping of the two packets. For both the PIC and Vlasov cases, strong temperature anisotropies are present during the evolution of the wave packets. Moreover, due to the absence of numerical noise, Vlasov simulations show that the collision of the counter-propagating solitary waves produces a significant beam in the velocity distribution functions [5], which, instead, cannot be appreciated in PIC simulations. We remark that, beyond the interest of studying a well-known MHD problem in the realm of the kinetic physics, our results allows also to compare different numerical codes. [1] H.K. Moffatt, Field generation in electrically conducting fluids (Cambridge University Press, 1978). [2] E.N. Parker, Cosmical magnetic fields: their origin and their activity (Oxford University Press, 1979). [3] T.N. Parashar, M.A. Shay, P.A. Cassak and W.H. Matthaeus, Physics of Plasmas 16, 032310 (2009). [4] F. Valentini, P. Trávníček, F. Califano, P. Hellinger & A. Mangeney, Journal of Computational Physics 225, 753-770 (2007). [5] J. He, C. Tu, E. Marsch, C.H. Chen, L. Wang, Z. Pei, L. Zhang, C.S. Salem and S.D. Bale, The Astrophysical Journal Letters 813, L30 (2015).

Collisions of two Alfvénic wave packets in a kinetic plasma

NASA Astrophysics Data System (ADS)

Pezzi, O.; Servidio, S.; Valentini, F.; Parashar, T.; Malara, F.; Matthaeus, W. H.; Veltri, P.

2016-12-01

The problem of two colliding and counter-propagating Alfvénic wave packets has been investigated in detail since the late Seventies. In particular Moffatt [1] and Parker [2] showed that, in the framework of the incompressible magnetohydrodynamics (MHD), nonlinear interactions can develop only during the overlapping of the two packets. Here we describe a similar problem in the framework of the kinetic physics. The collision of two quasi-Alfvénic packets has been analyzed by means of MHD, Hall-MHD and kinetic simulations performed with two different hybrid codes: a PIC code [3] and a Vlasov-Maxwell code [4]. Due to the huge computational cost, only a 2D-3V phase space is allowed (two dimensions in the physical space, three dimensions in the velocity space). Preliminary results suggest that, as well as in the MHD case, the most relevant nonlinear effects occur during the overlapping of the two packets. For both the PIC and Vlasov cases, strong temperature anisotropies are present during the evolution of the wave packets. Moreover, due to the absence of numerical noise, Vlasov simulations show that the collision of the counter-propagating solitary waves produces a significant beam in the velocity distribution functions [5], which, instead, cannot be appreciated in PIC simulations. We remark that, beyond the interest of studying a well-known MHD problem in the realm of the kinetic physics, our results allows also to compare different numerical codes. [1] H.K. Moffatt, Field generation in electrically conducting fluids (Cambridge University Press, 1978). [2] E.N. Parker, Cosmical magnetic fields: their origin and their activity (Oxford University Press, 1979). [3] T.N. Parashar, M.A. Shay, P.A. Cassak and W.H. Matthaeus, Physics of Plasmas 16, 032310 (2009). [4] F. Valentini, P. Trávníček, F. Califano, P. Hellinger & A. Mangeney, Journal of Computational Physics 225, 753-770 (2007). [5] J. He, C. Tu, E. Marsch, C.H. Chen, L. Wang, Z. Pei, L. Zhang, C.S. Salem and S.D. Bale, The Astrophysical Journal Letters 813, L30 (2015).

Featured Image: Tests of an MHD Code

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2016-09-01

Creating the codes that are used to numerically model astrophysical systems takes a lot of work and a lot of testing! A new, publicly available moving-mesh magnetohydrodynamics (MHD) code, DISCO, is designed to model 2D and 3D orbital fluid motion, such as that of astrophysical disks. In a recent article, DISCO creator Paul Duffell (University of California, Berkeley) presents the code and the outcomes from a series of standard tests of DISCOs stability, accuracy, and scalability.From left to right and top to bottom, the test outputs shown above are: a cylindrical Kelvin-Helmholtz flow (showing off DISCOs numerical grid in 2D), a passive scalar in a smooth vortex (can DISCO maintain contact discontinuities?), a global look at the cylindrical Kelvin-Helmholtz flow, a Jupiter-mass planet opening a gap in a viscous disk, an MHD flywheel (a test of DISCOs stability), an MHD explosion revealing shock structures, an MHD rotor (a more challenging version of the explosion), a Flock 3D MRI test (can DISCO study linear growth of the magnetorotational instability in disks?), and a nonlinear 3D MRI test.Check out the gif below for a closer look at each of these images, or follow the link to the original article to see even more!CitationPaul C. Duffell 2016 ApJS 226 2. doi:10.3847/0067-0049/226/1/2

The Statistical Mechanics of Ideal MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2003-01-01

Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

A conservative MHD scheme on unstructured Lagrangian grids for Z-pinch hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Wu, Fuyuan; Ramis, Rafael; Li, Zhenghong

2018-03-01

A new algorithm to model resistive magnetohydrodynamics (MHD) in Z-pinches has been developed. Two-dimensional axisymmetric geometry with azimuthal magnetic field Bθ is considered. Discretization is carried out using unstructured meshes made up of arbitrarily connected polygons. The algorithm is fully conservative for mass, momentum, and energy. Matter energy and magnetic energy are managed separately. The diffusion of magnetic field is solved using a derivative of the Symmetric-Semi-Implicit scheme, Livne et al. (1985) [23], where unconditional stability is obtained without needing to solve large sparse systems of equations. This MHD package has been integrated into the radiation-hydrodynamics code MULTI-2D, Ramis et al. (2009) [20], that includes hydrodynamics, laser energy deposition, heat conduction, and radiation transport. This setup allows to simulate Z-pinch configurations relevant for Inertial Confinement Fusion.

Symmetry, Statistics and Structure in MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

Fully implicit adaptive mesh refinement algorithm for reduced MHD

NASA Astrophysics Data System (ADS)

Philip, Bobby; Pernice, Michael; Chacon, Luis

2006-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)

Resistive Wall Modes Identification and Control in RFX-mod low qedge tokamak discharges

NASA Astrophysics Data System (ADS)

Baruzzo, Matteo; Bolzonella, Tommaso; Cavazzana, Roberto; Marchiori, Giuseppe; Marrelli, Lionello; Martin, Piero; Paccagnella, Roberto; Piovesan, Paolo; Piron, Lidia; Soppelsa, Anton; Zanca, Paolo; in, Yongkyoon; Liu, Yueqiang; Okabayashi, Michio; Takechi, Manabu; Villone, Fabio

2011-10-01

In this work the MHD stability of RFX mode tokamak discharges with qedge < 3 will be studied. The target plasma scenario is characterized by a plasma current 100kA

A stochastic approach to uncertainty in the equations of MHD kinematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillips, Edward G., E-mail: egphillips@math.umd.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2015-03-01

The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertaintymore » in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.« less

Nonlinear MHD simulation of magnetic relaxation during DC helicity injection in spherical torus plasmas

NASA Astrophysics Data System (ADS)

Kanki, Takashi; Nagata, Masayoshi; Kagei, Yasuhiro

2009-11-01

Recently, the intermittent plasma flow has been observed to be correlated with the fluctuations of the toroidal current It and n=1 mode in the HIST spherical torus device. During the partially driven phase mixed with a resistive decay, the toroidal ion flow velocity (˜ 40 km/s) in the opposite direction of It is driven in the central open flux region, and the oscillations in n=1 mode occur there, while during the resistive decay phase, this flow velocity reverses and results in the same as that of It, and the oscillations in n=1 mode disappear there. The purpose of the present study is to investigate the plasma flow reversal process and the relevant MHD relaxation by using the 3-D nonlinear MHD simulations. The numerical results exhibit that during the driven phase, the toroidal flow velocity (˜ 37 km/s) is in the opposite direction to It, but in the same direction as the ExB rotation induced by an applied voltage. This flow is driven by the magnetic reconnection occurring at the X-point during the repetitive process of the non-axisymmetric magnetized plasmoid ejection from the helicity injector. The oscillations of poloidal flux ψp are out of phase with those of toroidal flux ψt and magnetic energy for the dominant n=1 mode, indicating the flux conversion from ψt to ψp. The effect of the vacuum toroidal field strength on the plasma dynamics is discussed.

Impact of helical boundary conditions in MHD modeling of RFP and tokamak plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Cappello, S.; Escande, D. F.; Piovesan, P.; Veranda, M.; Chacón, L.

2012-10-01

Helical boundary conditions imposed by the active control system of the RFX-mod device provide a handle to govern the plasma dynamics in both RFP and Ohmic tokamak discharges [1]. By applying an edge radial magnetic field with proper helicity, it is possible to increase the persistence of the spontaneous helical RFP states at high current,and to stimulate them also at low current or high density. Helical BCs even allow to access helical states with different helicity than the spontaneous one [2]. In Ohmic tokamak operation at q(a)<2, the presence of the 2/1 RWM reduces the sawtoothing activity of the 1/1 internal kink, which takes a stationary snake-like character instead. Many of these features are qualitatively reproduced in 3D nonlinear MHD modeling. We study the impact of helical BCs on the MHD dynamics in both RFP and tokamak with two successfully benchmarked numerical tools, SpeCyl and PIXIE3D [3]. We recover the bifurcation from a sawtooth to a snake solution when imposing a 2/1 BC in the tokamak case and we interpret this as a toroidal/nonlinear coupling effect. We show that the bifurcation is more easily stimulated with a 1/1 BC.[4pt] [1] P. Piovesan, invited talk this meeting[0pt] [2] M. Veranda et al EPS-ICPP Conference (2012) P4.004[0pt] [3] D. Bonfiglio et al Phys. Plasmas (2010)

Local Existence of MHD Contact Discontinuities

NASA Astrophysics Data System (ADS)

Morando, Alessandro; Trakhinin, Yuri; Trebeschi, Paola

2018-05-01

We prove the local-in-time existence of solutions with a contact discontinuity of the equations of ideal compressible magnetohydrodynamics (MHD) for two dimensional planar flows provided that the Rayleigh-Taylor sign condition {[partial p/partial N] <0 } on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity. MHD contact discontinuities are characteristic discontinuities with no flow across the discontinuity for which the pressure, the magnetic field and the velocity are continuous whereas the density and the entropy may have a jump. This paper is a natural completion of our previous analysis (Morando et al. in J Differ Equ 258:2531-2571, 2015) where the well-posedness in Sobolev spaces of the linearized problem was proved under the Rayleigh-Taylor sign condition satisfied at each point of the unperturbed discontinuity. The proof of the resolution of the nonlinear problem given in the present paper follows from a suitable tame a priori estimate in Sobolev spaces for the linearized equations and a Nash-Moser iteration.

Scalable Parallel Computation for Extended MHD Modeling of Fusion Plasmas

NASA Astrophysics Data System (ADS)

Glasser, Alan H.

2008-11-01

Parallel solution of a linear system is scalable if simultaneously doubling the number of dependent variables and the number of processors results in little or no increase in the computation time to solution. Two approaches have this property for parabolic systems: multigrid and domain decomposition. Since extended MHD is primarily a hyperbolic rather than a parabolic system, additional steps must be taken to parabolize the linear system to be solved by such a method. Such physics-based preconditioning (PBP) methods have been pioneered by Chac'on, using finite volumes for spatial discretization, multigrid for solution of the preconditioning equations, and matrix-free Newton-Krylov methods for the accurate solution of the full nonlinear preconditioned equations. The work described here is an extension of these methods using high-order spectral element methods and FETI-DP domain decomposition. Application of PBP to a flux-source representation of the physics equations is discussed. The resulting scalability will be demonstrated for simple wave and for ideal and Hall MHD waves.

Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with Newtonian heat/mass transfer

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

NASA Astrophysics Data System (ADS)

Zhu, Jia; Ma, Zhiwei; Wang, Sheng; Zhang, Wei

2016-10-01

A new hybrid kinetic-MHD code CLT-K is developed to study nonlinear dynamics of n =1 toroidal Alfvén eigenmodes (TAEs) with the m/n =2/1 tearing mode. It is found that the n =1 TAE is first excited by isotropic energetic particles in the earlier stage and reaches the steady state due to wave-particle interaction. After the saturation of the n =1 TAE, the tearing mode intervenes and triggers the second growth of the mode. The modes goes into the second steady state due to multiple tearing mode-mode nonlinear coupling. Both wave-particle and wave-wave interactions are observed in our hybrid simulation.

Universal nonlinear small-scale dynamo.

PubMed

Beresnyak, A

2012-01-20

We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C(E) of the total turbulent dissipation rate. On the basis of locality bounds we claim that this "efficiency of the small-scale dynamo", C(E), is a true constant for large Re and is determined only by strongly nonlinear dynamics at the equipartition scale. We measured C(E) in numerical simulations and observed a value around 0.05 in the highest resolution simulations. We address the issue of C(E) being small, unlike the Kolmogorov constant which is of order unity. © 2012 American Physical Society

Three-Dimensional Numerical Modeling of Magnetohydrodynamic Augmented Propulsion Experiment

NASA Technical Reports Server (NTRS)

Turner, M. W.; Hawk, C. W.; Litchford, R. J.

2009-01-01

Over the past several years, NASA Marshall Space Flight Center has engaged in the design and development of an experimental research facility to investigate the use of diagonalized crossed-field magnetohydrodynamic (MHD) accelerators as a possible thrust augmentation device for thermal propulsion systems. In support of this effort, a three-dimensional numerical MHD model has been developed for the purpose of analyzing and optimizing accelerator performance and to aid in understanding critical underlying physical processes and nonideal effects. This Technical Memorandum fully summarizes model development efforts and presents the results of pretest performance optimization analyses. These results indicate that the MHD accelerator should utilize a 45deg diagonalization angle with the applied current evenly distributed over the first five inlet electrode pairs. When powered at 100 A, this configuration is expected to yield a 50% global efficiency with an 80% increase in axial velocity and a 50% increase in centerline total pressure.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

Stability of ideal MHD configurations. I. Realizing the generality of the G operator

NASA Astrophysics Data System (ADS)

Keppens, R.; Demaerel, T.

2016-12-01

A field theoretical approach, applied to the time-reversible system described by the ideal magnetohydrodynamic (MHD) equations, exposes the full generality of MHD spectral theory. MHD spectral theory, which classified waves and instabilities of static or stationary, usually axisymmetric or translationally symmetric configurations, actually governs the stability of flowing, (self-)gravitating, single fluid descriptions of nonlinear, time-dependent idealized plasmas, and this at any time during their nonlinear evolution. At the core of this theory is a self-adjoint operator G , discovered by Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] in its application to stationary (i.e., time-independent) plasma states. This Frieman-Rotenberg operator dictates the acceleration identified by a Lagrangian displacement field ξ , which connects two ideal MHD states in four-dimensional space-time that share initial conditions for density, entropy, and magnetic field. The governing equation reads /d 2 ξ d t 2 = G [ ξ ] , as first noted by Cotsaftis and Newcomb [Nucl. Fusion, Suppl. Part 2, 447 and 451 (1962)]. The time derivatives at left are to be taken in the Lagrangian way, i.e., moving with the flow v. Physically realizable displacements must have finite energy, corresponding to being square integrable in the Hilbert space of displacements equipped with an inner product rule, for which the G operator is self-adjoint. The acceleration in the left-hand side features the Doppler-Coriolis operator v . ∇ , which is known to become an antisymmetric operator when restricting attention to stationary equilibria. Here, we present all derivations needed to get to these insights and connect results throughout the literature. A first illustration elucidates what can happen when self-gravity is incorporated and presents aspects that have been overlooked even in simple uniform media. Ideal MHD flows, as well as Euler flows, have essentially 6 + 1 wave types, where the 6 wave modes are organized through the essential spectrum of the G operator. These 6 modes are actually three pairs of modes, in which the Alfvén pair (a shear wave pair in hydro) sits comfortably at the middle. Each pair of modes consists of a leftgoing wave and a rightgoing wave, or equivalently stated, with one type traveling from past to future (forward) and the other type that goes from future to past (backward). The Alfvén pair is special, in its left-right categorization, while there is full degeneracy for the slow and fast pairs when reversing time and mirroring space. The Alfvén pair group speed diagram leads to the familiar Elsässer variables.

Particle acceleration in regions of magnetic flux emergence: a statistical approach using test-particle- and MHD-simulations

NASA Astrophysics Data System (ADS)

Vlahos, Loukas; Archontis, Vasilis; Isliker, Heinz

We consider 3D nonlinear MHD simulations of an emerging flux tube, from the convection zone into the corona, focusing on the coronal part of the simulations. We first analyze the statistical nature and spatial structure of the electric field, calculating histograms and making use of iso-contour visualizations. Then test-particle simulations are performed for electrons, in order to study heating and acceleration phenomena, as well as to determine HXR emission. This study is done by comparatively exploring quiet, turbulent explosive, and mildly explosive phases of the MHD simulations. Also, the importance of collisional and relativistic effects is assessed, and the role of the integration time is investigated. Particular aim of this project is to verify the quasi- linear assumptions made in standard transport models, and to identify possible transport effects that cannot be captured with the latter. In order to determine the relation of our results to Fermi acceleration and Fokker-Planck modeling, we determine the standard transport coefficients. After all, we find that the electric field of the MHD simulations must be downscaled in order to prevent an un-physically high degree of acceleration, and the value chosen for the scale factor strongly affects the results. In different MHD time-instances we find heating to take place, and acceleration that depends on the level of MHD turbulence. Also, acceleration appears to be a transient phenomenon, there is a kind of saturation effect, and the parallel dynamics clearly dominate the energetics. The HXR spectra are not yet really compatible with observations, we have though to further explore the scaling of the electric field and the integration times used.

Relationship between mono-hydroxy-carbazepine serum concentrations and adverse effects in patients on oxcarbazepine monotherapy.

PubMed

Sattler, Annika; Schaefer, Marion; May, Theodor W

2015-09-01

To evaluate the relationship between serum concentrations of mono-hydroxy-carbazepine (MHD), the main metabolite of oxcarbazepine (OXC), and the occurrence of adverse effects (AE) in a large group of patients on OXC monotherapy. An antiepileptic drug (AED) therapeutic drug monitoring (TDM) database was analyzed especially with regard to OXC dosage, MHD serum concentration, and the occurrence of AE. In total, 893 blood samples of 442 patients were included in this retrospective study. The statistical evaluation was performed by means of Kaplan-Meier estimates, log-rank tests and generalized estimating equations (GEE). At least one AE was reported in 78 (17.6%) of the 442 patients. At MHD serum concentrations of 30.0 μg/ml and 43.7 μg/ml and OXC dosages of 33.1 mg/kg and 62.3 mg/kg, 25% and 75% of patients, respectively, experienced at least one AE. Log-rank tests indicated that younger patients (<18 years) may be able to tolerate higher MHD serum levels (p = 0.006) and higher OXC dosages per body weight (p < 0.001) compared to adult patients (≥ 18 years). Furthermore, AEs occurred at higher body-weight adjusted OXC dosages of extended release formulations compared to immediate-release formulations (p = 0.010), whereas MHD serum levels at which AEs occurred did not differ significantly between formulations (p = 0.125). Multivariate GEE confirmed the results. The occurrence of AEs is significantly (and non-linearly) dependent on MHD serum level, whereas the dependence of OXC dosage is less distinctive. But, tolerability of OXC seems to depend on age of the patients as well as on pharmaceutical formulation of OXC. Copyright © 2015 British Epilepsy Association. Published by Elsevier Ltd. All rights reserved.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Suppression of high-energy electrons generated in both disrupting and sustained MST tokamak plasmas

NASA Astrophysics Data System (ADS)

Pandya, M. D.; Chapman, B. E.; Munaretto, S.; Cornille, B. S.; McCollam, K. J.; Sovinec, C. R.; Dubois, A. M.; Almagri, A. F.; Goetz, J. A.

2017-10-01

High-energy electrons appearing during MST tokamak plasma disruptions are rapidly lost from the plasma due apparently to internal MHD activity. Work has just recently begun on generating and diagnosing disruptions in MST tokamak plasmas. Initial measurements show the characteristic drop in central temperature and density preceding a quench of the plasma current. This corresponds to a burst of dominantly n=1 MHD activity, which is accompanied by a short-lived burst of high-energy electrons. The short-lived nature of these electrons is suspected to be due to stochastic transport associated with the increased MHD. Earlier work shows that runaway electrons generated in low density, sustained plasmas are suppressed by a sufficiently large m=3 RMP in plasmas with q(a) <3. RMPs of various poloidal mode number can be generated with an array of saddle coils wound around the vertical insulated gap in MST's thick conducting shell. With an m=3 RMP, the degree of runaway suppression increases with RMP amplitude, while an m=1 RMP has little effect on the runaways. Nonlinear MHD modeling with NIMROD of these MST plasmas indicates increased stochasticity with an m=3 RMP, while no such increase in stochasticity is observed with an m=1 RMP. Work supported by US DOE.

Signatures Of Coronal Heating Driven By Footpoint Shuffling: Closed and Open Structures.

NASA Astrophysics Data System (ADS)

Velli, M. C. M.; Rappazzo, A. F.; Dahlburg, R. B.; Einaudi, G.; Ugarte-Urra, I.

2017-12-01

We have previously described the characteristic state of the confined coronal magnetic field as a special case of magnetically dominated magnetohydrodynamic (MHD) turbulence, where the free energy in the transverse magnetic field is continuously cascaded to small scales, even though the overall kinetic energy is small. This coronal turbulence problem is defined by the photospheric boundary conditions: here we discuss recent numerical simulations of the fully compressible 3D MHD equations using the HYPERION code. Loops are forced at their footpoints by random photospheric motions, energizing the field to a state with continuous formation and dissipation of field-aligned current sheets: energy is deposited at small scales where heating occurs. Only a fraction of the coronal mass and volume gets heated at any time. Temperature and density are highly structured at scales that, in the solar corona, remain observationally unresolved: the plasma of simulated loops is multithermal, where highly dynamical hotter and cooler plasma strands are scattered throughout the loop at sub-observational scales. We will also compare Reduced MHD simulations with fully compressible simulations and photospheric forcings with different time-scales compared to the Alfv'en transit time. Finally, we will discuss the differences between the closed field and open field (solar wind) turbulence heating problem, leading to observational consequences that may be amenable to Parker Solar Probe and Solar Orbiter.

Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Ye; Oughton, Sean

2011-07-15

Magnetohydrodynamic (MHD) systems can be strongly nonlinear (turbulent) when their kinetic and magnetic Reynolds numbers are high, as is the case in many astrophysical and space plasma flows. Unfortunately these high Reynolds numbers are typically much greater than those currently attainable in numerical simulations of MHD turbulence. A natural question to ask is how can researchers be sure that their simulations have reproduced all of the most influential physics of the flows and magnetic fields? In this paper, a metric is defined to indicate whether the necessary physics of interest has been captured. It is found that current computing resourcesmore » will typically not be sufficient to achieve this minimum state metric.« less

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

Thermal radiation and mass transfer effects on unsteady MHD free convection flow past a vertical oscillating plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.

On Kinetic Slow Modes, Fluid Slow Modes, and Pressure-balanced Structures in the Solar Wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Verscharen, Daniel; Chen, Christopher H. K.; Wicks, Robert T., E-mail: daniel.verscharen@unh.edu, E-mail: christopher.chen@imperial.ac.uk, E-mail: r.wicks@ucl.ac.uk

Observations in the solar wind suggest that the compressive component of inertial-range solar-wind turbulence is dominated by slow modes. The low collisionality of the solar wind allows for nonthermal features to survive, which suggests the requirement of a kinetic plasma description. The least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave and a nonpropagating (NP) mode. We derive analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compare them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD). This comparison shows major discrepancies in the predictedmore » wave phase speeds from MHD and kinetic theory at moderate to high β . MHD and kinetic theory also dictate that all plasma normal modes exhibit a unique signature in terms of their polarization. We quantify the relative amplitude of fluctuations in the three lowest particle velocity moments associated with IA and NP modes in the gyrokinetic limit and compare these predictions with MHD results and in situ observations of the solar-wind turbulence. The agreement between the observations of the wave polarization and our MHD predictions is better than the kinetic predictions, which suggests that the plasma behaves more like a fluid in the solar wind than expected.« less

Shear-induced opening of the coronal magnetic field

NASA Technical Reports Server (NTRS)

Wolfson, Richard

1995-01-01

This work describes the evolution of a model solar corona in response to motions of the footpoints of its magnetic field. The mathematics involved is semianalytic, with the only numerical solution being that of an ordinary differential equation. This approach, while lacking the flexibility and physical details of full MHD simulations, allows for very rapid computation along with complete and rigorous exploration of the model's implications. We find that the model coronal field bulges upward, at first slowly and then more dramatically, in response to footpoint displacements. The energy in the field rises monotonically from that of the initial potential state, and the field configuration and energy appraoch asymptotically that of a fully open field. Concurrently, electric currents develop and concentrate into a current sheet as the limiting case of the open field is approached. Examination of the equations shows rigorously that in the asymptotic limit of the fully open field, the current layer becomes a true ideal MHD singularity.

Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Philip, Bobby; Chacón, Luis; Pernice, Michael

2008-10-01

An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.

Anelastic Models of Fully-Convective Stars: Differential Rotation, Meridional Circulation and Residual Entropy

NASA Astrophysics Data System (ADS)

Sainsbury-Martinez, Felix; Browning, Matthew; Miesch, Mark; Featherstone, Nicholas A.

2018-01-01

Low-Mass stars are typically fully convective, and as such their dynamics may differ significantly from sun-like stars. Here we present a series of 3D anelastic HD and MHD simulations of fully convective stars, designed to investigate how the meridional circulation, the differential rotation, and residual entropy are affected by both varying stellar parameters, such as the luminosity or the rotation rate, and by the presence of a magnetic field. We also investigate, more specifically, a theoretical model in which isorotation contours and residual entropy (σ‧ = σ ‑ σ(r)) are intrinsically linked via the thermal wind equation (as proposed in the Solar context by Balbus in 2009). We have selected our simulation parameters in such as way as to span the transition between Solar-like differential rotation (fast equator + slow poles) and ‘anti-Solar’ differential rotation (slow equator + fast poles), as characterised by the convective Rossby number and △Ω. We illustrate the transition from single-celled to multi-celled MC profiles, and from positive to negative latitudinal entropy gradients. We show that an extrapolation involving both TWB and the σ‧/Ω link provides a reasonable estimate for the interior profile of our fully convective stars. Finally, we also present a selection of MHD simulations which exhibit an almost unsuppressed differential rotation profile, with energy balances remaining dominated by kinetic components.

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

NASA Technical Reports Server (NTRS)

Sjoegreen, Bjoern; Yee, Helen C.; Mansour, Nagi (Technical Monitor)

2002-01-01

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Ideal MHD stability and performance of ITER steady-state scenarios with ITBs

NASA Astrophysics Data System (ADS)

Poli, F. M.; Kessel, C. E.; Chance, M. S.; Jardin, S. C.; Manickam, J.

2012-06-01

Non-inductive steady-state scenarios on ITER will need to operate with internal transport barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. The large pressure gradients at the location of the internal barrier are conducive to the development of ideal MHD instabilities that may limit the plasma performance and may lead to plasma disruptions. Fully non-inductive scenario simulations with five combinations of heating and current drive sources are presented in this work, with plasma currents in the range 7-10 MA. For each configuration the linear, ideal MHD stability is analysed for variations of the Greenwald fraction and of the pressure peaking factor around the operating point, aiming at defining an operational space for stable, steady-state operations at optimized performance. It is shown that plasmas with lower hybrid heating and current drive maintain the minimum safety factor above 1.5, which is desirable in steady-state operations to avoid neoclassical tearing modes. Operating with moderate ITBs at 2/3 of the minor radius, these plasmas have a minimum safety factor above 2, are ideal MHD stable and reach Q ≳ 5 operating above the ideal no-wall limit.

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

DOE PAGES

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-06-13

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this study, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and themore » resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. Finally, this also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.« less

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

NASA Astrophysics Data System (ADS)

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-06-01

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this paper, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and the resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. This also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.

Magnetohydrodynamic simulation study of plasma jets and plasma-surface contact in coaxial plasma accelerators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Subramaniam, Vivek; Raja, Laxminarayan L.

Recent experiments by Loebner et al. [IEEE Trans. Plasma Sci. 44, 1534 (2016)] studied the effect of a hypervelocity jet emanating from a coaxial plasma accelerator incident on target surfaces in an effort to mimic the transient loading created during edge localized mode disruption events in fusion plasmas. In this study, we present a magnetohydrodynamic (MHD) numerical model to simulate plasma jet formation and plasma-surface contact in this coaxial plasma accelerator experiment. The MHD system of equations is spatially discretized using a cell-centered finite volume formulation. The temporal discretization is performed using a fully implicit backward Euler scheme and themore » resultant stiff system of nonlinear equations is solved using the Newton method. The numerical model is employed to obtain some key insights into the physical processes responsible for the generation of extreme stagnation conditions on the target surfaces. Simulations of the plume (without the target plate) are performed to isolate and study phenomena such as the magnetic pinch effect that is responsible for launching pressure pulses into the jet free stream. The simulations also yield insights into the incipient conditions responsible for producing the pinch, such as the formation of conductive channels. The jet-target impact studies indicate the existence of two distinct stages involved in the plasma-surface interaction. A fast transient stage characterized by a thin normal shock transitions into a pseudo-steady stage that exhibits an extended oblique shock structure. A quadratic scaling of the pinch and stagnation conditions with the total current discharged between the electrodes is in qualitative agreement with the results obtained in the experiments. Finally, this also illustrates the dominant contribution of the magnetic pressure term in determining the magnitude of the quantities of interest.« less

The ins and outs of modelling vertical displacement events

NASA Astrophysics Data System (ADS)

Pfefferle, David

2017-10-01

Of the many reasons a plasma discharge disrupts, Vertical Displacement Events (VDEs) lead to the most severe forces and stresses on the vacuum vessel and Plasma Facing Components (PFCs). After loss of positional control, the plasma column drifts across the vacuum vessel and comes in contact with the first wall, at which point the stored magnetic and thermal energy is abruptly released. The vessel forces have been extensively modelled in 2D but, with the constraint of axisymmetry, the fundamental 3D effects that lead to toroidal peaking, sideways forces, field-line stochastisation and halo current rotation have been vastly overlooked. In this work, we present the main results of an intense VDE modelling activity using the implicit 3D extended MHD code M3D-C1 and share our experience with the multi-domain and highly non-linear physics encountered. At the culmination of code development by the M3D-C1 group over the last decade, highlighted by the inclusion of a finite-thickness resistive vacuum vessel within the computational domain, a series of fully 3D non-linear simulations are performed using realistic transport coefficients based on the reconstruction of so-called NSTX frozen VDEs, where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase, the evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed and investigated in detail. The sensitivity of the current quench to parameter changes is assessed via 2D non-linear runs. The growth of individual toroidal modes is monitored via linear-complex runs. The intricate evolution of the plasma, which is decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D non-linear runs. The location, amplitude and rotation of normal currents and wall forces are analysed and compared with experimental traces.

Magnetic field reconnection. [energy conversion in space plasma

NASA Technical Reports Server (NTRS)

Sonnerup, U. O.

1979-01-01

A reasonably detailed description is obtained of the current status of our understanding of magnetic field reconnection. The picture that emerges is of a process, simple in concept but extremely complicated and multifaceted in detail. Nonlinear MHD processes in the external flow region, governed by distant boundary conditions, are coupled to nonlinear microscopic plasma processes in the diffusion region, in a manner not clearly understood. It appears that reconnection may operate in entirely different ways for different plasma parameters and different external boundary conditions. Steady reconnection may be allowed in some cases, forbidden in others, with intermediate situations involving impulsive or pulsative events.

Viscous dissipation and Joule heating effects in MHD 3D flow with heat and mass fluxes

NASA Astrophysics Data System (ADS)

Muhammad, Taseer; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

The present research explores the three-dimensional stretched flow of viscous fluid in the presence of prescribed heat (PHF) and concentration (PCF) fluxes. Mathematical formulation is developed in the presence of chemical reaction, viscous dissipation and Joule heating effects. Fluid is electrically conducting in the presence of an applied magnetic field. Appropriate transformations yield the nonlinear ordinary differential systems. The resulting nonlinear system has been solved. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are computed and analyzed.

MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations

DOE PAGES

King, Jacob R.; Kruger, S. E.; Burrell, K. H.; ...

2017-03-07

Extended-MHD modeling of DIII-D tokamak quiescent H-mode (QH-mode) discharges with nonlinear NIMROD simulations saturates into a turbulent state but does not saturate when the steady-state flow inferred from measurements is not included. This is consistent with the experimental observations of the quiescent regime on DIII-D. The simulation with flow develops into a saturated turbulent state where the n Φ = 1 and 2 toroidal modes become dominant through an inverse cascade. Each mode in the range of n Φ = 1–5 is dominant at a different time. Consistent with experimental observations during QH-mode, the simulated state leads to large particlemore » transport relative to the thermal transport. Analysis shows that the amplitude and phase of the density and temperature perturbations differ resulting in greater fluctuation-induced convective particle transport relative to the convective thermal transport. As a result, comparison to magnetic-coil measurements shows that rotation frequencies differ between the simulation and experiment, which indicates that more sophisticated extended-MHD two-fluid modeling is required.« less

Coupled Kinetic-MHD Simulations of Divertor Heat Load with ELM Perturbations

NASA Astrophysics Data System (ADS)

Cummings, Julian; Chang, C. S.; Park, Gunyoung; Sugiyama, Linda; Pankin, Alexei; Klasky, Scott; Podhorszki, Norbert; Docan, Ciprian; Parashar, Manish

2010-11-01

The effect of Type-I ELM activity on divertor plate heat load is a key component of the DOE OFES Joint Research Target milestones for this year. In this talk, we present simulations of kinetic edge physics, ELM activity, and the associated divertor heat loads in which we couple the discrete guiding-center neoclassical transport code XGC0 with the nonlinear extended MHD code M3D using the End-to-end Framework for Fusion Integrated Simulations, or EFFIS. In these coupled simulations, the kinetic code and the MHD code run concurrently on the same massively parallel platform and periodic data exchanges are performed using a memory-to-memory coupling technology provided by EFFIS. The M3D code models the fast ELM event and sends frequent updates of the magnetic field perturbations and electrostatic potential to XGC0, which in turn tracks particle dynamics under the influence of these perturbations and collects divertor particle and energy flux statistics. We describe here how EFFIS technologies facilitate these coupled simulations and discuss results for DIII-D, NSTX and Alcator C-Mod tokamak discharges.

Evolution of energy-containing turbulent eddies in the solar wind

NASA Technical Reports Server (NTRS)

Matthaeus, William H.; Oughton, Sean; Pontius, Duane H., Jr.; Zhou, YE

1994-01-01

Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.

MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, Jacob R.; Kruger, S. E.; Burrell, K. H.

Extended-MHD modeling of DIII-D tokamak quiescent H-mode (QH-mode) discharges with nonlinear NIMROD simulations saturates into a turbulent state but does not saturate when the steady-state flow inferred from measurements is not included. This is consistent with the experimental observations of the quiescent regime on DIII-D. The simulation with flow develops into a saturated turbulent state where the n Φ = 1 and 2 toroidal modes become dominant through an inverse cascade. Each mode in the range of n Φ = 1–5 is dominant at a different time. Consistent with experimental observations during QH-mode, the simulated state leads to large particlemore » transport relative to the thermal transport. Analysis shows that the amplitude and phase of the density and temperature perturbations differ resulting in greater fluctuation-induced convective particle transport relative to the convective thermal transport. As a result, comparison to magnetic-coil measurements shows that rotation frequencies differ between the simulation and experiment, which indicates that more sophisticated extended-MHD two-fluid modeling is required.« less

Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere

NASA Technical Reports Server (NTRS)

Matsumoto, R.; Tajima, T.; Shibata, K.; Kaisig, M.

1993-01-01

The nonlinear evolution of an emerging magnetic flux tube or sheet in the solar atmosphere is studied through 3D MHD simulations. In the initial state, a horizontal magnetic flux sheet or tube is assumed to be embedded at the bottom of MHD two isothermal gas layers, which approximate the solar photosphere/chromosphere and the corona. The magnetic flux sheet or tube is unstable against the undular mode of the magnetic buoyancy instability. The magnetic loop rises due to the linear and then later nonlinear instabilities caused by the buoyancy enhanced by precipitating the gas along magnetic field lines. We find by 3D simulation that during the ascendance of loops the bundle of flux tubes or even the flux sheet develops into dense gas filaments pinched between magnetic loops. The interchange modes help produce a fine fiber flux structure perpendicular to the magnetic field direction in the linear stage, while the undular modes determine the overall buoyant loop structure. The expansion of such a bundle of magnetic loops follows the self-similar behavior observed in 2D cases studied earlier. Our study finds the threshold flux for arch filament system (AFS) formation to be about 0.3 x 10 exp 20 Mx.

Effect of Cattaneo-Christov heat flux on buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts

NASA Astrophysics Data System (ADS)

Dogonchi, A. S.; Ganji, D. D.

2018-06-01

In this study, buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts, are studied. Cattaneo-Christov heat flux model instead of conventional Fourier's law of heat conduction is applied to investigate the heat transfer characteristics. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved numerically. The impacts of diverse active parameters such as the magnetic parameter, the radiation parameter, the buoyancy parameter, the heat source parameter, the volume fraction of nanofluid and the thermal relaxation parameter are examined on the velocity and temperature profiles. In addition, the value of the Nusselt number is calculated and presented through figures. The results demonstrate that the temperature profile is lower in the case of Cattaneo-Christov heat flux model as compared to Fourier's law. Moreover, the Nusselt number raises with the raising volume fraction of nanofluid and it abates with the ascending the radiation parameter.

Simulation of MST tokamak discharges with resonant magnetic perturbations

NASA Astrophysics Data System (ADS)

Cornille, B. S.; Sovinec, C. R.; Chapman, B. E.; Dubois, A.; McCollam, K. J.; Munaretto, S.

2016-10-01

Nonlinear MHD modeling of MST tokamak plasmas with an applied resonant magnetic perturbation (RMP) reveals degradation of flux surfaces that may account for the experimentally observed suppression of runaway electrons with the RMP. Runaway electrons are routinely generated in MST tokamak discharges with low plasma density. When an m = 3 RMP is applied these electrons are strongly suppressed, while an m = 1 RMP of comparable amplitude has little effect. The computations are performed using the NIMROD code and use reconstructed equilibrium states of MST tokamak plasmas with q (0) < 1 and q (a) = 2.2 . Linear computations show that the (1 , 1) -kink and (2 , 2) -tearing modes are unstable, and nonlinear simulations produce sawtoothing with a period of approximately 0.5 ms, which is comparable to the period of MHD activity observed experimentally. Adding an m = 3 RMP in the computation degrades flux surfaces in the outer region of the plasma, while no degradation occurs with an m = 1 RMP. The outer flux surface degradation with the m = 3 RMP, combined with the sawtooth-induced distortion of flux surfaces in the core, may account for the observed suppression of runaway electrons. Work supported by DOE Grant DE-FC02-08ER54975.

DISCO: A 3D Moving-mesh Magnetohydrodynamics Code Designed for the Study of Astrophysical Disks

NASA Astrophysics Data System (ADS)

Duffell, Paul C.

2016-09-01

This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide variety of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.

DISCO: A 3D MOVING-MESH MAGNETOHYDRODYNAMICS CODE DESIGNED FOR THE STUDY OF ASTROPHYSICAL DISKS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duffell, Paul C., E-mail: duffell@berkeley.edu

2016-09-01

This work presents the publicly available moving-mesh magnetohydrodynamics (MHD) code DISCO. DISCO is efficient and accurate at evolving orbital fluid motion in two and three dimensions, especially at high Mach numbers. DISCO employs a moving-mesh approach utilizing a dynamic cylindrical mesh that can shear azimuthally to follow the orbital motion of the gas. The moving mesh removes diffusive advection errors and allows for longer time-steps than a static grid. MHD is implemented in DISCO using an HLLD Riemann solver and a novel constrained transport (CT) scheme that is compatible with the mesh motion. DISCO is tested against a wide varietymore » of problems, which are designed to test its stability, accuracy, and scalability. In addition, several MHD tests are performed which demonstrate the accuracy and stability of the new CT approach, including two tests of the magneto-rotational instability, one testing the linear growth rate and the other following the instability into the fully turbulent regime.« less

On chemical reaction and porous medium effect in the MHD flow due to a rotating disk with variable thickness

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Nazar, Hira; Imtiaz, Maria; Alsaedi, Ahmed

2017-06-01

The present analysis describes the magnetohydrodynamic (MHD) axisymmetric flow of a viscous fluid due to a rotating disk with variable thickness. An electrically conducting fluid fills the porous space. The first-order chemical reaction is considered. The equations of the present problem representing the flow of a fluid are reduced into nonlinear ordinary differential equations. Convergent series solutions are obtained. The impacts of the various involved dimensionless parameters on fluid flow, temperature, concentration, skin frction coefficient and Nusselt number are examined. The radial, tangential and axial components of velocity are affected in a similar manner on changing the thickness coefficient of the disk. Similar effects of the disk thickness coefficient are observed for both the temperature and concentration profile.

Vector processing efficiency of plasma MHD codes by use of the FACOM 230-75 APU

NASA Astrophysics Data System (ADS)

Matsuura, T.; Tanaka, Y.; Naraoka, K.; Takizuka, T.; Tsunematsu, T.; Tokuda, S.; Azumi, M.; Kurita, G.; Takeda, T.

1982-06-01

In the framework of pipelined vector architecture, the efficiency of vector processing is assessed with respect to plasma MHD codes in nuclear fusion research. By using a vector processor, the FACOM 230-75 APU, the limit of the enhancement factor due to parallelism of current vector machines is examined for three numerical codes based on a fluid model. Reasonable speed-up factors of approximately 6,6 and 4 times faster than the highly optimized scalar version are obtained for ERATO (linear stability code), AEOLUS-R1 (nonlinear stability code) and APOLLO (1-1/2D transport code), respectively. Problems of the pipelined vector processors are discussed from the viewpoint of restructuring, optimization and choice of algorithms. In conclusion, the important concept of "concurrency within pipelined parallelism" is emphasized.

Experimental Measurement of the Nonlinear Interaction between Counterpropagating Alfv'en Waves in the LaPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Drake, D. J.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Dorfman, S.; Auerbach, D.

2012-10-01

Turbulence plays an important role in the transport of mass and energy in many space and astrophysical plasmas ranging from galaxy clusters to Earth's magnetosphere. One active topic of research is the application of idealized Alfv'enic turbulence models to plasma conditions relevant to space and astrophysical plasmas. Alfv'enic turbulence models based on incompressible magnetohydrodynamics (MHD) contain a nonlinear interaction that drives the cascade of energy to smaller scales. We describe experiments at the Large Plasma Device (LaPD) that focus on the interaction of an Alfv'en wave traveling parallel to the mean magnetic field with a counterpropagating Alfv'en wave. Theory predicts the nonlinear interaction of the two primary waves will produce a secondary daughter Alfv'en wave. In this study, we present the first experimental identification of the daughter wave generated by nonlinear interactions between the primary Alfv'en waves.

Ideal MHD stability and characteristics of edge localized modes on CFETR

NASA Astrophysics Data System (ADS)

Li, Ze-Yu; Chan, V. S.; Zhu, Yi-Ren; Jian, Xiang; Chen, Jia-Le; Cheng, Shi-Kui; Zhu, Ping; Xu, Xue-Qiao; Xia, Tian-Yang; Li, Guo-Qiang; Lao, L. L.; Snyder, P. B.; Wang, Xiao-Gang; the CFETR Physics Team

2018-01-01

Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R  =  5.7 m, B T  =  5 T) derived from multi-code integrated modeling, with key parameters {{β }N},{{β }T},{{β }p} varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a  =  1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R  =  6.6 m, B T  =  6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.

Measurements of Two-Fluid Relaxation in the Madison Symmetric Torus

NASA Astrophysics Data System (ADS)

Triana, Joseph C.

Recent measurements and extended MHD simulations expose the importance of two-fluid physics in the relaxation and self-organization of the current and momentum profiles in RFP plasmas. A hallmark of relaxation is that the inductive electric field is not balanced by resistive dissipation, prompting the study of fluctuation-induced emfs in the generalized Ohm's law, E ∥ - etaJ∥ = - ∥ + 1/ne , where the two terms on the right are known as the MHD and Hall dynamo terms, respectively. The Hall emf is measured in the outer half of the MST plasma minor radius using an armored deep-insertion Hall probe. The emf matches previously measurements in the edge ( r/a > 0.8) but in the new region examined (0.6 < r/a < 0.8) it is much larger than E - etaJ, implying the MHD dynamo must also be large and oppositely directed. Recent nonlinear simulations that include two-fluid effects using the extended-MHD NIMROD code show complex radial structure for the emf terms, but the size of the measured Hall emf is much larger than predicted by the simulations. In the two-fluid model, the Hall dynamo couples to the parallel momentum as the mean-field Maxwell stress. The simulations predict relaxation of the parallel flow profiles that is also qualitatively consistent with measurements in MST plasmas.

Two-fluid Magnetic Relaxation in the MST Reversed Field Pinch

NASA Astrophysics Data System (ADS)

Triana, Joseph; Almagri, Af; McCollam, Kj; Sarff, Js; Sovinec, Cr

2016-10-01

Recent measurements and extended MHD simulations expose the importance of two-fluid physics in the relaxation and self-organization of the current and momentum profiles in RFP plasmas. A hallmark of relaxation is that the inductive electric field is not balanced by resistive dissipation, prompting the study of fluctuation-induced emfs in the generalized Ohm's law, E- ηJ =- +/ne, the two terms on the right known as the MHD and Hall dynamo terms, respectively. The Hall emf is measured in the outer half of the MST plasma minor radius using an armored deep-insertion probe. The emf matches previous measurements in the edge (r/a>0.8) but in the new region examined (0.8>r/a>0.6) it is much larger than E- ηJ, implying the MHD dynamo must also be large and oppositely directed. Recent nonlinear simulations that include two-fluid effects using the extended-MHD NIMROD code show complex radial structure for the emf terms, but the size of the measured Hall emf is much larger than predicted by the simulations. In the two-fluid model, the Hall dynamo couples to the parallel momentum as the mean-field Maxwell stress. The simulations predict relaxation of the parallel flow profiles that is also qualitatively consistent with measurements in MST plasmas. Work supported by US DoE and NSF.

Numerical and analytical modelling of the MHD buoyancy-driven flow in a Bridgman crystal growth configuration

NASA Astrophysics Data System (ADS)

Davoust, L.; Moreau, R.; Cowley, M. D.; Tanguy, P. A.; Bertrand, F.

1997-10-01

We present analytical and numerical models of magnetohydrodynamic(MHD) buoyancy-driven flow within the liquid pool of a horizontal Bridgman crystal growth furnace, under the influence of a uniform vertical magnetic field B0. A horizontal differentially heated cylinder, whose aspect ratio (radius to length) is small enough for a fully developed regime to be established in the central core, is considered. With Hartmann layers remaining electrically inactive, a modified Rayleigh number RaG, which is the ration of the ordinary Rayleigh number to the square of the Hartmann number, is found to control the MHD reorganisation of the flow. This modified Rayleigh number is a measure of the importance of thermal convection relative to diffusion if velocity is estimated from the balance between the torques of buoyancy and the Laplace force. When RaG is much smaller than unity (quasi-diffusive regime), an analytical modelling of the flow, based on a power series of RaG, demonstrates that this balance requires secondary vortices within vertical mid-planes of the cylinder, both within the core flow and near the end walls. A 3-D numerical calculation of the flow provides evidence of the transition from a convective MHD flow (when RaG is still of the order of unity) to the quasi-diffusive flow, analytically studied. Indeed, this transition takes the form of a rather complex 3-D MHD organisation of the flow which is due to the nonuniformity of the axial temperature gradient along the cylinder.

Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-05-01

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.

Nonlinear stability of Halley comethosheath with transverse plasma motion

NASA Technical Reports Server (NTRS)

Srivastava, Krishna M.; Tsurutani, Bruce T.

1994-01-01

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Ijaz; Qayyum, Sumaira; Alsaedi, A.; Khan, M. Imran

2018-03-01

This research addressed entropy generation for MHD stagnation point flow of viscous nanofluid over a stretching surface. Characteristics of heat transport are analyzed through nonlinear radiation and heat generation/absorption. Nanoliquid features for Brownian moment and thermophoresis have been considered. Fluid in the presence of constant applied inclined magnetic field is considered. Flow problem is mathematically modeled and governing expressions are changed into nonlinear ordinary ones by utilizing appropriate transformations. The effects of pertinent variables on velocity, nanoparticle concentration and temperature are discussed graphically. Furthermore Brownian motion and thermophoresis effects on entropy generation and Bejan number have been examined. Total entropy generation is inspected through various flow variables. Consideration is mainly given to the convergence process. Velocity, temperature and mass gradients at the surface of sheet are calculated numerically.

Quasi-periodic Counter-propagating Fast Magnetosonic Wave Trains from Neighboring Flares: SDO/AIA Observations and 3D MHD Modeling

NASA Astrophysics Data System (ADS)

Ofman, Leon; Liu, Wei

2018-06-01

Since their discovery by the Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA) in the extreme ultraviolet, rapid (phase speeds of ∼1000 km s‑1), quasi-periodic, fast-mode propagating (QFP) wave trains have been observed accompanying many solar flares. They typically propagate in funnel-like structures associated with the expanding magnetic field topology of the active regions (ARs). The waves provide information on the associated flare pulsations and the magnetic structure through coronal seismology (CS). The reported waves usually originate from a single localized source associated with the flare. Here we report the first detection of counter-propagating QFPs associated with two neighboring flares on 2013 May 22, apparently connected by large-scale, trans-equatorial coronal loops. We present the first results of a 3D MHD model of counter-propagating QFPs in an idealized bipolar AR. We investigate the excitation, propagation, nonlinearity, and interaction of the counter-propagating waves for a range of key model parameters, such as the properties of the sources and the background magnetic structure. In addition to QFPs, we also find evidence of trapped fast- (kink) and slow-mode waves associated with the event. We apply CS to determine the magnetic field strength in an oscillating loop during the event. Our model results are in qualitative agreement with the AIA-observed counter-propagating waves and used to identify the various MHD wave modes associated with the observed event, providing insights into their linear and nonlinear interactions. Our observations provide the first direct evidence of counter-propagating fast magnetosonic waves that can potentially lead to turbulent cascade and carry significant energy flux for coronal heating in low-corona magnetic structures.

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.; Federrath, Christoph

2015-02-01

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment—magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures—models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ({{β }p}=0.25,1,2.5,5,25) and sonic Mach numbers ({{M}s}=2,2.5,4). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and α -β -γ closures. We find only mediocre performance of the kinetic eddy-viscosity and α -β -γ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.

Switch-on Shock and Nonlinear Kink Alfvén Waves in Solar Polar Jets

NASA Astrophysics Data System (ADS)

DeVore, C. Richard; Karpen, Judith T.; Antiochos, Spiro K.; Uritsky, Vadim

2016-05-01

It is widely accepted that solar polar jets are produced by fast magnetic reconnection in the low corona, whether driven directly by flux emergence from below or indirectly by instability onset above the photosphere. In either scenario, twisted flux on closed magnetic field lines reconnects with untwisted flux on nearby open field lines. Part of the twist is inherited by the newly reconnected open flux, which rapidly relaxes due to magnetic tension forces that transmit the twist impulsively into the outer corona and heliosphere. We propose that this transfer of twist launches switch-on MHD shock waves, which propagate parallel to the ambient coronal magnetic field ahead of the shock and convect a perpendicular component of magnetic field behind the shock. In the frame moving with the shock front, the post-shock flow is precisely Alfvénic in all three directions, whereas the pre-shock flow is super-Alfvénic along the ambient magnetic field, yielding a density enhancement at the shock front. Nonlinear kink Alfvén waves are exact solutions of the time-dependent MHD equations in the post-shock region when the ambient corona is uniform and the magnetic field is straight. We have performed and analyzed 3D Cartesian and spherical simulations of polar jets driven by instability onset in the corona. The results of both simulations are consistent with the generation of MHD switch-on shocks trailed predominantly by incompressible kink Alfvén waves. It is noteworthy that the kink waves are irrotational, in sharp contrast to the vorticity-bearing torsional waves reported from previous numerical studies. We will discuss the implications of the results for understanding solar polar jets and predicting their heliospheric signatures. Our research was supported by NASA’s LWS TR&T and H-SR programs.

Resistive tearing instability in electron MHD: application to neutron star crusts

NASA Astrophysics Data System (ADS)

Gourgouliatos, Konstantinos N.; Hollerbach, Rainer

2016-12-01

We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the electron magnetohydrodynamic limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as γ ∝ B2/3σ-1/3, where B is the magnetic field and σ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane-parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed, the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few metres thick, covering as little as 1 per cent of the total surface, can provide 1042 erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

Nonlinear theory of magnetohydrodynamic flows of a compressible fluid in the shallow water approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klimachkov, D. A., E-mail: klimchakovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru

2016-09-15

Shallow water magnetohydrodynamic (MHD) theory describing incompressible flows of plasma is generalized to the case of compressible flows. A system of MHD equations is obtained that describes the flow of a thin layer of compressible rotating plasma in a gravitational field in the shallow water approximation. The system of quasilinear hyperbolic equations obtained admits a complete simple wave analysis and a solution to the initial discontinuity decay problem in the simplest version of nonrotating flows. In the new equations, sound waves are filtered out, and the dependence of density on pressure on large scales is taken into account that describesmore » static compressibility phenomena. In the equations obtained, the mass conservation law is formulated for a variable that nontrivially depends on the shape of the lower boundary, the characteristic vertical scale of the flow, and the scale of heights at which the variation of density becomes significant. A simple wave theory is developed for the system of equations obtained. All self-similar discontinuous solutions and all continuous centered self-similar solutions of the system are obtained. The initial discontinuity decay problem is solved explicitly for compressible MHD equations in the shallow water approximation. It is shown that there exist five different configurations that provide a solution to the initial discontinuity decay problem. For each configuration, conditions are found that are necessary and sufficient for its implementation. Differences between incompressible and compressible cases are analyzed. In spite of the formal similarity between the solutions in the classical case of MHD flows of an incompressible and compressible fluids, the nonlinear dynamics described by the solutions are essentially different due to the difference in the expressions for the squared propagation velocity of weak perturbations. In addition, the solutions obtained describe new physical phenomena related to the dependence of the height of the free boundary on the density of the fluid. Self-similar continuous and discontinuous solutions are obtained for a system on a slope, and a solution is found to the initial discontinuity decay problem in this case.« less

Stable Spheromaks Sustained by Neutral Beam Injection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fowler, T K; Jayakumar, R; McLean, H S

It is shown that spheromak equilibria, stable at zero-beta but departing from the Taylor state, could be sustained by non-inductive current drive at acceptable power levels. Stability to both ideal MHD and tearing modes is verified using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive and pressure effects could point the way to improved fusion reactors.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Yao

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities. Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In thismore » thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation. Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands. We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.« less

Vector Third Moment of Turbulent MHD Fluctuations: Theory and Interpretation

NASA Astrophysics Data System (ADS)

Forman, M. A.; MacBride, B. T.; Smith, C. W.

2006-12-01

We call attention to the fact that a certain vector third moment of turbulent MHD fluctuations, even if they are anisotropic, obeys an exact scaling relation in the inertial range. Politano and Pouquet (1998, PP) proved it from the MHD equations specifically. It is a direct analog of the long-known von Karman-Howarth-Monin (KHM) vector relation in anisotropic hydrodynamic turbulence, which follows from the Navier-Stokes equations (see Frisch, 1995). The relevant quantities in MHD are the plus and minus Elsasser vectors and their fluctuations over vector spatial differences. These are used in the mixed vector third moment S+/-(r). The mixed moment is essential, because in the MHD equations for the Elsasser variables, the z + and z- are mixed in the non-linear term. The PP relation is div (S+/-(r))= -4*(epsilon +/-) where (epsilon +/-) is the turbulent energy dissipation rate in the +/- cascade, in Joules/(kg-sec). Of the many possible vector and tensor third moments of MHD vector fluctuations, S+/-(r) is the only one known to have an exact (although vector differential) scaling valid in anisotropic MHD in the inertial range. The PP scaling of a distinctly non-zero third moment indicates that an inertial range cascade is present. The PP scaling does NOT simply result from a dimensional argument, but is derived directly from the MHD equations. A power-law power spectrum alone does not necessarily imply an inertial cascade is present. Furthermore, only the scaling of S+/-(r) gives the epsilon +/- directly. Earlier methods of determining epsilon +/-, based on the amplitude of the power spectrum, make assumptions about isotropy, Alfvenicity and scaling that are not exact. Thus, the observation of a finite S+/-(r) and its scaling with vector r, are fundamental to MHD turbulence in the solar wind, or in any magnetized plasma. We are engaged in evaluating S+/-(r )and its anisotropic scaling in the solar wind, beginning with ACE field and plasma data. For this, we are using the Taylor hypothesis that r = Vt, where t is a time lag of fluctuations seen at a single spacecraft. Because we use a forward time lag, we actually measure -S+/-(r ) which is positive in a direct cascade. We report some results in an accompanying poster. This presentation concentrates on the theory, and how the results are to be interpreted. References: Frisch, U., Turbulence, Cambridge U. Press, 1995, p. 78 Politano, H. and Pouquet, A. Geophys. Res. Lett., 25, 273, 1998

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

NASA Astrophysics Data System (ADS)

Hou, Yawei; Zhu, Ping; Kim, Charlson C.; Hu, Zhaoqing; Zou, Zhihui; Wang, Zhengxiong; Nimrod Team

2018-01-01

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. It is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

Viscous, resistive MHD stability computed by spectral techniques

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Zang, T. A.; Montgomery, D.; Hussaini, M. Y.

1983-01-01

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder

NASA Astrophysics Data System (ADS)

Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.

2018-06-01

An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.

Stationary equatorial MHD flows in general relativity

NASA Astrophysics Data System (ADS)

Daigne, F.; Drenkhahn, G.

2002-01-01

We derive a new formulation of the fully general relativistic equations describing a stationary equatorial MHD outflow from a rotating central object. The wind solution appears as a level contour of a ``Bernoulli'' function fixed by the requirements that it must pass through the slow and fast critical points. This approach is the general relativistic extension to the classical treatment of Sakurai (\\cite{sakurai:85}). We discuss in details how the efficiency of the magnetic to kinetic energy conversion depends mainly on the geometry of the flux tubes and show that the magnetic acceleration can work very well under some conditions. We show how this tool can be used for the study of several astrophysical phenomena, among which gamma-ray bursts.

On Wave Processes in the Solar Atmosphere

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1998-01-01

This grant was awarded by NASA/MSFC to The University of Alabama in Huntsville (UAH) to investigate the physical processes responsible for heating and wind acceleration in the solar atmosphere, and to construct theoretical, self-consistent and time-dependent solar wind models based on the momentum deposition by finite amplitude and nonlinear Alfven waves. In summary, there are three main goals of the proposed research: (1) Calculate the wave energy spectra and wave energy fluxes carried by magnetic non- magnetic waves. (2) Find out which mechanism dominates in supplying the wave energy to different parts of the solar atmosphere. (3) Use the results obtained in (1) and (2) to construct theoretical, self-consistent and time- dependent models of the solar wind. We have completed the first goal by calculating the amount of non-radiative energy generated in the solar convection zone as acoustic waves and as magnetic tube waves. To calculate the amount of wave energy carried by acoustic waves, we have used the Lighthill-Stein theory for sound generation modified by Musielak, Rosner, Stein & Ulmschneider (1994). The acoustic wave energy fluxes for stars located in different regions of the Hertzsprung-Russell (H-R) diagram have also been computed. The wave energy fluxes carried by longitudinal and transverse waves along magnetic flux tubes have been calculated by using both analytical and numerical methods. Our analytical approach is based a theory developed by Musielak, Rosner & Ulmschnelder and Musielak, Rosner, Gall & Ulmschneider, which allows computing the wave energy fluxes for linear tube waves. A numerical approach has been developed by Huang, Musielak & Ulmschneider and Ulmschneider & Musielak to compute the energy fluxes for nonlinear tube waves. Both methods have been used to calculate the wave energy fluxes for stars located in different regions of the HR diagram (Musielak, Rosner & Ulmschneider 1998; Ulmschneider, Musielak & Fawzy 1998). Having obtained the wave energy fluxes for acoustic and magnetic tube waves, we have investigated the behavior of these waves in the solar and stellar atmospheres. The results of our extensive studies have been published in many papers and presented at numerous scientific meetings. In these studies we have investigated different aspects of propagation of acoustic and magnetic waves, the efficiency of energy transfer along magnetic structures in the solar atmosphere, and behavior of Alfven waves in stgeady and expanding solar and stellar atmospheres. Recently, we have used some of these results to construct first purely theoretical, two component and time-dependent models of solar and stellar chromospheres. Finally, to address the third goal, we have constructed first fully theoretical, self-consistent and time dependent wind models based on the momentum deposition by non-linear Alfven waves. The full set of single-fluid MHD equations with the background flow has been solved by using a modified version of the ZEUS MHD code. The constructed wind models are radially symmetric with the magnetic field decreasing radially and the initial outflow is described by the standard Parker wind solution. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; the models thus naturally account for the backreaction of the wind on the waves as well as for the nonlinear interaction between different types of MHD waves. The models have been used to explain the origin of fast speed streams in solar coronal holes. The obtained results clearly demonstrate that the momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast stream components of the solar wind. The range of wave amplitudes required to obtain the desired results seems to be in good agreement with recent observations.

MHD Simulations of Plasma Dynamics with Non-Axisymmetric Boundaries

NASA Astrophysics Data System (ADS)

Hansen, Chris; Levesque, Jeffrey; Morgan, Kyle; Jarboe, Thomas

2015-11-01

The arbitrary geometry, 3D extended MHD code PSI-TET is applied to linear and non-linear simulations of MCF plasmas with non-axisymmetric boundaries. Progress and results from simulations on two experiments will be presented: 1) Detailed validation studies of the HIT-SI experiment with self-consistent modeling of plasma dynamics in the helicity injectors. Results will be compared to experimental data and NIMROD simulations that model the effect of the helicity injectors through boundary conditions on an axisymmetric domain. 2) Linear studies of HBT-EP with different wall configurations focusing on toroidal asymmetries in the adjustable conducting wall. HBT-EP studies the effect of active/passive stabilization with an adjustable ferritic wall. Results from linear verification and benchmark studies of ideal mode growth with and without toroidal asymmetries will be presented and compared to DCON predictions. Simulations of detailed experimental geometries are enabled by use of the PSI-TET code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-TET will also be presented including work to support resistive wall regions within extended MHD simulations. Work supported by DoE.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Wei; Li Hui; Li Shengtai

Nonlinear ideal magnetohydrodynamic (MHD) simulations of the propagation and expansion of a magnetic ''bubble'' plasma into a lower density, weakly magnetized background plasma, are presented. These simulations mimic the geometry and parameters of the Plasma Bubble Expansion Experiment (PBEX) [A. G. Lynn, Y. Zhang, S. C. Hsu, H. Li, W. Liu, M. Gilmore, and C. Watts, Bull. Am. Phys. Soc. 52, 53 (2007)], which is studying magnetic bubble expansion as a model for extragalactic radio lobes. The simulations predict several key features of the bubble evolution. First, the direction of bubble expansion depends on the ratio of the bubble toroidalmore » to poloidal magnetic field, with a higher ratio leading to expansion predominantly in the direction of propagation and a lower ratio leading to expansion predominantly normal to the direction of propagation. Second, a MHD shock and a trailing slow-mode compressible MHD wavefront are formed ahead of the bubble as it propagates into the background plasma. Third, the bubble expansion and propagation develop asymmetries about its propagation axis due to reconnection facilitated by numerical resistivity and to inhomogeneous angular momentum transport mainly due to the background magnetic field. These results will help guide the initial experiments and diagnostic measurements on PBEX.« less

Extended MHD modeling of tearing-driven magnetic relaxation

NASA Astrophysics Data System (ADS)

Sauppe, J. P.; Sovinec, C. R.

2017-05-01

Discrete relaxation events in reversed-field pinch relevant configurations are investigated numerically with nonlinear extended magnetohydrodynamic (MHD) modeling, including the Hall term in Ohm's law and first-order ion finite Larmor radius effects. Results show variability among relaxation events, where the Hall dynamo effect may help or impede the MHD dynamo effect in relaxing the parallel current density profile. The competitive behavior arises from multi-helicity conditions where the dominant magnetic fluctuation is relatively small. The resulting changes in parallel current density and parallel flow are aligned in the core, consistent with experimental observations. The analysis of simulation results also confirms that the force density from fluctuation-induced Reynolds stress arises subsequent to the drive from the fluctuation-induced Lorentz force density. Transport of the momentum density is found to be dominated by the fluctuation-induced Maxwell stress over most of the cross section with viscous and gyroviscous contributions being large in the edge region. The findings resolve a discrepancy with respect to the relative orientation of current density and flow relaxation, which had not been realized or investigated in King et al. [Phys. Plasmas 19, 055905 (2012)], where only the magnitude of flow relaxation is actually consistent with experimental results.

Influence of Thermal Anisotropy on Equilibrium Stellarator Beta Limits

NASA Astrophysics Data System (ADS)

Bechtel, T. A.; Hegna, C. C.; Sovinec, C. R.

2017-10-01

The effect of anisotropic heat conduction on the upper beta limit of stellarator plasmas is studied using the nonlinear, extended MHD code NIMROD. The configuration under investigation is an l=2, M=10 torsatron with vacuum rotational transform near unity. Finite-beta plasmas are created using a volumetric heating source and temperature dependent resistivity; modeled with 22 stellarator symmetric (integer multiples of M) toroidal modes. Extended MHD simulations are then performed to generate steady state solutions that represent 3D equilibria. With increased heating, Shafranov shifts occur, and the associated break up of edge magnetic surfaces limits the achievable beta. Due to the presence of finite parallel heat conduction, pressure profiles can exist in regions of magnetic stochasticity. Here, we present results of independently varying the parallel and perpendicular thermal anisotropy. In particular, simulations show that the attained stored energy is a function of the magnitude of parallel and perpendicular thermal conduction for a given heat source, indicating that equilibrium beta limits are sensitive to anisotropic transport properties. Preliminary studies of MHD stability with non-stellarator symmetric modes, near the highest achievable beta, are also presented. Research supported by US DOE under Grant No. DE-FG02-99ER54546.

MHD modeling of a DIII-D low-torque QH-mode discharge and comparison to observations

NASA Astrophysics Data System (ADS)

King, J. R.; Kruger, S. E.; Burrell, K. H.; Chen, X.; Garofalo, A. M.; Groebner, R. J.; Olofsson, K. E. J.; Pankin, A. Y.; Snyder, P. B.

2017-05-01

Extended-MHD modeling of DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] quiescent H-mode (QH-mode) discharges with nonlinear NIMROD [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] simulations saturates into a turbulent state but does not saturate when the steady-state flow inferred from measurements is not included. This is consistent with the experimental observations of the quiescent regime on DIII-D. The simulation with flow develops into a saturated turbulent state where the nϕ=1 and 2 toroidal modes become dominant through an inverse cascade. Each mode in the range of nϕ=1 -5 is dominant at a different time. Consistent with experimental observations during QH-mode, the simulated state leads to large particle transport relative to the thermal transport. Analysis shows that the amplitude and phase of the density and temperature perturbations differ resulting in greater fluctuation-induced convective particle transport relative to the convective thermal transport. Comparison to magnetic-coil measurements shows that rotation frequencies differ between the simulation and experiment, which indicates that more sophisticated extended-MHD two-fluid modeling is required.

Simulation of Shear Alfvén Waves in LAPD using the BOUT++ code

NASA Astrophysics Data System (ADS)

Wei, Di; Friedman, B.; Carter, T. A.; Umansky, M. V.

2011-10-01

The linear and nonlinear physics of shear Alfvén waves is investigated using the 3D Braginskii fluid code BOUT++. The code has been verified against analytical calculations for the dispersion of kinetic and inertial Alfvén waves. Various mechanisms for forcing Alfvén waves in the code are explored, including introducing localized current sources similar to physical antennas used in experiments. Using this foundation, the code is used to model nonlinear interactions among shear Alfvén waves in a cylindrical magnetized plasma, such as that found in the Large Plasma Device (LAPD) at UCLA. In the future this investigation will allow for examination of the nonlinear interactions between shear Alfvén waves in both laboratory and space plasmas in order to compare to predictions of MHD turbulence.

III Potsdam-V Kiev International Workshop on Nonlinear Processes in Physics. Held in Potsdam, New York on August 1-11, 1991

DTIC Science & Technology

1991-08-01

Bona, Burke, Grundbaum, Hasagawa, Horton, Krichever, Kruskal, Kuznetsov , Lax, McLaughlin, Mikhailov., Rubenchik, Sabatier, Tabor, Zabusky) for their...British Telecom Lab., GB Fibers Oleg Bogoyavlenskij Breaking Solitons Steklov Mathematical Institute USSR Marco Boiti Real and Virtual Multidimensional...Beyond Rutgers University, USA Boris Kupershmidt Relativistic Analogs of Lax Equations Tennessee Space Institute, USA E.A. Kuznetsov Weak MHD Turbulence

Thermophysical analysis for three-dimensional MHD stagnation-point flow of nano-material influenced by an exponential stretching surface

NASA Astrophysics Data System (ADS)

Ur Rehman, Fiaz; Nadeem, Sohail; Ur Rehman, Hafeez; Ul Haq, Rizwan

2018-03-01

In the present paper a theoretical investigation is performed to analyze heat and mass transport enhancement of water-based nanofluid for three dimensional (3D) MHD stagnation-point flow caused by an exponentially stretched surface. Water is considered as a base fluid. There are three (3) types of nanoparticles considered in this study namely, CuO (Copper oxide), Fe3O4 (Magnetite), and Al2O3 (Alumina) are considered along with water. In this problem we invoked the boundary layer phenomena and suitable similarity transformation, as a result our three dimensional non-linear equations of describing current problem are transmuted into nonlinear and non-homogeneous differential equations involving ordinary derivatives. We solved the final equations by applying homotopy analysis technique. Influential outcomes of aggressing parameters involved in this study, effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. It is worth mentioning that Skin-friction along x and y-direction is maximum for Copper oxide-water nanofluid and minimum for Alumina-water nanofluid. Result for local Nusselt number is maximum for Copper oxide-water nanofluid and is minimum for magnetite-water nanofluid.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Dispersive MHD Shock Properties and Interactions with Alfven Solitons

NASA Astrophysics Data System (ADS)

Hamilton, R.; Toll, K.; Ellis, C.

2017-12-01

The weakly nonlinear, weakly dispersive limit of Hall MHD with resistivity for 1D waves travelling nearly parallel to the ambient magnetic field reduces to the derivative nonlinear Schrödinger-Burgers (DNLSB) equation. This model equation describes the coupling between the Alfvenic and magnetosonic modes for a low b plasma. Without dissipation this model equation reduces to the DNLS which can be solved as an initial value problem using the Inverse Scattering Transformation through which the nonlinear component of the magnetic field profile can be represented as a combination of one-parameter bright and dark solitons as well as two-parameter solitons. The one-parameter solitons are constrained to travel at speeds ranging between the Alfvenic and magnetosonic characteristic speeds of the ambient field. We have found that these one-parameter solitons are effectively bound to a 1-2 Fast Shock and will pass back and forth across the shock until they are damped away with no apparent effect on the Fast Shock. A similar mechanism is expected for a sufficiently compressive Intermediate Shock as it arises simply from two effects: damping of a one-parameter soliton causes it to speed up and, if it does not damp away, it will eventually overtake the shock; passing forwards through a compressive shock the decrease of the field strength leads to a slowing of the soliton. We also discuss an extension of results [C. F. Kennel, R. D. Blandford, C. C. Wu, Phys. Fluids B 2(2), 1990] related to the time dependence of Intermediate Shocks in the presence of dispersion.

Impact of E × B shear flow on low-n MHD instabilities.

PubMed

Chen, J G; Xu, X Q; Ma, C H; Xi, P W; Kong, D F; Lei, Y A

2017-05-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al. , Phys. Plasmas 23 , 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E  ×  B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E  ×  B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the E r shear. Adopting the much more general shape of E  ×  B shear ([Formula: see text]) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

Impact of E × B shear flow on low-n MHD instabilities

NASA Astrophysics Data System (ADS)

Chen, J. G.; Xu, X. Q.; Ma, C. H.; Xi, P. W.; Kong, D. F.; Lei, Y. A.

2017-05-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear ( ω E = E r / R B θ ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

Impact of E × B shear flow on low-n MHD instabilities

PubMed Central

Chen, J. G.; Ma, C. H.; Xi, P. W.; Lei, Y. A.

2017-01-01

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear (ωE=Er/RBθ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode. PMID:28579732

Nonhelical inverse transfer of a decaying turbulent magnetic field.

PubMed

Brandenburg, Axel; Kahniashvili, Tina; Tevzadze, Alexander G

2015-02-20

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower k^{2} subinertial range spectrum of kinetic energy forcing the magnetic field with a k^{4} subinertial range to attain larger-scale coherence. The inertial range shows a clear k^{-2} spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

MHD Wind Models in X-Ray Binaries and AGN

NASA Astrophysics Data System (ADS)

Behar, Ehud; Fukumura, Keigo; Kazanas, Demosthenes; Shrader, Chris R.; Tombesi, Francesco; Contopoulos, Ioannis

2017-08-01

Self-similar magnetohydrodynamic (MHD) wind models that can explain both the kinematics and the ionization structure of outflows from accretion sources will be presented.The X-ray absorption-line properties of these outflows are diverse, their velocity ranging from 0.001c to 0.1c, and their ionization ranging from neutral to fully ionized.We will show how the velocity structure and density profile of the wind can be tightly constrained, by finding the scaling of the magnetic flux with the distance from the center that best matches observations, and with no other priors.It will be demonstrated that the same basic MHD wind structure that successfully accounts for the X-ray absorber properties of outflows from supermassive black holes, also reproduces the high-resolution X-ray spectrum of the accreting stellar-mass black hole GRO J1655-40 for a series of ions between ~1A and ~12A.These results support both the magnetic nature of these winds, as well as the universal nature of magnetic outflows across all black hole sizes.

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE PAGES

Luce, Timothy C.

2017-02-23

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

A simplified analytic form for generation of axisymmetric plasma boundaries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luce, Timothy C.

An improved method has been formulated for generating analytic boundary shapes as input for axisymmetric MHD equilibria. This method uses the family of superellipses as the basis function, as previously introduced. The improvements are a simplified notation, reduction of the number of simultaneous nonlinear equations to be solved, and the realization that not all combinations of input parameters admit a solution to the nonlinear constraint equations. The method tests for the existence of a self-consistent solution and, when no solution exists, it uses a deterministic method to find a nearby solution. As a result, examples of generation of boundaries, includingmore » tests with an equilibrium solver, are given.« less

Turbulence scaling study in an MHD wind tunnel on the Swarthmore Spheromak Experiment

NASA Astrophysics Data System (ADS)

Schaffner, D. A.; Wan, A.; Owusu-Boateng, J.; Brown, M. R.; Lukin, V. S.

2013-10-01

The turbulence of colliding spheromaks are explored in the MHD wind tunnel on the SSX. Fully ionized hydrogen plasma is produced by two plasma guns on opposite sides of a 1 m by 15 cm copper cylinder. Modification of B-field, Ti and β are made through stuffing flux variation of the plasma guns. Presented here are turbulent f-/ k-spectra and correlation times/lengths of B-field fluctuations as measured by a 16 channel B-dot radial probe array at the chamber midplane. Power-law fits to spectra show scaling that is robust to changes in stuffing flux; fits are on the order of f-3 and k - 2 . 1 for all flux variations. Dissipation range modification of the spectra is observed; changes to the f-spectra slopes occur around f =fci while changes in k-spectra slopes appear around ~ 5ρi . Dissipation range fits are made with an exponentially modified power-law model [Terry et al., PoP 2012]. Fluctuations in axial velocity are made using a Mach probe. Both B-field and velocity fluctuations persist on the same timescale in these experiments. Mach velocity f-spectra show power-laws similar to that for B-field. Comparison of spectra from MHD and Hall MHD simulations of SSX performed within the HiFi modeling framework are made to the experimental results.

Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

This communication explores magnetohydrodynamic (MHD) boundary-layer flow of Jeffrey nanofluid over a nonlinear stretching surface with active and passive controls of nanoparticles. A nonlinear stretching surface generates the flow. Effects of thermophoresis and Brownian diffusion are considered. Jeffrey fluid is electrically conducted subject to non-uniform magnetic field. Low magnetic Reynolds number and boundary-layer approximations have been considered in mathematical modelling. The phenomena of impulsing the particles away from the surface in combination with non-zero mass flux condition is known as the condition of zero mass flux. Convergent series solutions for the nonlinear governing system are established through optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the temperature and concentration distributions are affected by distinct physical flow parameters. Skin friction coefficient and local Nusselt and Sherwood numbers are also computed and analyzed. Our findings show that the temperature and concentration distributions are increasing functions of Hartman number and thermophoresis parameter.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

2016-06-01

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.

Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shehzad, S. A.; Rauf, A.; Kumar, P. B. Sampath

2018-05-01

This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed.

The temporal behaviour of MHD waves in a partially ionized prominence-like plasma: Effect of heating and cooling

NASA Astrophysics Data System (ADS)

Ballester, J. L.; Carbonell, M.; Soler, R.; Terradas, J.

2018-01-01

Context. During heating or cooling processes in prominences, the plasma microscopic parameters are modified due to the change of temperature and ionization degree. Furthermore, if waves are excited on this non-stationary plasma, the changing physical conditions of the plasma also affect wave dynamics. Aims: Our aim is to study how temporal variation of temperature and microscopic plasma parameters modify the behaviour of magnetohydrodynamic (MHD) waves excited in a prominence-like hydrogen plasma. Methods: Assuming optically thin radiation, a constant external heating, the full expression of specific internal energy, and a suitable energy equation, we have derived the profiles for the temporal variation of the background temperature. We have computed the variation of the ionization degree using a Saha equation, and have linearized the single-fluid MHD equations to study the temporal behaviour of MHD waves. Results: For all the MHD waves considered, the period and damping time become time dependent. In the case of Alfvén waves, the cut-off wavenumbers also become time dependent and the attenuation rate is completely different in a cooling or heating process. In the case of slow waves, while it is difficult to distinguish the slow wave properties in a cooling partially ionized plasma from those in an almost fully ionized plasma, the period and damping time of these waves in both plasmas are completely different when the plasma is heated. The temporal behaviour of the Alfvén and fast wave is very similar in the cooling case, but in the heating case, an important difference appears that is related with the time damping. Conclusions: Our results point out important differences in the behaviour of MHD waves when the plasma is heated or cooled, and show that a correct interpretation of the observed prominence oscillations is very important in order to put accurate constraints on the physical situation of the prominence plasma under study, that is, to perform prominence seismology.

MHD simulations of coronal dark downflows considering thermal conduction

NASA Astrophysics Data System (ADS)

Zurbriggen, E.; Costa, A.; Esquivel, A.; Schneiter, M.; Cécere, M.

2017-10-01

While several scenarios have been proposed to explain supra-arcade downflows (SADs) observed descending through turbulent hot regions, none of them have systematically addressed the consideration of thermal conduction. The SADs are known to be voided cavities. Our model assumes that SADs are triggered by bursty localized reconnection events that produce non-linear waves generating the voided cavity. These subdense cavities are sustained in time because they are hotter than their surrounding medium. Due to the low density and large temperature values of the plasma we expect the thermal conduction to be an important process. Our main aim here is to study if it is possible to generate SADs in the framework of our model considering thermal conduction. We carry on 2D MHD simulations including anisotropic thermal conduction, and find that if the magnetic lines envelope the cavities, they can be isolated from the hot environment and be identified as SADs.

Resistive MHD Simulation of Quasi-Single-Helicity State on KTX

NASA Astrophysics Data System (ADS)

Luo, Bing; Zhu, Ping; Li, Hong; Liu, Wandong

2016-10-01

The potential formation of quasi-single-helicity (QSH) state on Keda Torus eXperiment (KTX) is evaluated in resistive MHD simulations using the NIMROD code. In this work, we focus on the effects of finite resistivity on the mode structure and characteristics of the dominant linear and nonlinear resistive tearing-mode instability in a finite β, cylindrical reversed field pinch model configuration for KTX. In the typical resistivity regimes of KTX where Lundquist number S =105 , the plasma reaches a steady QSH state after the initial transient phase of multiple helicities. The dominat mode of the QSH state is developed from the dominat linear tearing mode instability. The conditions for and the variations of the formation of QSH states in different resistivity regimes of KTX will be reported and discussed. Supported by National Magnetic Confinement Fusion Science Program of China Grant Nos. 2014GB124002, 2015GB101004, 2011GB106000, and 2011GB106003.

Resistive MHD modelling of the quasi-single helicity state in the KTX regimes

NASA Astrophysics Data System (ADS)

Luo, Bing; Zhu, Ping; Li, Hong; Liu, Wandong; KTX Team

2018-01-01

The potential formation of a quasi-single-helicity (QSH) state in the Keda Torus eXperiment (KTX) is investigated in resistive MHD simulations using the NIMROD code. We focus on the effects of finite resistivity on the mode structure and characteristics of the dominant linear and nonlinear resistive tearing-mode in a finite β, cylindrical configuration of a reversed field pinch model for KTX. In the typical resistive regimes of KTX where the Lundquist number S=5 × 104 , the plasma transitions to a steady QSH state after evolving through an initial transient phase with multiple helicities. The dominant mode of the QSH state develops from the dominant linear tearing mode instability. In the lower β regime, the QSH state is intermittent and short in duration; in the higher β regime, the QSH state persists for a longer time and should be more easily observed in experiments.

Tearing mode dynamics and sawtooth oscillation in Hall-MHD

NASA Astrophysics Data System (ADS)

Ma, Zhiwei; Zhang, Wei; Wang, Sheng

2017-10-01

Tearing mode instability is one of the most important dynamic processes in space and laboratory plasmas. Hall effects, resulted from the decoupling of electron and ion motions, could cause the fast development and perturbation structure rotation of the tearing mode and become non-negligible. We independently developed high accuracy nonlinear MHD code (CLT) to study Hall effects on the dynamic evolution of tearing modes with Tokamak geometries. It is found that the rotation frequency of the mode in the electron diamagnetic direction is in a good agreement with analytical prediction. The linear growth rate increases with increase of the ion inertial length, which is contradictory to analytical solution in the slab geometry. We further find that the self-consistently generated rotation largely alters the dynamic behavior of the double tearing mode and the sawtooth oscillation. National Magnetic Confinement Fusion Science Program of China under Grant No. 2013GB104004 and 2013GB111004.

Introduction to Plasma Physics

NASA Astrophysics Data System (ADS)

Gurnett, Donald A.; Bhattacharjee, Amitava

2017-03-01

Preface; 1. Introduction; 2. Characteristic parameters of a plasma; 3. Single particle motions; 4. Waves in a cold plasma; 5. Kinetic theory and the moment equations; 6. Magnetohydrodynamics; 7. MHD equilibria and stability; 8. Discontinuities and shock waves; 9. Electrostatic waves in a hot unmagnetized plasma; 10. Waves in a hot magnetized plasma; 11. Nonlinear effects; 12. Collisional processes; Appendix A. Symbols; Appendix B. Useful trigonometric identities; Appendix C. Vector differential operators; Appendix D. Vector calculus identities; Index.

Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Matthaeus, William H.

1990-01-01

A framework based on turbulence theory is presented to develop approximations for the local turbulence effects that are required in transport models. An approach based on Kolmogoroff-style dimensional analysis is presented as well as one based on a wave-number diffusion picture. Particular attention is given to the case of MHD turbulence with arbitrary cross helicity and with arbitrary ratios of the Alfven time scale and the nonlinear time scale.

Long Pulse Operation on Tore-Supra: Towards Steady State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moreau, P.; Bucalossi, J.; Brosset, C.

The experimental programme of Tore Supra is devoted to the study of technology and physics issues associated to long-duration high performance discharges. This new domain of operation requires simultaneously and in steady state: heat removal capability, particle exhaust, fully non-inductive current drive, advanced technology integration and real time plasma control. The long discharge allows for addressing new time scale physic such as the wall particle retention and erosion. Moreover, the physics of fully non-inductive discharges is full of novelty, namely: the MHD stability, the slow spontaneous oscillation of the central electron temperature or the outstanding inward particle pinch.

Dense Plasma Focus Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Hui; Li, Shengtai; Jungman, Gerard

2016-08-31

The mechanisms for pinch formation in Dense Plasma Focus (DPF) devices, with the generation of high-energy ions beams and subsequent neutron production over a relatively short distance, are not fully understood. Here we report on high-fidelity 2D and 3D numerical magnetohydrodynamic (MHD) simulations using the LA-COMPASS code to study the pinch formation dynamics and its associated instabilities and neutron production.

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

PubMed

Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

2016-01-01

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.

Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Tsurutani, B. T.

1989-01-01

Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.

The role of kinetic ion physics in the interaction of magnetic islands

NASA Astrophysics Data System (ADS)

Stanier, A.

2016-12-01

Magnetic islands are two-dimensional representations of magnetic flux-ropes, a fundamental building block of magnetized plasmas. Here we model magnetic reconnection during the coalescence of magnetic islands with a range of guide fields that have application to the Earth's magnetosphere. It is demonstrated that the Hall-MHD model is able to reproduce the reconnection rates of the fully kinetic system only in the presence of a fairly strong guide field (Bg≥ 3Bx). In the weak guide field limit non-isotropic ion pressure tensor effects that are missing from Hall-MHD are crucial to describe many key features of this reconnection test-problem [1], including the peak and average rates, pile-up field, outflow velocity, and global evolution of the system. A hybrid model which retains the full kinetic physics for ions along with mass-less fluid electrons gives good agreement with fully kinetic results for the full range of guide fields considered. These results suggest that kinetic ions may be important for a large number of reconnection events in the Earth's magnetosphere. References: [1] A. Stanier, W. Daughton, L. Chacon, H. Karimabadi, J. Ng, Y.-M. Huang, A. Hakim, and A. Bhattacharjee, Phys. Rev. Lett. 115, 175004 (2015).

Fully nonlinear Goertler vortices in constricted channel flows and their effect on the onset of separation

NASA Technical Reports Server (NTRS)

Denier, James P.; Hall, Philip

1992-01-01

The development of fully nonlinear Goertler vortices in high Reynolds number flow in a symmetrically constricted channel is investigated. Attention is restricted to the case of 'strongly' constricted channels considered by Smith and Daniels (1981) for which the scaled constriction height is asymptotically large. Such flows are known to develop a Goldstein singularity and subsequently become separated at some downstream station past the point of maximum channel constriction. It is shown that these flows can support fully nonlinear Goertler vortices, of the form elucidated by Hall and Lakin (1988), for constrictions which have an appreciable region of local concave curvature upstream of the position at which separation occurs. The effect on the onset of separation due to the nonlinear Goertler modes is discussed. A brief discussion of other possible nonlinear states which may also have a dramatic effect in delaying (or promoting) separation is given.

EXTRAPOLATION OF THE SOLAR CORONAL MAGNETIC FIELD FROM SDO/HMI MAGNETOGRAM BY A CESE-MHD-NLFFF CODE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang Chaowei; Feng Xueshang, E-mail: cwjiang@spaceweather.ac.cn, E-mail: fengx@spaceweather.ac.cn

Due to the absence of direct measurement, the magnetic field in the solar corona is usually extrapolated from the photosphere in a numerical way. At the moment, the nonlinear force-free field (NLFFF) model dominates the physical models for field extrapolation in the low corona. Recently, we have developed a new NLFFF model with MHD relaxation to reconstruct the coronal magnetic field. This method is based on CESE-MHD model with the conservation-element/solution-element (CESE) spacetime scheme. In this paper, we report the application of the CESE-MHD-NLFFF code to Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) data with magnetograms sampled for two activemore » regions (ARs), NOAA AR 11158 and 11283, both of which were very non-potential, producing X-class flares and eruptions. The raw magnetograms are preprocessed to remove the force and then inputted into the extrapolation code. Qualitative comparison of the results with the SDO/AIA images shows that our code can reconstruct magnetic field lines resembling the EUV-observed coronal loops. Most important structures of the ARs are reproduced excellently, like the highly sheared field lines that suspend filaments in AR 11158 and twisted flux rope which corresponds to a sigmoid in AR 11283. Quantitative assessment of the results shows that the force-free constraint is fulfilled very well in the strong-field regions but apparently not that well in the weak-field regions because of data noise and numerical errors in the small currents.« less

Three-dimensional rotational plasma flows near solid surfaces in an axial magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorshunov, N. M., E-mail: gorshunov-nm@nrcki.ru; Potanin, E. P., E-mail: potanin45@yandex.ru

2016-11-15

A rotational flow of a conducting viscous medium near an extended dielectric disk in a uniform axial magnetic field is analyzed in the magnetohydrodynamic (MHD) approach. An analytical solution to the system of nonlinear differential MHD equations of motion in the boundary layer for the general case of different rotation velocities of the disk and medium is obtained using a modified Slezkin–Targ method. A particular case of a medium rotating near a stationary disk imitating the end surface of a laboratory device is considered. The characteristics of a hydrodynamic flow near the disk surface are calculated within the model ofmore » a finite-thickness boundary layer. The influence of the magnetic field on the intensity of the secondary flow is studied. Calculations are performed for a weakly ionized dense plasma flow without allowance for the Hall effect and plasma compressibility. An MHD flow in a rotating cylinder bounded from above by a retarding cap is considered. The results obtained can be used to estimate the influence of the end surfaces on the main azimuthal flow, as well as the intensities of circulating flows in various devices with rotating plasmas, in particular, in plasma centrifuges and laboratory devices designed to study instabilities of rotating plasmas.« less

Modeling the heliolatitudinal gradient of the solar wind parameters with exact MHD solutions

NASA Technical Reports Server (NTRS)

Lima, J. J. G.; Tsinganos, K.

1995-01-01

The heliolatitudinal dependence of observations of the solar wind macroscopic quantities such as the averaged proton speed, density and the mass and momentum flux are modeled. The published observations covering the last two and a half solar cycles, are obtained either via the technique of interplanetary scintillations for the last 2 solar cycles (1970-1990), or, from the plasma experiment aboard the ULYSSES spacecraft for the recent period 1990-1994. Exact, two dimensional solutions of the full set of the steady MHD equations are used which are obtained through a nonlinear separation of the variables in the MHD equations. The three parameters emerging from the solutions are fixed from these observations, as well as from observations of the solar rotation. It is found that near solar maximum the solar wind speed is uniformly low, around the 400 km/s over a wide range of latitudes. On the other hand, during solar minimum and the declining phase of the solar activity cycle, there is a strong heliolatitudinal gradient in proton speed between 400-800 from equator to pole. This modeling also agrees with previous findings that the gradient in wind speed with the latitude is offset by a gradient in density such that the mass and momentum flux vary relatively little.

Ideal Magnetohydrodynamic Simulations of Magnetic Bubble Expansion as a Model for Extragalactic Radio Lobes

NASA Astrophysics Data System (ADS)

Liu, Wei; Hsu, Scott; Li, Hui; Li, Shengtai; Lynn, Alan

2009-05-01

Recent astronomical observations indicate that radio lobes are gigantic relaxed magnetized plasmas with kilo-to-megaparsec scale jets providing a source of magnetic energy from the galaxy to the lobes. Therefore we are conducting a laboratory plasma experiment, the Plasma Bubble Expansion Experiment (PBEX) in which a higher pressure magnetized plasma bubble (i.e., the lobe) is injected into a lower pressure background plasma (i.e., the intergalactic medium) to study key nonlinear plasma physics issues. Here we present detailed ideal magnetohydrodynamic (MHD) three-dimensional simulations of PBEX. First, the direction of bubble expansion depends on the ratio of the bubble toroidal to poloidal magnetic field, with a higher ratio leading to expansion predominantly in the direction of propagation and a lower ratio leading to expansion predominantly normal to the direction of propagation. Second, a leading MHD shock and a trailing slow-mode compressible MHD wave front are formed ahead of the bubble as it propagates into the background plasma. Third, the bubble expansion and propagation develop asymmetries about its propagation axis due to reconnection arising from numerical resistivity and to inhomogeneous angular momentum transport due to the background magnetic field. These results will help guide the initial experiments and diagnostic measurements on PBEX.

Sawtooth mitigation in 3D MHD tokamak modelling with applied magnetic perturbations

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Veranda, M.; Cappello, S.; Chacón, L.; Escande, D. F.

2017-01-01

The effect of magnetic perturbations (MPs) on the sawtoothing dynamics of the internal kink mode in the tokamak is discussed in the framework of nonlinear 3D MHD modelling. Numerical simulations are performed with the pixie3d code (Chacón 2008 Phys. Plasmas 15 056103) based on a D-shaped configuration in toroidal geometry. MPs are applied as produced by two sets of coils distributed along the toroidal direction, one set located above and the other set below the outboard midplane, like in experimental devices such as DIII-D and ASDEX Upgrade. The capability of n  =  1 MPs to affect quasi-periodic sawteeth is shown to depend on the toroidal phase difference Δ φ between the perturbations produced by the two sets of coils. In particular, sawtooth mitigation is obtained for the Δ φ =π phasing, whereas no significant effect is observed for Δ φ =0 . Numerical findings are explained by the interplay between different poloidal harmonics in the spectrum of applied MPs, and appear to be consistent with experiments performed in the DIII-D device. Sawtooth mitigation and stimulation of self-organized helical states by applied MPs have been previously demonstrated in both circular tokamak and reversed-field pinch (RFP) experiments in the RFX-mod device, and in related 3D MHD modelling.

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1992-01-01

In the area of solar physics, new calculations of the acoustic wave energy fluxes generated in the solar convective zone was performed. The original theory developed was corrected by including a new frequency factor describing temporal variations of the turbulent energy spectrum. We have modified the original Stein code by including this new frequency factor, and tested the code extensively. Another possible source of the mechanical energy generated in the solar convective zone is the excitation of magnetic flux tube waves which can carry energy along the tubes far away from the region. The problem as to how efficiently those waves are generated in the Sun was recently solved. The propagation of nonlinear magnetic tube waves in the solar atmosphere was calculated, and mode coupling, shock formation, and heating of the local medium was studied. The wave trapping problems and evaluation of critical frequencies for wave reflection in the solar atmosphere was studied. It was shown that the role played by Alfven waves in the wind accelerations and the coronal hole heating is dominant. Presently, we are performing calculations of wave energy fluxes generated in late-type dwarf stars and studying physical processes responsible for the heating of stellar chromospheres and coronae. In the area of physics of waves, a new analytical approach for studying linear Alfven waves in smoothly nonuniform media was recently developed. This approach is presently being extended to study the propagation of linear and nonlinear magnetohydrodynamic (MHD) waves in stratified, nonisothermal and solar atmosphere. The Lighthill theory of sound generation to nonisothermal media (with a special temperature distribution) was extended. Energy cascade by nonlinear MHD waves and possible chaos driven by these waves are presently considered.

Extended MHD Modeling of Tearing-Driven Magnetic Relaxation

NASA Astrophysics Data System (ADS)

Sauppe, Joshua

2016-10-01

Driven plasma pinch configurations are characterized by the gradual accumulation and episodic release of free energy in discrete relaxation events. The hallmark of this relaxation in a reversed-field pinch (RFP) plasma is flattening of the parallel current density profile effected by a fluctuation-induced dynamo emf in Ohm's law. Nonlinear two-fluid modeling of macroscopic RFP dynamics has shown appreciable coupling of magnetic relaxation and the evolution of plasma flow. Accurate modeling of RFP dynamics requires the Hall effect in Ohm's law as well as first order ion finite Larmor radius (FLR) effects, represented by the Braginskii ion gyroviscous stress tensor. New results find that the Hall dynamo effect from < J × B > / ne can counter the MHD effect from - < V × B > in some of the relaxation events. The MHD effect dominates these events and relaxes the current profile toward the Taylor state, but the opposition of the two dynamos generates plasma flow in the direction of equilibrium current density, consistent with experimental measurements. Detailed experimental measurements of the MHD and Hall emf terms are compared to these extended MHD predictions. Tracking the evolution of magnetic energy, helicity, and hybrid helicity during relaxation identifies the most important contributions in single-fluid and two-fluid models. Magnetic helicity is well conserved relative to the magnetic energy during relaxation. The hybrid helicity is dominated by magnetic helicity in realistic low-beta pinch conditions and is also well conserved. Differences of less than 1 % between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution through ion FLR effects, which have not been included in contemporary relaxation theories. The kinetic energy driven by relaxation in the computations is dominated by velocity components perpendicular to the magnetic field, an effect that had not been predicted. Work performed at University of Wisconsin-Madison. LA-UR-16-24727.

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, B. J.; Kruger, S. E.; Hegna, C. C.

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition tomore » instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10{sup 8} and 10{sup 3} for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10{sup 5}, which is much larger than experimentally measured values using T{sub e} values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.« less

Numerical study for heat generation/absorption in flow of nanofluid by a rotating disk

NASA Astrophysics Data System (ADS)

Aziz, Arsalan; Alsaedi, Ahmed; Muhammad, Taseer; Hayat, Tasawar

2018-03-01

Here MHD three-dimensional flow of viscous nanoliquid by a rotating disk with heat generation/absorption and slip effects is addressed. Thermophoresis and random motion features are also incorporated. Velocity, temperature and concentration slip conditions are imposed at boundary. Applied magnetic field is utilized. Low magnetic Reynolds number and boundary layer approximations have been employed in the problem formulation. Suitable transformations lead to strong nonlinear ordinary differential system. The obtained nonlinear system is solved numerically through NDSolve technique. Graphs have been sketched in order to analyze that how the velocity, temperature and concentration fields are affected by various pertinent variables. Moreover the numerical values for rates of heat and mass transfer have been tabulated and discussed.

Dual Solutions for Nonlinear Flow Using Lie Group Analysis

PubMed Central

Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman

2015-01-01

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996

Wave Propagation Around Coronal Structures: Stratification, Buoyancy, Small Scale Formation

NASA Astrophysics Data System (ADS)

Tomlinson, S. M.; Rappazzo, F.; Velli, M.

2017-12-01

We study the propagation of waves in a coronal medium characterized by stratification and structure in density. temperature and magnetic field. It is well known that average gradients affect the propagation of Alfvén and other MHD waves via reflection, phase mixing, resonant absorption and other coupling phenomena. Here we discuss how the interplay of propagation on inhomogeneous, stratified structures with nonlinear interactions may lead to interesting effects including preferential heating, buoyancy, and plasma acceleration.

Self-Organized Stationary States of Tokamaks

DOE PAGES

Jardin, S. C.; Ferraro, N.; Krebs, I.

2015-11-17

We demonstrate that in a 3D resistive magnetohydrodynamic (MHD) simulation, for some parameters it is possible to form a stationary state in a tokamak where a saturated interchange mode in the center of the discharge drives a near helical flow pattern that acts to non-linearly sustain the configuration by adjusting the central loop voltage through a dynamo action. This could explain the physical mechanism for maintaining stationary non-sawtoothing “hybrid” discharges, often referred to as “flux-pumping”.

Well-posedness of the plasma-vacuum interface problem

NASA Astrophysics Data System (ADS)

Secchi, Paolo; Trakhinin, Yuri

2014-01-01

We consider the free-boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we consider the pre-Maxwell dynamics for the magnetic field. At the free interface, driven by the plasma velocity, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, because of a given surface current on the fixed boundary that forces oscillations. Under a suitable stability condition satisfied at each point of the initial interface, stating that the magnetic fields on either side of the interface are not collinear, we show the existence and uniqueness of the solution to the nonlinear plasma-vacuum interface problem in suitable anisotropic Sobolev spaces. The proof is based on the results proved in the companion paper (Secchi and Trakhinin 2013 Interfaces Free Boundaries 15 323-57), about the well-posedness of the homogeneous linearized problem and the proof of a basic a priori energy estimate. The proof of the resolution of the nonlinear problem given in the present paper follows from the analysis of the elliptic system for the vacuum magnetic field, a suitable tame estimate in Sobolev spaces for the full linearized equations, and a Nash-Moser iteration.

Global Particle-in-Cell Simulations of Mercury's Magnetosphere

NASA Astrophysics Data System (ADS)

Schriver, D.; Travnicek, P. M.; Lapenta, G.; Amaya, J.; Gonzalez, D.; Richard, R. L.; Berchem, J.; Hellinger, P.

2017-12-01

Spacecraft observations of Mercury's magnetosphere have shown that kinetic ion and electron particle effects play a major role in the transport, acceleration, and loss of plasma within the magnetospheric system. Kinetic processes include reconnection, the breakdown of particle adiabaticity and wave-particle interactions. Because of the vast range in spatial scales involved in magnetospheric dynamics, from local electron Debye length scales ( meters) to solar wind/planetary magnetic scale lengths (tens to hundreds of planetary radii), fully self-consistent kinetic simulations of a global planetary magnetosphere remain challenging. Most global simulations of Earth's and other planet's magnetosphere are carried out using MHD, enhanced MHD (e.g., Hall MHD), hybrid, or a combination of MHD and particle in cell (PIC) simulations. Here, 3D kinetic self-consistent hybrid (ion particle, electron fluid) and full PIC (ion and electron particle) simulations of the solar wind interaction with Mercury's magnetosphere are carried out. Using the implicit PIC and hybrid simulations, Mercury's relatively small, but highly kinetic magnetosphere will be examined to determine how the self-consistent inclusion of electrons affects magnetic reconnection, particle transport and acceleration of plasma at Mercury. Also the spatial and energy profiles of precipitating magnetospheric ions and electrons onto Mercury's surface, which can strongly affect the regolith in terms of space weathering and particle outflow, will be examined with the PIC and hybrid codes. MESSENGER spacecraft observations are used both to initiate and validate the global kinetic simulations to achieve a deeper understanding of the role kinetic physics play in magnetospheric dynamics.

Capabilities of Fully Parallelized MHD Stability Code MARS

NASA Astrophysics Data System (ADS)

Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang

2016-10-01

Results of full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. Parallel version of MARS, named PMARS, has been recently developed at FAR-TECH. Parallelized MARS is an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, implemented in MARS. Parallelization of the code included parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse vector iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the MARS algorithm using parallel libraries and procedures. Parallelized MARS is capable of calculating eigenmodes with significantly increased spatial resolution: up to 5,000 adapted radial grid points with up to 500 poloidal harmonics. Such resolution is sufficient for simulation of kink, tearing and peeling-ballooning instabilities with physically relevant parameters. Work is supported by the U.S. DOE SBIR program.

Analytical modeling of Cosmic Winds and Jets

NASA Astrophysics Data System (ADS)

Vlahakis, Nektarios

1998-11-01

A widespread phenomenon in astrophysics is the outflow of plasma from the environment of stellar or galactic objects. This plasma outflows range from nonuniform winds to highly collimated jets which are common to many stages of stellar evolution. For example, collimated outflows are found around young stars (e.g., as in HH 30), older mass losing stars (as in eta-Carinae), symbiotic stars (e.g. in R Aqr), planetary nebulae nuclei (as in the hourglass nebula), black hole X-ray transients (as in GRS 1915+105 and GRO J1655-40), low- and high-mass X-ray binaries and recently also in cataclysmic variables (e.g. T Pyxidis). Similarly, they are also found emerging from the nuclei of many radio galaxies and quasars. Nevertheless, despite their abundance the questions of the formation, acceleration and propagation of nonuniform winds and jets have not been fully resolved. One of the main difficulties in dealing with the theoretical problem posed by cosmical outflows is that their dynamics needs to be described - even to lowest order - by the highly intractable set of the MHD equations. As is well known, this is a nonlinear system of partial differential equations with several critical points, and only very few classes of solutions are available for axisymmetric systems obtained by assuming a separation of variables in several key functions. This hypothesis allows an analysis in a 2-D geometry of the full MHD equations which reduce then to a system of ordinary differential equations. By a systematic method we construct general classes of exact and self-consistent axisymmetric MHD solutions. The unifying scheme contains three large groups of exact MHD outflow models, (I) meridionally self-similar ones with spherical critical surfaces, (II) radially self-similar models with conical critical surfaces and (III) generalized self-similar models with arbitrary shape critical surfaces. This classification includes known polytropic models, such as the classical Parker description of a stellar wind and the Blandford and Payne (1982) model of a disk-wind; it also contains nonpolytropic models, such as those of winds/jets in Sauty and Tsinganos (1994), Lima et al (1996) and Trussoni et al (1997). Besides the unification of all known cases under a common scheme, several new classes emerge and some are briefly analyzed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized astrophysical rotators. We also propose a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the magnetized atmosphere of a rotating gravitating central object with possibly an orbiting accretion disk. The plasma is driven by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflows start almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is given, as well as a brief sketch of its applicability to a self-consistent modeling of collimated outflows from various astrophysical objects. For example, the obtained characteristics of the collimated outflow in agreement with those in jets associated with YSO's. General theoretical arguments and various analytic self-similar solutions have recently shown that magnetized and rotating astrophysical outflows may become asymptotically cylindrical, in agreement with observations of cosmical jets. A notable common feature in all such self-consistent, self-similar MHD solutions is that before final cylindrical collimation is achieved, the jet passes from a stage of oscillations in its radius, Mach number and other physical parameters. It is shown that under rather general assumptions this oscillatory behaviour of collimated outflows is not restricted to the few specific models examined so far, but instead it seems to be a rather general physical property of an MHD outflow which starts noncylindrically before it reaches collimation. It is concluded thence that astrophysical jets are topologically stable to small amplitude, time-independent perturbations in their asymptotically cylindrical shape. Also, similarly to the familiar fluid instabilities these oscillations may give rise to brightness enhancements along jets.

Thermal Diagnostics with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions

NASA Astrophysics Data System (ADS)

Cheung, Mark C. M.; Boerner, P.; Schrijver, C. J.; Testa, P.; Chen, F.; Peter, H.; Malanushenko, A.

2015-07-01

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parkin, E. R.; Bicknell, G. V., E-mail: parkin@mso.anu.edu.au

Global three-dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when nonlinear motions-perhaps triggered by the onset of turbulence-upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once themore » disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure <{alpha}{sub P}>bar = 0.034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23-35 cells per scale height (in the vertical direction).« less

THERMAL DIAGNOSTICS WITH THE ATMOSPHERIC IMAGING ASSEMBLY ON BOARD THE SOLAR DYNAMICS OBSERVATORY: A VALIDATED METHOD FOR DIFFERENTIAL EMISSION MEASURE INVERSIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheung, Mark C. M.; Boerner, P.; Schrijver, C. J.

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magneticmore » flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.« less

Transport and Dynamics in Toroidal Fusion Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schnack, Dalton D

2006-05-16

This document reports the successful completion of the OFES Theory Milestone for FY2005, namely, Perform parametric studies to better understand the edge physics regimes of laboratory experiments. Simulate at increased resolution (up to 20 toroidal modes), with density evolution, late into the nonlinear phase and compare results from different types of edge modes. Simulate a single case including a study of heat deposition on nearby material walls. The linear stability properties and nonlinear evolution of Edge Localized Modes (ELMs) in tokamak plasmas are investigated through numerical computation. Data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/) is used for themore » magnetohydrodynamic (MHD) equilibria, but edge parameters are varied to reveal important physical effects. The equilibrium with very low magnetic shear produces an unstable spectrum that is somewhat insensitive to dissipation coefficient values. Here, linear growth rates from the non-ideal NIMROD code (http://nimrodteam.org) agree reasonably well with ideal, i.e. non-dissipative, results from the GATO global linear stability code at low toroidal mode number (n) and with ideal results from the ELITE edge linear stability code at moderate to high toroidal mode number. Linear studies with a more realistic sequence of MHD equilibria (based on DIII-D discharge 86166) produce more significant discrepancies between the ideal and non-ideal calculations. The maximum growth rate for the ideal computations occurs at toroidal mode index n=10, whereas growth rates in the non-ideal computations continue to increase with n unless strong anisotropic thermal conduction is included. Recent modeling advances allow drift effects associated with the Hall electric field and gyroviscosity to be considered. A stabilizing effect can be observed in the preliminary results, but while the distortion in mode structure is readily apparent at n=40, the growth rate is only 13% less than the non-ideal MHD result. Computations performed with a non-local kinetic closure for parallel electron thermal conduction that is valid over all collisionality regimes identify thermal diffusivity ratios of {chi}{sub ||}/{chi}{sub {perpendicular}} ~ 10{sup 7} - 10{sup 8} as appropriate when using collisional heat flux modeling for these modes. Adding significant parallel viscosity proves to have little effect. Nonlinear ELM computations solve the resistive MHD model with toroidal resolution 0{<=}n{<=}21, including anisotropic thermal conduction, temperature-dependent resistivity, and number density evolution. The computations are based on a realistic equilibrium with high pedestal temperature from the linear study. When the simulated ELM grows to appreciable amplitude, ribbon-like thermal structures extend from the separatrix to the wall as the spectrum broadens about a peak at n=13. Analysis of the results finds the heat flux on the wall to be very nonuniform with greatest intensity occurring in spots on the top and bottom of the chamber. Net thermal energy loss occurs on a time-scale of 100 {micro}s, and the instantaneous loss rate exceeds 1 GW.« less

Prevention of Mental Health Disorders Using Internet- and Mobile-Based Interventions: A Narrative Review and Recommendations for Future Research

PubMed Central

Ebert, David Daniel; Cuijpers, Pim; Muñoz, Ricardo F.; Baumeister, Harald

2017-01-01

Although psychological interventions might have a tremendous potential for the prevention of mental health disorders (MHD), their current impact on the reduction of disease burden is questionable. Possible reasons include that it is not practical to deliver those interventions to the community en masse due to limited health care resources and the limited availability of evidence-based interventions and clinicians in routine practice, especially in rural areas. Therefore, new approaches are needed to maximize the impact of psychological preventive interventions. Limitations of traditional prevention programs could potentially be overcome by providing Internet- and mobile-based interventions (IMIs). This relatively new medium for promoting mental health and preventing MHD introduces a fresh array of possibilities, including the provision of evidence-based psychological interventions that are free from the restraints of travel and time and allow reaching participants for whom traditional opportunities are not an option. This article provides an introduction to the subject and narratively reviews the available evidence for the effectiveness of IMIs with regard to the prevention of MHD onsets. The number of randomized controlled trials that have been conducted to date is very limited and so far it is not possible to draw definite conclusions about the potential of IMIs for the prevention of MHD for specific disorders. Only for the indicated prevention of depression there is consistent evidence across four different randomized trial trials. The only trial on the prevention of general anxiety did not result in positive findings in terms of eating disorders (EDs), effects were only found in post hoc subgroup analyses, indicating that it might be possible to prevent ED onset for subpopulations of people at risk of developing EDs. Future studies need to identify those subpopulations likely to profit from preventive. Disorders not examined so far include substance use disorders, bipolar disorders, stress-related disorders, phobic disorders and panic disorder, obsessive–compulsive disorder, impulse-control disorders, somatic symptom disorder, and insomnia. In summary, there is a need for more rigorously conducted large scale randomized controlled trials using standard clinical diagnostic instruments for the selection of participants without MHD at baseline and the assessment of MHD onset. Subsequently, we discuss future directions for the field in order to fully exploit the potential of IMI for the prevention of MHD. PMID:28848454

Prevention of Mental Health Disorders Using Internet- and Mobile-Based Interventions: A Narrative Review and Recommendations for Future Research.

PubMed

Ebert, David Daniel; Cuijpers, Pim; Muñoz, Ricardo F; Baumeister, Harald

2017-01-01

Although psychological interventions might have a tremendous potential for the prevention of mental health disorders (MHD), their current impact on the reduction of disease burden is questionable. Possible reasons include that it is not practical to deliver those interventions to the community en masse due to limited health care resources and the limited availability of evidence-based interventions and clinicians in routine practice, especially in rural areas. Therefore, new approaches are needed to maximize the impact of psychological preventive interventions. Limitations of traditional prevention programs could potentially be overcome by providing Internet- and mobile-based interventions (IMIs). This relatively new medium for promoting mental health and preventing MHD introduces a fresh array of possibilities, including the provision of evidence-based psychological interventions that are free from the restraints of travel and time and allow reaching participants for whom traditional opportunities are not an option. This article provides an introduction to the subject and narratively reviews the available evidence for the effectiveness of IMIs with regard to the prevention of MHD onsets. The number of randomized controlled trials that have been conducted to date is very limited and so far it is not possible to draw definite conclusions about the potential of IMIs for the prevention of MHD for specific disorders. Only for the indicated prevention of depression there is consistent evidence across four different randomized trial trials. The only trial on the prevention of general anxiety did not result in positive findings in terms of eating disorders (EDs), effects were only found in post hoc subgroup analyses, indicating that it might be possible to prevent ED onset for subpopulations of people at risk of developing EDs. Future studies need to identify those subpopulations likely to profit from preventive. Disorders not examined so far include substance use disorders, bipolar disorders, stress-related disorders, phobic disorders and panic disorder, obsessive-compulsive disorder, impulse-control disorders, somatic symptom disorder, and insomnia. In summary, there is a need for more rigorously conducted large scale randomized controlled trials using standard clinical diagnostic instruments for the selection of participants without MHD at baseline and the assessment of MHD onset. Subsequently, we discuss future directions for the field in order to fully exploit the potential of IMI for the prevention of MHD.

Nonlinear Evolution of the Kelvin-Helmholtz Instability in the High Latitude Ionosphere.

DTIC Science & Technology

1987-12-21

field. Both cases have been studied in the MHD [Mikhailovskii, 1974; Sen, 1964; -. Southwood, 19681 and electrostatic [D’Angelo, 1965; Smith and von ...1293, 1964. Smith, C.G. and S. von Goeler, Kelviri-Helmholtz instability for a collisionless plasma model, Phys. Fluids, 11, 2665,1968. Southwood...ELECTRIC COMPANY P.O. BOX 85154 SPACE DIVISION SAN DIEGO, CA 92138 VALLEY FORGE SPACE CENTER OCY ATTN J.L. SPERLING GODDARD BLVD KING OF PRUSSIA P.O. BOX

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations

NASA Astrophysics Data System (ADS)

Sotoudeh, Zahra

2011-07-01

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Kinetic effects on turbulence driven by the magnetorotational instability in black hole accretion

NASA Astrophysics Data System (ADS)

Sharma, Prateek

Many astrophysical objects (e.g., spiral galaxies, the solar system, Saturn's rings, and luminous disks around compact objects) occur in the form of a disk. One of the important astrophysical problems is to understand how rotationally supported disks lose angular momentum, and accrete towards the bottom of the gravitational potential, converting gravitational energy into thermal (and radiation) energy. The magnetorotational instability (MRI), an instability causing turbulent transport in ionized accretion disks, is studied in the kinetic regime. Kinetic effects are important because radiatively inefficient accretion flows (RIAFs), like the one around the supermassive black hole in the center of our Galaxy, are collisionless. The ion Larmor radius is tiny compared to the scale of MHD turbulence so that the drift kinetic equation (DKE), obtained by averaging the Vlasov equation over the fast gyromotion, is appropriate for evolving the distribution function. The kinetic MHD formalism, based on the moments of the DKE, is used for linear and nonlinear studies. A Landau fluid closure for parallel heat flux, which models kinetic effects like collisionless damping, is used to close the moment hierarchy. We show, that the kinetic MHD and drift kinetic formalisms give the same set of linear modes for a Keplerian disk. The BGK collision operator is used to study the transition of the MRI from kinetic to the MHD regime. The ZEUS MHD code is modified to include the key kinetic MHD terms: anisotropy, pressure tensor and anisotropic thermal conduction. The modified code is used to simulate the collisionless MRI in a local shearing box. As magnetic field is amplified by the MRI, pressure anisotropy ( p [perpendicular] > p || ) is created because of the adiabatic invariance (m 0( p [perpendicular] / B ). Larmor radius scale instabilities---mirror, ion-cyclotron, and firehose---are excited even at small pressure anisotropies (D p/p ~ 1/b). Pressure isotropization due to pitch angle scattering by these instabilities is included as a subgrid model. A key result of the kinetic MHD simulations is that the anisotropy stress can be as large as the Maxwell stress. It is shown, with the help of simple tests, that the centered differencing of anisotropic thermal conduction can cause the heat to flow from lower to higher temperatures, giving negative temperatures in regions with large temperature gradients. A new method, based on limiting the transverse temperature gradient, allows heat to flow only from higher to lower temperatures. Several tests and convergence studies are presented to compare the different methods.

Hall effects on the Walén relation in rotational discontinuities and Alfvén waves

NASA Astrophysics Data System (ADS)

Wu, B. H.; Lee, L. C.

2000-08-01

For Alfvénic fluctuations in magnetohydrodynamics (MHD) the perturbed transverse velocity Vt and magnetic field Bt can be related by the Walén relation, Vt = ±Bt/(μ0ρ)1/2 ≡;±VAt, where ρ is the plasma density, VAt is the transverse Alfvén velocity, and the plus (minus) sign is for antiparallel (parallel) propagation. However, observations of Vt and Bt for Alfvén waves and rotational discontinuities in the solar wind and at the magnetopause showed an obvious deviation from the relation. In this paper, modifications of the Walén relation for linear and nonlinear Alfvén waves and rotational discontinuities (RDs) are examined in the Hall-MHD formulation. Let Vit (≈ Vt) be the transverse ion velocity and Vet be the transverse electron velocity. It is found that Vit = ±Bt(z)/(μ0ρ1)1/2 = ±(ρ(z)/ρ1)1/2 VAt(z) and Vet = ±(ρ1/μ0)1/2Bt(z)/ρ(z) = ±(ρ1/ρ(z))1/2 VAt(z)for RDs in Hall-MHD, where ρ1 is the upstream plasma density. The ion and electron Walén ratios are defined as Ai = Vit/VAt and Ae = Vet/VAt, respectively. It is found in Hall-MHD that ?, AiAe = 1 and Ai < 1 (Ai > 1) for Alfvén waves and RDs with right-hand (left-hand) polarization. The Hall dispersive effect may modify the ion Walén ratio by ΔAi≈±0.14 for the magnetopause RDs and by ΔAi≈±0.07 for the interplanetary RDs.

A new technique for observationally derived boundary conditions for space weather

NASA Astrophysics Data System (ADS)

Pagano, Paolo; Mackay, Duncan Hendry; Yeates, Anthony Robinson

2018-04-01

Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods: To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions: In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adcock, T. A. A.; Taylor, P. H.

2016-01-15

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest whichmore » leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum.« less

MULTI-FLUID APPROACH TO HIGH-FREQUENCY WAVES IN PLASMAS. I. SMALL-AMPLITUDE REGIME IN FULLY IONIZED MEDIUM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume, E-mail: david.martinez@uib.es

Ideal magnetohydrodynamics (MHD) provides an accurate description of low-frequency Alfvén waves in fully ionized plasmas. However, higher-frequency waves in many plasmas of the solar atmosphere cannot be correctly described by ideal MHD and a more accurate model is required. Here, we study the properties of small-amplitude incompressible perturbations in both the low- and the high-frequency ranges in plasmas composed of several ionized species. We use a multi-fluid approach and take into account the effects of collisions between ions and the inclusion of Hall’s term in the induction equation. Through the analysis of the corresponding dispersion relations and numerical simulations, wemore » check that at high frequencies ions of different species are not as strongly coupled as in the low-frequency limit. Hence, they cannot be treated as a single fluid. In addition, elastic collisions between the distinct ionized species are not negligible for high-frequency waves, since an appreciable damping is obtained. Furthermore, Coulomb collisions between ions remove the cyclotron resonances and the strict cutoff regions, which are present when collisions are not taken into account. The implications of these results for the modeling of high-frequency waves in solar plasmas are discussed.« less

3D MHD Modeling of Prominence Formation by Plasma Evaporation and Condensation

NASA Astrophysics Data System (ADS)

Torok, T.; Lionello, R.; Mikic, Z.; Downs, C.; Titov, V. S.

2017-12-01

The formation of prominence material in the solar corona still belongs to the open questions of solar physics. There exists a consensus that prominence plasma has to be of chromospheric origin, but the mechanisms by which it accumulates in the corona are still not well understood. The presently most accepted scenario invokes the evaporation of chromospheric plasma via foot point heating and its subsequent condensation in the corona via thermal instabilities. This scenario has been successfully modeled in 1D hydrodynamic simulations along single field lines of a static magnetic field, but a more appropriate, fully 3D treatment of the thermodynamics in time-dependent magnetic fields was started just very recently by Xia et al. Our group at PSI has recently begun to engage in this challenging task as well, using our time-dependent, fully 3D thermodynamic MHD code MAS. For our investigation we consider two different coronal flux-rope configurations, using the analytical model by Titov and Démoulin and a model in which an elongated flux rope is constructed by photospheric flows. We investigate the plasma behavior for both configurations, using heating models of different complexity, and accompany our analysis by 1D loop simulations performed along selected field lines. In this presentation, we outline our modeling approach and discuss the results obtained so far.

Attempts to Simulate Anisotropies of Solar Wind Fluctuations Using MHD with a Turning Magnetic Field

NASA Technical Reports Server (NTRS)

Ghosh, Sanjoy; Roberts, D. Aaron

2010-01-01

We examine a "two-component" model of the solar wind to see if any of the observed anisotropies of the fields can be explained in light of the need for various quantities, such as the magnetic minimum variance direction, to turn along with the Parker spiral. Previous results used a 3-D MHD spectral code to show that neither Q2D nor slab-wave components will turn their wave vectors in a turning Parker-like field, and that nonlinear interactions between the components are required to reproduce observations. In these new simulations we use higher resolution in both decaying and driven cases, and with and without a turning background field, to see what, if any, conditions lead to variance anisotropies similar to observations. We focus especially on the middle spectral range, and not the energy-containing scales, of the simulation for comparison with the solar wind. Preliminary results have shown that it is very difficult to produce the required variances with a turbulent cascade.

MHD effects and heat transfer for the UCM fluid along with Joule heating and thermal radiation using Cattaneo-Christov heat flux model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shah, S., E-mail: sajidshah313@yahoo.com; Hussain, S.; Sagheer, M.

2016-08-15

Present study examines the numerical analysis of MHD flow of Maxwell fluid with thermal radiation and Joule heating by considering the recently developed Cattaneo-Christov heat flux model which explains the time relaxation characteristics for the heat flux. The objective is to analyze the governing parameters such as viscoelastic fluid parameter, Magnetic parameter, Eckert and Prandtl number’s impact on the velocity and temperature profiles through graphs and tables. Suitable similarity transformations have been used to reduce the formulated PDEs into a system of coupled non-linear ODEs. Shooting technique has been invoked for finding the numerical solutions of the dimensionless velocity andmore » temperature profiles. Additionally, the MATLAB built-in routine bvp4c has also been used to verify and strengthen the results obtained by shooting method. From some special cases of the present work, a comparison with the previously published results has been presented.« less

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

NASA Astrophysics Data System (ADS)

Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.

2016-06-01

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite-Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

MHD Calculation of halo currents and vessel forces in NSTX VDEs

NASA Astrophysics Data System (ADS)

Breslau, J. A.; Strauss, H. R.; Paccagnella, R.

2012-10-01

Research tokamaks such as ITER must be designed to tolerate a limited number of disruptions without sustaining significant damage. It is therefore vital to have numerical tools that can accurately predict the effects of these events. The 3D nonlinear extended MHD code M3D [1] can be used to simulate disruptions and calculate the associated wall currents and forces. It has now been validated against halo current data from NSTX experiments in which vertical displacement events (VDEs) were deliberately induced by turning off vertical feedback control. The results of high-resolution numerical simulations at realistic Lundquist numbers show reasonable agreement with the data, supporting a model in which the most dangerously asymmetric currents and heat loads, and the largest horizontal forces, arise in situations where a fast-growing ideal 2,1 external kink mode is destabilized by the scraping-off of flux surfaces with safety factor q>2 during the course of the VDE. [4pt] [1] W. Park, et al., Phys. Plasmas 6 (1999) 1796.

MHD Effect on Unsteady Mixed Convection Boundary Layer Flow past a Circular Cylinder with Constant Wall Temperature

NASA Astrophysics Data System (ADS)

Ismail, M. A.; Mohamad, N. F.; Ilias, M. R.; Shafie, S.

2017-09-01

Magnetohydrodynamic (MHD) effect is a study on motion of electrical-conducting fluid under magnetic fields. This effect has great intention due to its applications such as design of heat exchanger and nuclear reactor. In the problem in fluid motion, flow of separation can reduced the effectiveness of the system as well as can increased the energy lost. This study will present the results on reducing the flow separation by considering magnetic effect. In this study, unsteady mixed convection boundary layer flow past a circular cylinder is given attention. Focus of study is on the separation times that affected by the magnetic fields. The mathematical models in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effect of magnetic parameter on velocity and temperature profiles as well as skin friction and Nusselt number are studied.

Computational manipulation of a radiative MHD flow with Hall current and chemical reaction in the presence of rotating fluid

NASA Astrophysics Data System (ADS)

Alias Suba, Subbu; Muthucumaraswamy, R.

2018-04-01

A numerical analysis of transient radiative MHD(MagnetoHydroDynamic) natural convective flow of a viscous, incompressible, electrically conducting and rotating fluid along a semi-infinite isothermal vertical plate is carried out taking into consideration Hall current, rotation and first order chemical reaction.The coupled non-linear partial differential equations are expressed in difference form using implicit finite difference scheme. The difference equations are then reduced to a system of linear algebraic equations with a tri-diagonal structure which is solved by Thomas Algorithm. The primary and secondary velocity profiles, temperature profile, concentration profile, skin friction, Nusselt number and Sherwood Number are depicted graphically for a range of values of rotation parameter, Hall parameter,magnetic parameter, chemical reaction parameter, radiation parameter, Prandtl number and Schmidt number.It is recognized that rate of heat transfer and rate of mass transfer decrease with increase in time but they increase with increasing values of radiation parameter and Schmidt number respectively.

Solar maximum mission: Ground support programs at the Harvard Radio Astronomy Station

NASA Technical Reports Server (NTRS)

Maxwell, A.

1983-01-01

Observations of the spectral characteristics of solar radio bursts were made with new dynamic spectrum analyzers of high sensitivity and high reliability, over the frequency range 25-580 MHz. The observations also covered the maximum period of the current solar cycle and the period of international cooperative programs designated as the Solar Maximum Year. Radio data on shock waves generated by solar flares were combined with optical data on coronal transients, taken with equipment on the SMM and other satellites, and then incorporated into computer models for the outward passage of fast-mode MHD shocks through the solar corona. The MHD models are non-linear, time-dependent and for the most recent models, quasi-three-dimensional. They examine the global response of the corona for different types of input pulses (thermal, magnetic, etc.) and for different magnetic topologies (for example, open and closed fields). Data on coronal shocks and high-velocity material ejected from solar flares have been interpreted in terms of a model consisting of three main velocity regimes.

3D-MHD Simulations of the Madison Dynamo Experiment

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Forest, C. B.; Wright, J. C.; O'Connell, R.

2003-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations are used to predict behavior of the experiment. The code solves the self-consistent full evolution of the magnetic and velocity fields. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James [Proc. R. Soc. Lond. A 425. 407-429 (1989)]. Initial results indicate that saturation of the magnetic field occurs so that the resulting perturbed backreaction of the induced magnetic field changes the velocity field such that it would no longer be linearly unstable, suggesting non-linear terms are necessary for explaining the resulting state. Saturation and self-excitation depend in detail upon the magnetic Prandtl number.

A revised model for Jeffrey nanofluid subject to convective condition and heat generation/absorption

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here magnetohydrodynamic (MHD) boundary layer flow of Jeffrey nanofluid by a nonlinear stretching surface is addressed. Heat generation/absorption and convective surface condition effects are considered. Novel features of Brownian motion and thermophoresis are present. A non-uniform applied magnetic field is employed. Boundary layer and small magnetic Reynolds number assumptions are employed in the formulation. A newly developed condition with zero nanoparticles mass flux is imposed. The resulting nonlinear systems are solved. Convergence domains are explicitly identified. Graphs are analyzed for the outcome of sundry variables. Further local Nusselt number is computed and discussed. It is observed that the effects of Hartman number on the temperature and concentration distributions are qualitatively similar. Both temperature and concentration distributions are enhanced for larger Hartman number. PMID:28231298

Cross diffusion effect on MHD mixed convection flow of nonlinear radiative heat and mass transfer of Casson fluid over a vertical plate

NASA Astrophysics Data System (ADS)

Ganesh Kumar, K.; Archana, M.; Gireesha, B. J.; Krishanamurthy, M. R.; Rudraswamy, N. G.

2018-03-01

A study on magnetohydrodynamic mixed convection flow of Casson fluid over a vertical plate has been modelled in the presence of Cross diffusion effect and nonlinear thermal radiation. The governing partial differential equations are remodelled into ordinary differential equations by using similarity transformation. The accompanied differential equations are resolved numerically by using Runge-Kutta-Fehlberg forth-fifth order along with shooting method (RKF45 Method). The results of various physical parameters on velocity and temperature profiles are given diagrammatically. The numerical values of the local skin friction coefficient, local Nusselt number and local Sherwood number also are shown in a tabular form. It is found that, effect of Dufour and Soret parameter increases the temperature and concentration component correspondingly.

Integrating Multiple Approaches to Solving Solar Wind Turbulence Problems (Invited)

NASA Astrophysics Data System (ADS)

Karimabadi, H.; Roytershteyn, V.

2013-12-01

The ultimate understanding of the solar wind turbulence must explain the physical process and their connection at all scales ranging from the largest down to electron kinetic scales. This is a daunting task and as a result a more piecemeal approach to the problem has been followed. For example, the role of each wave has been explored in isolation and in simulations with scales limited to those of the underlying waves. In this talk, we present several issues with this approach and offer an alternative with an eye towards more realistic simulations of solar wind turbulence. The main simulation techniques used have been MHD, Hall MHD, hybrid, fully kinetic, and gyrokinetic. We examine the limitations of each approach and their viability for studies of solar wind turbulence. Finally, the effect of initial conditions on the resulting turbulence and their comparison with solar wind are demonstrated through several kinetic simulations.

The distinguishing signature of magnetic Penrose process

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Tursunov, Arman; Ahmedov, Bobomurat; Stuchlík, Zdeněk

2018-07-01

In this Letter, we wish to point out that the distinguishing feature of magnetic Penrose process (MPP) is its super high-efficiency exceeding 100 per cent (which was established in mid 1980s for discrete particle accretion) of extraction of rotational energy of a rotating black hole electromagnetically for a magnetic field of milli Gauss order. Another similar process, which is also driven by the electromagnetic field, is Blandford-Znajek mechanism (BZ) that could be envisaged as high magnetic field limit MPP as it requires threshold magnetic field of order 104 G. Recent simulation studies of fully relativistic magnetohydrodynamic (MHD) flows have borne out super high-efficiency signature of the process for high magnetic field regime; viz BZ. We would like to make a clear prediction that similar simulation studies of MHD flows for low magnetic field regime, where BZ would be inoperative, would also have superefficiency.

MHD simulation of relaxation transition to a flipped relaxed state in spherical torus

NASA Astrophysics Data System (ADS)

Kanki, Takashi; Nagata, Masayoshi; Kagei, Yasuhiro

2008-11-01

Recently, it has been demonstrated in the HIST device that in spite of the violation of the Kruskal-Shafranov stability condition, a normal spherical torus (ST) plasma has relaxed to a flipped ST state through a transient reversed-field pinch-like state when the vacuum toroidal field is decreased and its direction is reversed [1]. It has been also observed during this relaxation transition process that not only the toroidal field but also the poloidal field reverses polarity spontaneously and that the ion flow velocity is strongly fluctuated and abruptly increased up to > 50 km/s. The purpose of the present study is to investigate the plasma flows and the relevant MHD relaxation phenomena to elucidate this transition mechanism by using three-dimensional MHD simulations [2]. It is found from the numerical results that the magnetic reconnection between the open and closed field lines occurs due to the non-linear growth of the n=1 kink instability of the central open flux, generating the toroidal flow ˜ 60 km/s in the direction of the toroidal current. The n=1 kink instability and the plasma flows driven by the magnetic reconnection are consider to be responsible for the self-reversal of the magnetic fields. [1] M. Nagata el al., Phys. Rev. Lett. 90, 225001 (2003). [2] Y. Kagei el al., Plasma. Phys. Control. Fusion 45, L17 (2003).

Observation of finite-. beta. MHD phenomena in tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGuire, K.M.

1984-09-01

Stable high-beta plasmas are required for the tokamak to attain an economical fusion reactor. Recently, intense neutral beam heating experiments in tokamaks have shown new effects on plasma stability and confinement associated with high beta plasmas. The observed spectrum of MHD fluctuations at high beta is clearly dominated by the n = 1 mode when the q = 1 surface is in the plasma. The m/n = 1/1 mode drives other n = 1 modes through toroidal coupling and n > 1 modes through nonlinear coupling. On PDX, with near perpendicular injection, a resonant interaction between the n = 1more » internal kink and the trapped fast ions results in loss of beam particles and heating power. Key parameters in the theory are the value of q/sub 0/ and the injection angle. High frequency broadband magnetic fluctuations have been observed on ISX-B and D-III and a correlation with the deterioration of plasma confinement was reported. During enhanced confinement (H-mode) discharges in divertor plasmas, two new edge instabilities were observed, both localized radially near the separatrix. By assembling results from the different tokamak experiments, it is found that the simple theoretical ideal MHD beta limit has not been exceeded. Whether this represents an ultimate tokamak limit or if beta optimized configurations (Dee- or bean-shaped plasmas) can exceed this limit and perhaps enter a second regime of stability remains to be clarified.« less

A quantitative, comprehensive analytical model for ``fast'' magnetic reconnection in Hall MHD

NASA Astrophysics Data System (ADS)

Simakov, Andrei N.

2008-11-01

Magnetic reconnection in nature usually happens on fast (e.g. dissipation independent) time scales. While such scales have been observed computationally [1], a fundamental analytical model capable of explaining them has been lacking. Here, we propose such a quantitative model for 2D Hall MHD reconnection without a guide field. The model recovers the Sweet-Parker and the electron MHD [2] results in the appropriate limits of the ion inertial length, di, and is valid everywhere in between [3]. The model predicts the dissipation region aspect ratio and the reconnection rate Ez in terms of dissipation and inertial parameters, and has been found to be in excellent agreement with non-linear simulations. It confirms a number of long-standing empirical results and resolves several controversies. In particular, we find that both open X-point and elongated dissipation regions allow ``fast'' reconnection and that Ez depends on di. Moreover, when applied to electron-positron plasmas, the model demonstrates that fast dispersive waves are not instrumental for ``fast'' reconnection [4]. [1] J. Birn et al., J. Geophys. Res. 106, 3715 (2001). [2] L. Chac'on, A. N. Simakov, and A. Zocco, Phys. Rev. Lett. 99, 235001 (2007). [3] A. N. Simakov and L. Chac'on, submitted to Phys. Rev. Lett. [4] L. Chac'on, A. N. Simakov, V. Lukin, and A. Zocco, Phys. Rev. Lett. 101, 025003 (2008).

Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation

NASA Astrophysics Data System (ADS)

Hayat, T.; Muhammad, Taseer; Alsaedi, A.; Alhuthali, M. S.

2015-07-01

Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect.

Impact of generalized Fourier's and Fick's laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions

NASA Astrophysics Data System (ADS)

Ramzan, M.; Bilal, M.; Chung, Jae Dong; Lu, Dian Chen; Farooq, Umer

2017-09-01

A mathematical model has been established to study the magnetohydrodynamic second grade nanofluid flow past a bidirectional stretched surface. The flow is induced by Cattaneo-Christov thermal and concentration diffusion fluxes. Novel characteristics of Brownian motion and thermophoresis are accompanied by temperature dependent thermal conductivity and convective heat and mass boundary conditions. Apposite transformations are betrothed to transform a system of nonlinear partial differential equations to nonlinear ordinary differential equations. Analytic solutions of the obtained nonlinear system are obtained via a convergent method. Graphs are plotted to examine how velocity, temperature, and concentration distributions are affected by varied physical involved parameters. Effects of skin friction coefficients along the x- and y-direction versus various parameters are also shown through graphs and are well debated. Our findings show that velocities along both the x and y axes exhibit a decreasing trend for the Hartmann number. Moreover, temperature and concentration distributions are decreasing functions of thermal and concentration relaxation parameters.

Calculation of continuum damping of Alfvén eigenmodes in tokamak and stellarator equilibria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bowden, G. W.; Hole, M. J.; Könies, A.

2015-09-15

In an ideal magnetohydrodynamic (MHD) plasma, shear Alfvén eigenmodes may experience dissipationless damping due to resonant interaction with the shear Alfvén continuum. This continuum damping can make a significant contribution to the overall growth/decay rate of shear Alfvén eigenmodes, with consequent implications for fast ion transport. One method for calculating continuum damping is to solve the MHD eigenvalue problem over a suitable contour in the complex plane, thereby satisfying the causality condition. Such an approach can be implemented in three-dimensional ideal MHD codes which use the Galerkin method. Analytic functions can be fitted to numerical data for equilibrium quantities inmore » order to determine the value of these quantities along the complex contour. This approach requires less resolution than the established technique of calculating damping as resistivity vanishes and is thus more computationally efficient. The complex contour method has been applied to the three-dimensional finite element ideal MHD Code for Kinetic Alfvén waves. In this paper, we discuss the application of the complex contour technique to calculate the continuum damping of global modes in tokamak as well as torsatron, W7-X and H-1NF stellarator cases. To the authors' knowledge, these stellarator calculations represent the first calculation of continuum damping for eigenmodes in fully three-dimensional equilibria. The continuum damping of global modes in W7-X and H-1NF stellarator configurations investigated is found to depend sensitively on coupling to numerous poloidal and toroidal harmonics.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrés, Nahuel, E-mail: nandres@iafe.uba.ar; Gómez, Daniel; Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, 1428 Buenos Aires

We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure, and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length λ{sub i} and the electron inertial length λ{sub e}, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dimensions. We have been able to reproduce different scaling laws in differentmore » spectral ranges, as it has been observed in the solar wind for the magnetic energy spectrum. At the smallest wavenumbers where plain MHD is valid, we obtain an inertial range following a Kolmogorov k{sup −5∕3} law. For intermediate wavenumbers such that λ{sub i}{sup −1}≪k≪λ{sub e}{sup −1}, the spectrum is modified to a k{sup −7∕3} power-law, as has also been obtained for Hall-MHD neglecting electron inertia terms. When electron inertia is retained, a new spectral region given by k>λ{sub e}{sup −1} arises. The power spectrum for magnetic energy in this region is given by a k{sup −11∕3} power law. Finally, when the terms of electron inertia are retained, we study the self-consistent electric field. Our results are discussed and compared with those obtained in the solar wind observations and previous simulations.« less

Analytical and computational investigations of a magnetohydrodynamics (MHD) energy-bypass system for supersonic gas turbine engines to enable hypersonic flight

NASA Astrophysics Data System (ADS)

Benyo, Theresa Louise

Historically, the National Aeronautics and Space Administration (NASA) has used rocket-powered vehicles as launch vehicles for access to space. A familiar example is the Space Shuttle launch system. These vehicles carry both fuel and oxidizer onboard. If an external oxidizer (such as the Earth's atmosphere) is utilized, the need to carry an onboard oxidizer is eliminated, and future launch vehicles could carry a larger payload into orbit at a fraction of the total fuel expenditure. For this reason, NASA is currently researching the use of air-breathing engines to power the first stage of two-stage-to-orbit hypersonic launch systems. Removing the need to carry an onboard oxidizer leads also to reductions in total vehicle weight at liftoff. This in turn reduces the total mass of propellant required, and thus decreases the cost of carrying a specific payload into orbit or beyond. However, achieving hypersonic flight with air-breathing jet engines has several technical challenges. These challenges, such as the mode transition from supersonic to hypersonic engine operation, are under study in NASA's Fundamental Aeronautics Program. One propulsion concept that is being explored is a magnetohydrodynamic (MHD) energy- bypass generator coupled with an off-the-shelf turbojet/turbofan. It is anticipated that this engine will be capable of operation from takeoff to Mach 7 in a single flowpath without mode transition. The MHD energy bypass consists of an MHD generator placed directly upstream of the engine, and converts a portion of the enthalpy of the inlet flow through the engine into electrical current. This reduction in flow enthalpy corresponds to a reduced Mach number at the turbojet inlet so that the engine stays within its design constraints. Furthermore, the generated electrical current may then be used to power aircraft systems or an MHD accelerator positioned downstream of the turbojet. The MHD accelerator operates in reverse of the MHD generator, re-accelerating the exhaust flow from the engine by converting electrical current back into flow enthalpy to increase thrust. Though there has been considerable research into the use of MHD generators to produce electricity for industrial power plants, interest in the technology for flight-weight aerospace applications has developed only recently. In this research, electromagnetic fields coupled with weakly ionzed gases to slow hypersonic airflow were investigated within the confines of an MHD energy-bypass system with the goal of showing that it is possible for an air-breathing engine to transition from takeoff to Mach 7 without carrying a rocket propulsion system along with it. The MHD energy-bypass system was modeled for use on a supersonic turbojet engine. The model included all components envisioned for an MHD energy-bypass system; two preionizers, an MHD generator, and an MHD accelerator. A thermodynamic cycle analysis of the hypothesized MHD energy-bypass system on an existing supersonic turbojet engine was completed. In addition, a detailed thermodynamic, plasmadynamic, and electromagnetic analysis was combined to offer a single, comprehensive model to describe more fully the proper plasma flows and magnetic fields required for successful operation of the MHD energy bypass system. The unique contribution of this research involved modeling the current density, temperature, velocity, pressure, electric field, Hall parameter, and electrical power throughout an annular MHD generator and an annular MHD accelerator taking into account an external magnetic field within a moving flow field, collisions of electrons with neutral particles in an ionized flow field, and collisions of ions with neutral particles in an ionized flow field (ion slip). In previous research, the ion slip term has not been considered. The MHD energy-bypass system model showed that it is possible to expand the operating range of a supersonic jet engine from a maximum of Mach 3.5 to a maximum of Mach 7. The inclusion of ion slip within the analysis further showed that it is possible to 'drive' this system with maximum magnetic fields of 3 T and with maximum conductivity levels of 11 mhos/m. These operating parameters better the previous findings of 5 T and 10 mhos/m, and reveal that taking into account collisions between ions and neutral particles within a weakly ionized flow provides a more realistic model with added benefits of lower magnetic fields and conductivity levels especially at the higher Mach numbers. (Abstract shortened by UMI.).

Magnetosphere Modeling: From Cartoons to Simulations

NASA Astrophysics Data System (ADS)

Gombosi, T. I.

2017-12-01

Over the last half a century physics-based global computer simulations became a bridge between experiment and basic theory and now it represents the "third pillar" of geospace research. Today, many of our scientific publications utilize large-scale simulations to interpret observations, test new ideas, plan campaigns, or design new instruments. Realistic simulations of the complex Sun-Earth system have been made possible by the dramatically increased power of both computing hardware and numerical algorithms. Early magnetosphere models were based on simple E&M concepts (like the Chapman-Ferraro cavity) and hydrodynamic analogies (bow shock). At the beginning of the space age current system models were developed culminating in the sophisticated Tsyganenko-type description of the magnetic configuration. The first 3D MHD simulations of the magnetosphere were published in the early 1980s. A decade later there were several competing global models that were able to reproduce many fundamental properties of the magnetosphere. The leading models included the impact of the ionosphere by using a height-integrated electric potential description. Dynamic coupling of global and regional models started in the early 2000s by integrating a ring current and a global magnetosphere model. It has been recognized for quite some time that plasma kinetic effects play an important role. Presently, global hybrid simulations of the dynamic magnetosphere are expected to be possible on exascale supercomputers, while fully kinetic simulations with realistic mass ratios are still decades away. In the 2010s several groups started to experiment with PIC simulations embedded in large-scale 3D MHD models. Presently this integrated MHD-PIC approach is at the forefront of magnetosphere simulations and this technique is expected to lead to some important advances in our understanding of magnetosheric physics. This talk will review the evolution of magnetosphere modeling from cartoons to current systems, to global MHD to MHD-PIC and discuss the role of state-of-the-art models in forecasting space weather.

Simulations of Magnetohydrodynamic Waves Driven by Photospheric Motions

NASA Astrophysics Data System (ADS)

Mumford, Stuart

2016-04-01

This thesis investigates the properties of various modelled photospheric motions as generation mechanisms for magnetohydrodynamic (MHD) waves in the low solar atmosphere. The solar atmosphere is heated to million-degree temperatures, yet there is no fully understood heating mechanism which can provide the ≈ 300 W/m^2) required to keep the quiet corona at its observed temperatures. MHD waves are one mechanism by which this energy could be provided to the upper solar atmosphere, however, these waves need to be excited. The excitation of these waves, in or below the photosphere is a complex interaction between the plasma and the magnetic field embedded within it. This thesis studies a model of a small-scale magnetic flux tube based upon a magnetic bright point (MBP). These features are very common in the photosphere and have been observed to be affected by the plasma motions. The modelled flux tube has a foot point magnetic field strength of 120 mT and a FWHM of 90 km, and is embedded in a realistic, stratified solar atmosphere based upon the VALIIIc model. To better understand the excitation of MHD waves in this type of magnetic structures, a selection of velocity profiles are implemented to excite waves. Initially a study of five different driving profiles was performed. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers which mimic observed torsional motions in the solar photosphere, along with vertical and horizontal drivers to mimic different motions caused by convection in the photosphere. The results are then analysed using a novel method for extracting the parallel, perpendicular and azimuthal components of the perturbations, which caters to both the linear and non-linear cases. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated, to enable the quantification of the relative strengths of excited modes. The torsional drivers primarily excite Alfvén modes (≈ 60 %) of the total flux) with contributions from the slow mode. The horizontal and vertical drivers primarily excite slow and fast modes respectively, with small variations dependent upon flux surface radius. This analysis is then applied to more in depth studies of the logarithmic spiral driver. Firstly, five different values for the (B_L) spiral expansion factor are chosen which control how rapidly the spiral expands. Larger values of (B_L) make the driving profile more radial. The results of this analysis show that the Alfvén wave is the dominant wave for lower values of the expansion factor, whereas, for the higher values the parallel component is dominant. This transition occurs within the range of the observational constraints, demonstrating that under realistic conditions spiral drivers may not excite most of their wave flux in the Alfvén mode. Finally, the logarithmic spiral is further studied, but with a variety of different periods. Ten periods from 30 to 300 seconds are chosen, and the simulations are again analysed using the flux surface method employed previously. The results of this study are minimal variation in the percentage wave flux in each mode, with no more than 20 % variation in any mode for any flux surface studied. Within this small variation, some non-linear changes in the wave flux were observed, especially around the more important small periods. Due to the short life time of the MBPs it is thought the short period waves would have more effect and therefore this non-linear variation in wave flux could have some impact on the modes present in the solar atmosphere.

MHD Turbulence and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Equilibrium and initial linear stability analysis of liquid metal falling film flows in a varying spanwise magnetic field

NASA Astrophysics Data System (ADS)

Gao, D.; Morley, N. B.

2002-12-01

A 2D model for MHD free surface flow in a spanwise field is developed. The model, designed to simulate film flows of liquid metals in future thermo­nuclear fusion reactors, considers an applied spanwise magnetic field with spatial and temporal variation and an applied streamwise external current. A special case - a thin falling film flow in spanwise magnetic field with constant gradient and constant applied external streamwise current, is here investigated in depth to gain insight into the behavior of the MHD film flow. The fully developed flow solution is derived and initial linear stability analysis is performed for this special case. It is seen that the velocity profile is significantly changed due to the presence of the MHD effect, resulting in the free surface analog of the classic M-shape velocity profile seen in developing pipe flows in a field gradient. The field gradient is also seen to destabilize the film flow under most conditions. The effect of external current depends on the relative direction of the field gradient to the current direction. By controlling the magnitude of an external current, it is possible to obtain a linearly stable falling film under these magnetic field conditions. Tables 1, Figs 12, Refs 20.

Constrained-transport Magnetohydrodynamics with Adaptive Mesh Refinement in CHARM

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Martin, Daniel F.

2011-07-01

We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

NASA Technical Reports Server (NTRS)

Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.

1995-01-01

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Impact of the plasma response in three-dimensional edge plasma transport modelling for RMP ELM control scenarios at ITER

NASA Astrophysics Data System (ADS)

Schmitz, Oliver

2014-10-01

The constrains used in magneto-hydrodynamic (MHD) modeling of the plasma response to external resonant magnetic perturbation (RMP) fields have a profound impact on the three-dimensional (3-D) shape of the plasma boundary induced by RMP fields. In this contribution, the consequences of the plasma response on the actual 3D boundary structure and transport during RMP application at ITER are investigated. The 3D fluid plasma and kinetic neutral transport code EMC3-Eirene is used for edge transport modeling. Plasma response modeling is conducted with the M3D-C1 code using a single fluid, non-linear and a two fluid, linear MHD constrain. These approaches are compared to results with an ideal MHD like plasma response. A 3D plasma boundary is formed for all cases consisting of magnetic finger structures at the X-point intersecting the divertor surface in a helical footprint pattern. The width of the helical footprint pattern is largely reduced compared to vacuum magnetic fields when using the ideal MHD like screening model. This yields increasing peak heat fluxes in contrast to a beneficial heat flux spreading seen with vacuum fields. The particle pump out as well as loss of thermal energy is reduced by a factor of two compared to vacuum fields. In contrast, the impact of the plasma response obtained from both MHD constrains in M3D-C1 is nearly negligible at the plasma boundary and only a small modification of the magnetic footprint topology is detected. Accordingly, heat and particle fluxes on the target plates as well as the edge transport characteristics are comparable to the vacuum solution. This span of modeling results with different plasma response models highlights the importance of thoroughly validating both, plasma response and 3D edge transport models for a robust extrapolation towards ITER. Supported by ITER Grant IO/CT/11/4300000497 and F4E Grant GRT-055 (PMS-PE) and by Start-Up Funds of the University of Wisconsin - Madison.

Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Dumbser, Michael

2015-10-01

Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on unstructured meshes. Several stringent two- and three-dimensional problems are shown to work well with the methods presented here.

Hybrid simulation of fishbone instabilities in the EAST tokamak

DOE PAGES

Shen, Wei; Wang, Feng; Fu, G. Y.; ...

2017-08-11

Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. Our results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvenmore » eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. Furthermore, for the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.« less

Nonlinear fishbone dynamics in spherical tokamaks

DOE Data Explorer

Wang, Feng [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Dalian Univ Technol, Sch Phys & Optoelect Technol, Minist Educ, Key Lab Mat Modificat Laser Ion & Electron Beams, Dalian 116024, Peoples R China.; Fu, G.Y. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Institute for Fusion Theory and Simulation and Department of Physics Hangzhou, Zhejiang University, Hangzhou, 310027, People's Republic of China; Shen, Wei [Institute of Plasma Physics, Chinese Academy of Science, Hefei 230031, People's Republic of China

2017-01-01

Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. The results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturates due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. A substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.

Nonlinear fishbone dynamics in spherical tokamaks

DOE PAGES

Wang, Feng; Fu, G. Y.; Shen, Wei

2016-11-22

Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. Our results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturatesmore » due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. Furthermore, a substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Finally, our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.« less

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Zhang, Kai

2018-06-01

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Axion as a Cold Dark Matter Candidate: Proof to Fully Nonlinear Order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Hyerim; Hwang, Jai-chan; Park, Chan-Gyung

2017-09-01

We present proof of the axion as a cold dark matter (CDM) candidate to the fully nonlinear order perturbations based on Einstein’s gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for ignoring the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein’s gravity. We show that the axion has the characteristic pressure and anisotropic stress; the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as themore » effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale that is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the CDM nature of such an axion in that scale.« less

Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems

NASA Astrophysics Data System (ADS)

Katzourakis, Nikos

2017-07-01

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to PDEs and is not based on either integration by parts or on the maximum principle. Instead, our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the Young measures over a toric compactification of the space of jets. After developing some basic theory, as a first application we consider the Dirichlet problem and we prove existence-uniqueness-partial regularity of solutions to fully nonlinear degenerate elliptic 2nd order systems and also existence of solutions to the ∞-Laplace system of vectorial Calculus of Variations in L∞.

Nonlinear electromagnetic gyrokinetic particle simulations with the electron hybrid model

NASA Astrophysics Data System (ADS)

Nishimura, Y.; Lin, Z.; Chen, L.; Hahm, T.; Wang, W.; Lee, W.

2006-10-01

The electromagnetic model with fluid electrons is successfully implemented into the global gyrokinetic code GTC. In the ideal MHD limit, shear Alfven wave oscillation and continuum damping is demonstrated. Nonlinear electromagnetic simulation is further pursued in the presence of finite ηi. Turbulence transport in the AITG unstable β regime is studied. This work is supported by Department of Energy (DOE) Grant DE-FG02-03ER54724, Cooperative Agreement No. DE-FC02-04ER54796 (UCI), DOE Contract No. DE-AC02-76CH03073 (PPPL), and in part by SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas. Z. Lin, et al., Science 281, 1835 (1998). F. Zonca and L. Chen, Plasma Phys. Controlled Fusion 30, 2240 (1998); G. Zhao and L. Chen, Phys. Plasmas 9, 861 (2002).

Casting the Coronal Magnetic Field Reconstructions with Magnetic Field Constraints above the Photosphere in 3D Using MHD Bifrost Model

NASA Astrophysics Data System (ADS)

Fleishman, G. D.; Anfinogentov, S.; Loukitcheva, M.; Mysh'yakov, I.; Stupishin, A.

2017-12-01

Measuring and modeling coronal magnetic field, especially above active regions (ARs), remains one of the central problems of solar physics given that the solar coronal magnetism is the key driver of all solar activity. Nowadays the coronal magnetic field is often modelled using methods of nonlinear force-free field reconstruction, whose accuracy has not yet been comprehensively assessed. Given that the coronal magnetic probing is routinely unavailable, only morphological tests have been applied to evaluate performance of the reconstruction methods and a few direct tests using available semi-analytical force-free field solution. Here we report a detailed casting of various tools used for the nonlinear force-free field reconstruction, such as disambiguation methods, photospheric field preprocessing methods, and volume reconstruction methods in a 3D domain using a 3D snapshot of the publicly available full-fledged radiative MHD model. We take advantage of the fact that from the realistic MHD model we know the magnetic field vector distribution in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored magnetic field and the true magnetic field in the 3D model volume. Our tests show that the available disambiguation methods often fail at the quiet sun areas, where the magnetic structure is dominated by small-scale magnetic elements, while they work really well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective `elevation' of the magnetic field components. The effective `elevation' height turns out to be different for the longitudinal and transverse components of the magnetic field, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolation performed starting from actual AR photospheric magnetogram (i.e., without preprocessing) are free from this systematic error, while have other metrics either comparable or only marginally worse than those estimated for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing.

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Numerical simulation of MHD turbulence in three dimensions

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Roberts, D. A.; Deane, A.

1997-01-01

The evolution of Alfvenic turbulence in 3D spherical geometry can now be studied. In simulations, a fast stream is sandwiched between two slower streams. The inflow is both supersonic and superAlfvenic. Alfven waves entering the box are convected into the medium and interact nonlinearly with the velocity shear and with any structures (i.e., flux tubes) that might be present. These initial simulations suggest that velocity shear, even in spherical geometry, is able to drive a turbulent cascade which results in approximately Kolmogoroff-like power spectra.

Stable Spheromaks with Profile Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fowler, T K; Jayakumar, R

A spheromak equilibrium with zero edge current is shown to be stable to both ideal MHD and tearing modes that normally produce Taylor relaxation in gun-injected spheromaks. This stable equilibrium differs from the stable Taylor state in that the current density j falls to zero at the wall. Estimates indicate that this current profile could be sustained by non-inductive current drive at acceptable power levels. Stability is determined using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive could point the way to improved fusion reactors.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description

NASA Astrophysics Data System (ADS)

Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.

2017-09-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar convection by leading-order 2D Elsässer fluctuations, with critical balance being achieved when Alfvén wave sweeping balances passive scalar convection by leading-order 2D Elsässer fluctuations. Besides yielding predictions of 2D and slab spectra for Elsässer fluctuations, NI MHD shows that density fluctuations are advected by the majority or dominant incompressible velocity fluctuations. In the case of β ∼ 1 or ≪ 1, the density spectrum is Kolmogorov in the perpendicular wave number, thus providing a possible explanation for the observed extended Kolmogorov-like power law spectrum for electron density fluctuations in the interstellar medium.

Effects of including electrojet turbulence in LFM-RCM simulations of geospace storms

NASA Astrophysics Data System (ADS)

Oppenheim, M. M.; Wiltberger, M. J.; Merkin, V. G.; Zhang, B.; Toffoletto, F.; Wang, W.; Lyon, J.; Liu, J.; Dimant, Y. S.

2016-12-01

Global geospace system simulations need to incorporate nonlinear and small-scale physical processes in order to accurately model storms and other intense events. During times of strong magnetospheric disturbances, large-amplitude electric fields penetrate from the Earth's magnetosphere to the E-region ionosphere where they drive Farley-Buneman instabilities (FBI) that create small-scale plasma density turbulence. This induces nonlinear currents and leads to anomalous electron heating. Current global Magnetosphere-Ionosphere-Thermosphere (MIT) models disregard these effects by assuming simple laminar ionospheric currents. This paper discusses the effects of incorporating accurate turbulent conductivities into MIT models. Recently, we showed in Liu et al. (2016) that during storm-time, turbulence increases the electron temperatures and conductivities more than precipitation. In this talk, we present the effect of adding these effects to the combined Lyon-Fedder-Mobarry (LFM) global MHD magnetosphere simulator and the Rice Convection Model (RCM). The LFM combines a magnetohydrodynamic (MHD) simulation of the magnetosphere with a 2D electrostatic solution of the ionosphere. The RCM uses drift physics to accurately model the inner magnetosphere, including a storm enhanced ring current. The LFM and coupled LFM-RCM simulations have previously shown unrealistically high cross-polar-cap potentials during strong solar wind driving conditions. We have recently implemented an LFM module that modifies the ionospheric conductivity to account for FBI driven anomalous electron heating and non-linear cross-field current enhancements as a function of the predicted ionospheric electric field. We have also improved the LFM-RCM code by making it capable of handling dipole tilts and asymmetric ionospheric solutions. We have tested this new LFM version by simulating the March 17, 2013 geomagnetic storm. These simulations showed a significant reduction in the cross-polar-cap potential during the strongest driving conditions, significant increases in the ionospheric conductivity in the auroral oval, and better agreement with DMSP observations of sub-auroral polarization streams. We conclude that accurate MIT simulations of geospace storms require the inclusion of turbulent conductivities.

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

A Mass Tracking Formulation for Bubbles in Incompressible Flow

DTIC Science & Technology

2012-10-14

incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of...using the ideas from [19] to couple together incompressible flow with fully nonlinear compressible flow including shocks and rarefactions . The results...compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of simplifying assumptions on the air flow

Magnetic Topology of the Global MHD Configuration on 2010 August 1-2

NASA Astrophysics Data System (ADS)

Titov, V. S.; Mikic, Z.; Torok, T.; Linker, J.; Panasenco, O.

2014-12-01

It appears that the global magnetic topology of the solar corona predetermines to a large extent the magnetic flux transfer during solar eruptions. We have recently analyzed the global topology for a source-surface model of the background magnetic field at the time of the 2010 August 1-2 sympathetic CMEs (Titov et al. 2012). Now we extend this analysis to a more accurate thermodynamic MHD model of the solar corona. As for the source-surface model, we find a similar triplet of pseudo-streamers in the source regions of the eruptions. The new study confirms that all these pseudo-streamers contain separatrix curtains that fan out from a basic magnetic null point, individual for each of the pseudo-streamers. In combination with the associated separatrix domes, these separatrix curtains fully isolate adjacent coronal holes of the like polarity from each other. However, the size and shape of the coronal holes, as well as their open magnetic fluxes and the fluxes in the lobes of the separatrix domes, are very different for the two models. The definition of the open separator field lines, where the (interchange) reconnection between open and closed magnetic flux takes place, is also modified, since the structurally unstable source-surface null lines do not exist anymore in the MHD model. In spite of all these differences, we reassert our earlier hypothesis that magnetic reconnection at these nulls and the associated separators likely plays a key role in coupling the successive eruptions observed by SDO and STEREO. The results obtained provide further validation of our recent simplified MHD model of sympathetic eruptions (Török et al. 2011). Research supported by NASA's Heliophysics Theory and LWS Programs, and NSF/SHINE and NSF/FESD.

Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, Xue-Ning, E-mail: xbai@cfa.harvard.edu

2017-08-10

The gas dynamics of weakly ionized protoplanetary disks (PPDs) are largely governed by the coupling between gas and magnetic fields, described by three non-ideal magnetohydrodynamical (MHD) effects (Ohmic, Hall, ambipolar). Previous local simulations incorporating these processes have revealed that the inner regions of PPDs are largely laminar and accompanied by wind-driven accretion. We conduct 2D axisymmetric, fully global MHD simulations of these regions (∼1–20 au), taking into account all non-ideal MHD effects, with tabulated diffusion coefficients and approximate treatment of external ionization and heating. With the net vertical field aligned with disk rotation, the Hall-shear instability strongly amplifies horizontal magneticmore » field, making the overall dynamics dependent on initial field configuration. Following disk formation, the disk likely relaxes into an inner zone characterized by asymmetric field configuration across the midplane, which smoothly transitions to a more symmetric outer zone. Angular momentum transport is driven by both MHD winds and laminar Maxwell stress, with both accretion and decretion flows present at different heights, and modestly asymmetric winds from the two disk sides. With anti-aligned field polarity, weakly magnetized disks settle into an asymmetric field configuration with supersonic accretion flow concentrated at one side of the disk surface, and highly asymmetric winds between the two disk sides. In all cases, the wind is magneto-thermal in nature, characterized by a mass loss rate exceeding the accretion rate. More strongly magnetized disks give more symmetric field configuration and flow structures. Deeper far-UV penetration leads to stronger and less stable outflows. Implications for observations and planet formation are also discussed.« less

Integration of Extended MHD and Kinetic Effects in Global Magnetosphere Models

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Wang, L.; Maynard, K. R. M.; Raeder, J.; Bhattacharjee, A.

2015-12-01

Computational models of Earth's geospace environment are an important tool to investigate the science of the coupled solar-wind -- magnetosphere -- ionosphere system, complementing satellite and ground observations with a global perspective. They are also crucial in understanding and predicting space weather, in particular under extreme conditions. Traditionally, global models have employed the one-fluid MHD approximation, which captures large-scale dynamics quite well. However, in Earth's nearly collisionless plasma environment it breaks down on small scales, where ion and electron dynamics and kinetic effects become important, and greatly change the reconnection dynamics. A number of approaches have recently been taken to advance global modeling, e.g., including multiple ion species, adding Hall physics in a Generalized Ohm's Law, embedding local PIC simulations into a larger fluid domain and also some work on simulating the entire system with hybrid or fully kinetic models, the latter however being to computationally expensive to be run at realistic parameters. We will present an alternate approach, ie., a multi-fluid moment model that is derived rigorously from the Vlasov-Maxwell system. The advantage is that the computational cost remains managable, as we are still solving fluid equations. While the evolution equation for each moment is exact, it depends on the next higher-order moment, so that truncating the hiearchy and closing the system to capture the essential kinetic physics is crucial. We implement 5-moment (density, momentum, scalar pressure) and 10-moment (includes pressure tensor) versions of the model, and use local approximations for the heat flux to close the system. We test these closures by local simulations where we can compare directly to PIC / hybrid codes, and employ them in global simulations using the next-generation OpenGGCM to contrast them to MHD / Hall-MHD results and compare with observations.

Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind.

PubMed

Weck, P J; Schaffner, D A; Brown, M R; Wicks, R T

2015-02-01

The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different turbulent plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD), and fully developed turbulent magnetic fluctuations of the solar wind taken from the Wind spacecraft. The entropy and complexity values are presented as coordinates on the CH plane for comparison among the different plasma environments and other fluctuation models. The solar wind is found to have the highest permutation entropy and lowest statistical complexity of the three data sets analyzed. Both laboratory data sets have larger values of statistical complexity, suggesting that these systems have fewer degrees of freedom in their fluctuations, with SSX magnetic fluctuations having slightly less complexity than the LAPD edge I(sat). The CH plane coordinates are compared to the shape and distribution of a spectral decomposition of the wave forms. These results suggest that fully developed turbulence (solar wind) occupies the lower-right region of the CH plane, and that other plasma systems considered to be turbulent have less permutation entropy and more statistical complexity. This paper presents use of this statistical analysis tool on solar wind plasma, as well as on an MHD turbulent experimental plasma.

Intermittency, coherent structures and dissipation in plasma turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wan, M.; Matthaeus, W. H.; Parashar, T. N.

Collisionless dissipation in turbulent plasmas such as the solar wind and the solar corona has been an intensively studied subject recently, with new insights often emerging from numerical simulation. Here we report results from high resolution, fully kinetic simulations of plasma turbulence in both two (2D) and three (3D) dimensions, studying the relationship between intermittency and dissipation. The simulations show development of turbulent coherent structures, characterized by sheet-like current density structures spanning a range of scales. An approximate dissipation measure is employed, based on work done by the electromagnetic field in the local electron fluid frame. This surrogate dissipation measuremore » is highly concentrated in small subvolumes in both 2D and 3D simulations. Fully kinetic simulations are also compared with magnetohydrodynamics (MHD) simulations in terms of coherent structures and dissipation. The interesting result emerges that the conditional averages of dissipation measure scale very similarly with normalized current density J in 2D and 3D particle-in-cell and in MHD. To the extent that the surrogate dissipation measure is accurate, this result implies that on average dissipation scales as ∼J{sup 2} in turbulent kinetic plasma. Multifractal intermittency is seen in the inertial range in both 2D and 3D, but at scales ∼ion inertial length, the scaling is closer to monofractal.« less

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makwana, K. D., E-mail: kirit.makwana@gmx.com; Cattaneo, F.; Zhdankin, V.

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k{sub ⊥}{sup −1.3}. The kinetic code shows a spectral slope of k{submore » ⊥}{sup −1.5} for smaller simulation domain, and k{sub ⊥}{sup −1.3} for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.« less

Dynamics of Magnetopause Reconnection in Response to Variable Solar Wind Conditions

NASA Astrophysics Data System (ADS)

Berchem, J.; Richard, R. L.; Escoubet, C. P.; Pitout, F.

2017-12-01

Quantifying the dynamics of magnetopause reconnection in response to variable solar wind driving is essential to advancing our predictive understanding of the interaction of the solar wind/IMF with the magnetosphere. To this end we have carried out numerical studies that combine global magnetohydrodynamic (MHD) and Large-Scale Kinetic (LSK) simulations to identify and understand the effects of solar wind/IMF variations. The use of the low dissipation, high resolution UCLA MHD code incorporating a non-linear local resistivity allows the representation of the global configuration of the dayside magnetosphere while the use of LSK ion test particle codes with distributed particle detectors allows us to compare the simulation results with spacecraft observations such as ion dispersion signatures observed by the Cluster spacecraft. We present the results of simulations that focus on the impacts of relatively simple solar wind discontinuities on the magnetopause and examine how the recent history of the interaction of the magnetospheric boundary with solar wind discontinuities can modify the dynamics of magnetopause reconnection in response to the solar wind input.

Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Khan, Zafar Hayat; Khan, Waqar Ahmed

2014-09-01

This article is intended for investigating the effects of magnetohydrodynamics (MHD) and volume fraction of carbon nanotubes (CNTs) on the flow and heat transfer in two lateral directions over a stretching sheet. For this purpose, three types of base fluids specifically water, ethylene glycol and engine oil with single and multi-walled carbon nanotubes are used in the analysis. The convective boundary condition in the presence of CNTs is presented first time and not been explored so far. The transformed nonlinear differential equations are solved by the Runge-Kutta-Fehlberg method with a shooting technique. The dimensionless velocity and shear stress are obtained in both directions. The dimensionless heat transfer is determined on the surface. Three different models of thermal conductivity are comparable for both CNTs and it is found that the Xue [1] model gives the best approach to guess the superb thermal conductivity in comparison with the Maxwell [2] and Hamilton and Crosser [3] models. And finally, another finding suggests the engine oil provides the highest skin friction and heat transfer rates.

Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Nadeem, Sohail; Khan, Z. H.; Noor, N. F. M.

2015-01-01

In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT.

Heat and Mass Transfer Analysis of MHD Nanofluid Flow with Radiative Heat Effects in the Presence of Spherical Au-Metallic Nanoparticles

NASA Astrophysics Data System (ADS)

Qureshi, M. Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M.

2016-10-01

Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.

Heat and Mass Transfer Analysis of MHD Nanofluid Flow with Radiative Heat Effects in the Presence of Spherical Au-Metallic Nanoparticles.

PubMed

Qureshi, M Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M

2016-12-01

Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2017-04-01

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

Energy spectrum of tearing mode turbulence in sheared background field

NASA Astrophysics Data System (ADS)

Hu, Di; Bhattacharjee, Amitava; Huang, Yi-Min

2018-06-01

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes excites a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction on the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects. One is the existence of many linearly stable small-scale modes which cause an effective damping during the energy cascade. The other is the scale-independent anisotropy induced by the large-scale modes tilting the sheared background field, as opposed to the scale-dependent anisotropy frequently encountered in traditional critically balanced turbulence theories. Due to these two differences, the energy spectrum deviates from a simple power law and takes the form of a power law multiplied by an exponential falloff. Numerical simulations are carried out using visco-resistive MHD equations to verify our theoretical predictions, and a reasonable agreement is found between the numerical results and our model.

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Simulations of Solar Wind Turbulence

NASA Technical Reports Server (NTRS)

Goldstein, Melvyn L.; Usmanov, A. V.; Roberts, D. A.

2008-01-01

Recently we have restructured our approach to simulating magnetohydrodynamic (MHD) turbulence in the solar wind. Previously, we had defined a 'virtual' heliosphere that contained, for example, a tilted rotating current sheet, microstreams, quasi-two-dimensional fluctuations as well as Alfven waves. In this new version of the code, we use the global, time-stationary, WKB Alfven wave-driven solar wind model developed by Usmanov and described in Usmanov and Goldstein [2003] to define the initial state of the system. Consequently, current sheets, and fast and slow streams are computed self-consistently from an inner, photospheric, boundary. To this steady-state configuration, we add fluctuations close to, but above, the surface where the flow become super-Alfvenic. The time-dependent MHD equations are then solved using a semi-discrete third-order Central Weighted Essentially Non-Oscillatory (CWENO) numerical scheme. The computational domain now includes the entire sphere; the geometrical singularity at the poles is removed using the multiple grid approach described in Usmanov [1996]. Wave packets are introduced at the inner boundary such as to satisfy Faraday's Law [Yeh and Dryer, 1985] and their nonlinear evolution are followed in time.

Neoclassical tearing mode seeding by coupling with infernal modes in low-shear tokamaks

NASA Astrophysics Data System (ADS)

Kleiner, A.; Graves, J. P.; Brunetti, D.; Cooper, W. A.; Halpern, F. D.; Luciani, J.-F.; Lütjens, H.

2016-09-01

A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter {{Δ }\\prime} is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

On radiative heat transfer in stagnation point flow of MHD Carreau fluid over a stretched surface

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Mudassar Gulzar, M.

2018-03-01

This paper investigates the behavior of MHD stagnation point flow of Carreau fluid in the presence of infinite shear rate viscosity. Additionally heat transfer analysis in the existence of non-linear radiation with convective boundary condition is performed. Moreover effects of Joule heating is observed and mathematical analysis is presented in the presence of viscous dissipation. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The subsequent non-straight common ordinary differential equations are solved numerically by an effective numerical approach specifically Runge-Kutta Fehlberg method alongside shooting technique. It is found that the higher values of Hartmann number (M) correspond to thickening of the thermal and thinning of momentum boundary layer thickness. The analysis further reveals that the fluid velocity is diminished by increasing the viscosity ratio parameter (β∗) and opposite trend is observed for temperature profile for both hydrodynamic and hydromagnetic flows. In addition the momentum boundary layer thickness is increased with velocity ratio parameter (α) and opposite is true for thermal boundary layer thickness.

Statistical Mechanics of Turbulent Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Implosive Collapse about Magnetic Null Points: A Quantitative Comparison between 2D and 3D Nulls

NASA Astrophysics Data System (ADS)

Thurgood, Jonathan O.; Pontin, David I.; McLaughlin, James A.

2018-03-01

Null collapse is an implosive process whereby MHD waves focus their energy in the vicinity of a null point, forming a current sheet and initiating magnetic reconnection. We consider, for the first time, the case of collapsing 3D magnetic null points in nonlinear, resistive MHD using numerical simulation, exploring key physical aspects of the system as well as performing a detailed parameter study. We find that within a particular plane containing the 3D null, the plasma and current density enhancements resulting from the collapse are quantitatively and qualitatively as per the 2D case in both the linear and nonlinear collapse regimes. However, the scaling with resistivity of the 3D reconnection rate—which is a global quantity—is found to be less favorable when the magnetic null point is more rotationally symmetric, due to the action of increased magnetic back-pressure. Furthermore, we find that, with increasing ambient plasma pressure, the collapse can be throttled, as is the case for 2D nulls. We discuss this pressure-limiting in the context of fast reconnection in the solar atmosphere and suggest mechanisms by which it may be overcome. We also discuss the implications of the results in the context of null collapse as a trigger mechanism of Oscillatory Reconnection, a time-dependent reconnection mechanism, and also within the wider subject of wave–null point interactions. We conclude that, in general, increasingly rotationally asymmetric nulls will be more favorable in terms of magnetic energy release via null collapse than their more symmetric counterparts.

On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

NASA Astrophysics Data System (ADS)

Londrillo, P.; del Zanna, L.

2004-03-01

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the constrained transport (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures [∇.B]num=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here upwind constrained transport (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second-order Roe-type positive scheme by Liu and Lax [J. Comput. Fluid Dyn. 5 (1996) 133], and both the second- and third-order versions of a central-type MHD scheme presented by Londrillo and Del Zanna [Astrophys. J. 530 (2000) 508], where the basic UCT strategies have been first outlined.

Geospace simulations on the Cell BE processor

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Raeder, J.; Larson, D.

2008-12-01

OpenGGCM (Open Geospace General circulation Model) is an established numerical code that simulates the Earth's space environment. The most computing intensive part is the MHD (magnetohydrodynamics) solver that models the plasma surrounding Earth and its interaction with Earth's magnetic field and the solar wind flowing in from the sun. Like other global magnetosphere codes, OpenGGCM's realism is limited by computational constraints on grid resolution. We investigate porting of the MHD solver to the Cell BE architecture, a novel inhomogeneous multicore architecture capable of up to 230 GFlops per processor. Realizing this high performance on the Cell processor is a programming challenge, though. We implemented the MHD solver using a multi-level parallel approach: On the coarsest level, the problem is distributed to processors based upon the usual domain decomposition approach. Then, on each processor, the problem is divided into 3D columns, each of which is handled by the memory limited SPEs (synergistic processing elements) slice by slice. Finally, SIMD instructions are used to fully exploit the vector/SIMD FPUs in each SPE. Memory management needs to be handled explicitly by the code, using DMA to move data from main memory to the per-SPE local store and vice versa. We obtained excellent performance numbers, a speed-up of a factor of 25 compared to just using the main processor, while still keeping the numerical implementation details of the code maintainable.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thurgood, Jonathan O.; McLaughlin, James A.; Pontin, David I., E-mail: jonathan.thurgood@northumbria.ac.uk

Here we detail the dynamic evolution of localized reconnection regions about 3D magnetic null points using numerical simulation. We demonstrate for the first time that reconnection triggered by the localized collapse of a 3D null point that is due to an external magnetohydrodynamic (MHD) wave involves a self-generated oscillation, whereby the current sheet and outflow jets undergo a reconnection reversal process during which back-pressure formation at the jet heads acts to prise open the collapsed field before overshooting the equilibrium into an opposite-polarity configuration. The discovery that reconnection at fully 3D nulls can proceed naturally in a time-dependent and periodicmore » fashion suggests that oscillatory reconnection mechanisms may play a role in explaining periodicity in astrophysical phenomena associated with magnetic reconnection, such as the observed quasi-periodicity of solar and stellar flare emission. Furthermore, we find that a consequence of oscillatory reconnection is the generation of a plethora of freely propagating MHD waves that escape the vicinity of the reconnection region.« less

Shear-Flow Instability Saturation by Stable Modes: Hydrodynamics and Gyrokinetics

NASA Astrophysics Data System (ADS)

Fraser, Adrian; Pueschel, M. J.; Terry, P. W.; Zweibel, E. G.

2017-10-01

We present simulations of shear-driven instabilities, focusing on the impact of nonlinearly excited, large-scale, linearly stable modes on the nonlinear cascade, momentum transport, and secondary instabilities. Stable modes, which have previously been shown to significantly affect instability saturation [Fraser et al. PoP 2017], are investigated in a collisionless, gyrokinetic, periodic zonal flow using the Gene code by projecting the results of nonlinear simulations onto a basis of linear eigenmodes that includes both stable and unstable modes. Benchmarking growth rates against previous gyrokinetic studies and an equivalent fluid system demonstrates comparable linear dynamics in the fluid and gyrokinetic systems. Cases of driven and decaying shear-flow turbulence are compared in Gene by using a Krook operator as an effective forcing. For comparison with existing hydrodynamic and MHD shear-flow instability studies, we present results for the shear layer obtained by similar means with the code Dedalus. Supported by U.S. DOE Grant No. DE-FG02-89ER53291, the NSF, and UW-Madison.

Data dependence for the amplitude equation of surface waves

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2016-04-01

We consider the amplitude equation for nonlinear surface wave solutions of hyperbolic conservation laws. This is an asymptotic nonlocal, Hamiltonian evolution equation with quadratic nonlinearity. For example, this equation describes the propagation of nonlinear Rayleigh waves (Hamilton et al. in J Acoust Soc Am 97:891-897, 1995), surface waves on current-vortex sheets in incompressible MHD (Alì and Hunter in Q Appl Math 61(3):451-474, 2003; Alì et al. in Stud Appl Math 108(3):305-321, 2002) and on the incompressible plasma-vacuum interface (Secchi in Q Appl Math 73(4):711-737, 2015). The local-in-time existence of smooth solutions to the Cauchy problem for the amplitude equation in noncanonical variables was shown in Hunter (J Hyperbolic Differ Equ 3(2):247-267, 2006), Secchi (Q Appl Math 73(4):711-737, 2015). In the present paper we prove the continuous dependence in strong norm of solutions on the initial data. This completes the proof of the well-posedness of the problem in the classical sense of Hadamard.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

A Fully Associative, Non-Linear Kinematic, Unified Viscoplastic Model for Titanium Based Matrices

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1994-01-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential based multiaxial unified viscoplastic model is obtained. This model possesses one tensorial internal state variable that is associated with dislocation substructure, with an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of non-linear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This non-linear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated) and greatly influences the multiaxial response under non-proportional loading paths. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. Specification of an experimental program for the complete determination of the material functions and parameters for characterizing a metallic matrix, e.g., TIMETAL 21S, is given. The experiments utilized are tensile, creep, and step creep tests. Finally, a comparison of this model and a commonly used Bodner-Partom model is made on the basis of predictive accuracy and numerical efficiency.

Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.

2004-01-01

The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Cascades, ``Blobby'' Turbulence, and Target Pattern Formation in Elastic Systems: A New Take on Classic Themes in Plasma Turbulence

NASA Astrophysics Data System (ADS)

Fan, Xiang

2017-10-01

Concerns central to understanding turbulence and transport include: 1) Dynamics of dual cascades in EM turbulence; 2) Understanding `negative viscosity phenomena' in drift-ZF systems; 3) The physics of blobby turbulence (re: SOL). Here, we present a study of a simple model - that of Cahn-Hilliard Navier-Stokes (CHNS) Turbulence - which sheds important new light on these issues. The CHNS equations describe the motion of binary fluid undergoing a second order phase transition and separation called spinodal decomposition. The CHNS system and 2D MHD are analogous, as they both contain a vorticity equation and a ``diffusion'' equation. The CHNS system differs from 2D MHD by the appearance of negative diffusivity, and a nonlinear dissipative flux. An analogue of the Alfven wave exists in the 2D CHNS system. DNS shows that mean square concentration spectrum Hkψ scales as k - 7 / 3 in the elastic range. This suggests an inverse cascade of Hψ . However, the kinetic energy spectrum EkK scales as k-3 , as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution is that the feedback of capillarity acts only at blob interfaces. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the weakened surface tension feedback and the outcome for EkK. We also examine the evolution of scalar concentration in a single eddy in the Cahn-Hilliard system. This extends the classic problem of flux expulsion in 2D MHD. The simulation results show that a target pattern is formed. Target pattern is a meta stable state, since the band merger process continues on a time scale exponentially long relative to the eddy turnover time. Band merger resembles step merger in drift-ZF staircases. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-04ER54738.

A numerical analysis for non-linear radiation in MHD flow around a cylindrical surface with chemically reactive species

NASA Astrophysics Data System (ADS)

Khan, Junaid Ahmad; Mustafa, M.

2018-03-01

Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail.

Role of electric fields in the MHD evolution of the kink instability

DOE PAGES

Lapenta, Giovanni; Skender, Marina

2017-02-17

Here, the discovery of electrostatic fields playing a crucial role in establishing plasma motion in the flux conversion and dynamo processes in reversed field pinches is revisited. In order to further elucidate the role of the electrostatic fields, a flux rope configuration susceptible to the kink instability is numerically studied with anMHDcode. Simulated nonlinear evolution of the kink instability is found to confirm the crucial role of the electrostatic fields. Anew insight is gained on the special function of the electrostatic fields: they lead the plasma towards the reconnection site at the mode resonant surface. Without this step the plasmamore » column could not relax to its nonlinear state, since no other agent is present to perform this role. While the inductive field generated directly by the kink instability is the dominant flow driver, the electrostatic field is found to allow the motion in the vicinity of the reconnection region.« less

Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM.

PubMed

Rashidi, Mohammad Mehdi; Freidoonimehr, Navid; Momoniat, Ebrahim; Rostami, Behnam

2015-01-01

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

PubMed Central

Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

Role of electric fields in the MHD evolution of the kink instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lapenta, Giovanni; Skender, Marina

Here, the discovery of electrostatic fields playing a crucial role in establishing plasma motion in the flux conversion and dynamo processes in reversed field pinches is revisited. In order to further elucidate the role of the electrostatic fields, a flux rope configuration susceptible to the kink instability is numerically studied with anMHDcode. Simulated nonlinear evolution of the kink instability is found to confirm the crucial role of the electrostatic fields. Anew insight is gained on the special function of the electrostatic fields: they lead the plasma towards the reconnection site at the mode resonant surface. Without this step the plasmamore » column could not relax to its nonlinear state, since no other agent is present to perform this role. While the inductive field generated directly by the kink instability is the dominant flow driver, the electrostatic field is found to allow the motion in the vicinity of the reconnection region.« less

Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM

PubMed Central

Rashidi, Mohammad Mehdi; Freidoonimehr, Navid; Momoniat, Ebrahim; Rostami, Behnam

2015-01-01

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N 1), dimensionless axial magnetic force strength parameter (N 2), dimensionless tangential magnetic force strength parameter (N 3), and magnetic Reynolds number (Re m) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics. PMID:26267247

The nonlinear breakup of the sun's toroidal field

NASA Technical Reports Server (NTRS)

Hughes, D. W.; Cattaneo, F.

1989-01-01

There are good reasons for believing that the sun has a strong toroidal magnetic field in the stably stratified region of convective overshoot sandwiched between the radiative zone and convective zone proper. The magnetic field in this region is modeled by studying the behavior of a layer of uniform field embedded in a subadiabatic atmosphere. Since the field can support extra mass, such a configuration is top-heavy, and instabilities of the Rayleigh-Taylor type can occur. Numerical integration of the two-dimensional compressible MHD equations makes it possible to follow the evolution of this instability into the nonlinear regime. The initial buoyancy-driven instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The somewhat surprising subsequent motions are determined primarily by the strong interactions between vortices.

Methods for discrete solitons in nonlinear lattices.

PubMed

Ablowitz, Mark J; Musslimani, Ziad H; Biondini, Gino

2002-02-01

A method to find discrete solitons in nonlinear lattices is introduced. Using nonlinear optical waveguide arrays as a prototype application, both stationary and traveling-wave solitons are investigated. In the limit of small wave velocity, a fully discrete perturbative analysis yields formulas for the mode shapes and velocity.

Hybrid simulation of fishbone instabilities in the EAST tokamak

NASA Astrophysics Data System (ADS)

Shen, Wei; Fu, Guoyong; Wang, Feng; Xu, Liqing; Li, Guoqiang; Liu, Chengyue; EAST Team

2017-10-01

Hybrid simulations with the global kinetic- MHD code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a BAE with much higher frequency. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11605245 and 11505022, and the CASHIPS Director's Fund under Grant No. YZJJ201510, and the Department of Energy Scientific Discovery through Advanced Computing (SciDAC) under Grant No. DE-AC02-09CH11466.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters

NASA Technical Reports Server (NTRS)

Smith, M.

1972-01-01

Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

The Role of Eigensolutions in Nonlinear Inverse Cavity-Flow-Theory. Revision.

DTIC Science & Technology

1985-06-10

The method of Levi Civita is applied to an isolated fully cavitating body at zero cavitation number and adapted to the solution of the inverse...Eigensolutions in Nonlinear Inverse Cavity-Flow Theory [Revised] Abstract: The method of Levi Civita is applied to an isolated fully cavitating body at...problem is not thought * to present much of a challenge at zero cavitation number. In this case, - the classical method of Levi Civita [7] can be

Structural optimization for joined-wing synthesis

NASA Technical Reports Server (NTRS)

Gallman, John W.; Kroo, Ilan M.

1992-01-01

The differences between fully stressed and minimum-weight joined-wing structures are identified, and these differences are quantified in terms of weight, stress, and direct operating cost. A numerical optimization method and a fully stressed design method are used to design joined-wing structures. Both methods determine the sizes of 204 structural members, satisfying 1020 stress constraints and five buckling constraints. Monotonic splines are shown to be a very effective way of linking spanwise distributions of material to a few design variables. Both linear and nonlinear analyses are employed to formulate the buckling constraints. With a constraint on buckling, the fully stressed design is shown to be very similar to the minimum-weight structure. It is suggested that a fully stressed design method based on nonlinear analysis is adequate for an aircraft optimization study.

Center for Extended Magnetohydrodynamic Modeling Cooperative Agreement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carl R. Sovinec

The Center for Extended Magnetohydrodynamic Modeling (CEMM) is developing computer simulation models for predicting the behavior of magnetically confined plasmas. Over the first phase of support from the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) initiative, the focus has been on macroscopic dynamics that alter the confinement properties of magnetic field configurations. The ultimate objective is to provide computational capabilities to predict plasma behavior—not unlike computational weather prediction—to optimize performance and to increase the reliability of magnetic confinement for fusion energy. Numerical modeling aids theoretical research by solving complicated mathematical models of plasma behavior including strong nonlinear effectsmore » and the influences of geometrical shaping of actual experiments. The numerical modeling itself remains an area of active research, due to challenges associated with simulating multiple temporal and spatial scales. The research summarized in this report spans computational and physical topics associated with state of the art simulation of magnetized plasmas. The tasks performed for this grant are categorized according to whether they are primarily computational, algorithmic, or application-oriented in nature. All involve the development and use of the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion (NIMROD) code, which is described at http://nimrodteam.org. With respect to computation, we have tested and refined methods for solving the large algebraic systems of equations that result from our numerical approximations of the physical model. Collaboration with the Terascale Optimal PDE Solvers (TOPS) SciDAC center led us to the SuperLU_DIST software library [http://crd.lbl.gov/~xiaoye/SuperLU/] for solving large sparse matrices using direct methods on parallel computers. Switching to this solver library boosted NIMROD’s performance by a factor of five in typical large nonlinear simulations, which has been publicized as a success story of SciDAC-fostered collaboration. Furthermore, the SuperLU software does not assume any mathematical symmetry, and its generality provides an important capability for extending the physical model beyond magnetohydrodynamics (MHD). With respect to algorithmic and model development, our most significant accomplishment is the development of a new method for solving plasma models that treat electrons as an independent plasma component. These ‘two-fluid’ models encompass MHD and add temporal and spatial scales that are beyond the response of the ion species. Implementation and testing of a previously published algorithm did not prove successful for NIMROD, and the new algorithm has since been devised, analyzed, and implemented. Two-fluid modeling, an important objective of the original NIMROD project, is now routine in 2D applications. Algorithmic components for 3D modeling are in place and tested; though, further computational work is still needed for efficiency. Other algorithmic work extends the ion-fluid stress tensor to include models for parallel and gyroviscous stresses. In addition, our hot-particle simulation capability received important refinements that permitted completion of a benchmark with the M3D code. A highlight of our applications work is the edge-localized mode (ELM) modeling, which was part of the first-ever computational Performance Target for the DOE Office of Fusion Energy Science, see http://www.science.doe.gov/ofes/performancetargets.shtml. Our efforts allowed MHD simulations to progress late into the nonlinear stage, where energy is conducted to the wall location. They also produced a two-fluid ELM simulation starting from experimental information and demonstrating critical drift effects that are characteristic of two-fluid physics. Another important application is the internal kink mode in a tokamak. Here, the primary purpose of the study has been to benchmark the two main code development lines of CEMM, NIMROD and M3D, on a relevant nonlinear problem. Results from the two codes show repeating nonlinear relaxation events driven by the kink mode over quantitatively comparable timescales. The work has launched a more comprehensive nonlinear benchmarking exercise, where realistic transport effects have an important role.« less

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

NASA Astrophysics Data System (ADS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1995-05-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

A fully associative, nonisothermal, nonlinear kinematic, unified viscoplastic model for titanium alloys

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Saleeb, A. F.; Castelli, M. G.

1995-01-01

Specific forms for both the Gibb's and complementary dissipation potentials are chosen such that a complete (i.e., fully associative) potential base multiaxial, nonisothermal unified viscoplastic model is obtained. This model possesses one tensorial internal state variable (that is, associated with dislocation substructure) and an evolutionary law that has nonlinear kinematic hardening and both thermal and strain induced recovery mechanisms. A unique aspect of the present model is the inclusion of nonlinear hardening through the use of a compliance operator, derived from the Gibb's potential, in the evolution law for the back stress. This nonlinear tensorial operator is significant in that it allows both the flow and evolutionary laws to be fully associative (and therefore easily integrated), greatly influences the multiaxial response under non-proportional loading paths, and in the case of nonisothermal histories, introduces an instantaneous thermal softening mechanism proportional to the rate of change in temperature. In addition to this nonlinear compliance operator, a new consistent, potential preserving, internal strain unloading criterion has been introduced to prevent abnormalities in the predicted stress-strain curves, which are present with nonlinear hardening formulations, during unloading and reversed loading of the external variables. The specific model proposed is characterized for a representative titanium alloy commonly used as the matrix material in SiC fiber reinforced composites, i.e., TIMETAL 21S. Verification of the proposed model is shown using 'specialized' non-standard isothermal and thermomechanical deformation tests.

Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer

NASA Technical Reports Server (NTRS)

Otto, S. R.; Bassom, Andrew P.

1992-01-01

The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described.

All-optical regenerator of multi-channel signals.

PubMed

Li, Lu; Patki, Pallavi G; Kwon, Young B; Stelmakh, Veronika; Campbell, Brandon D; Annamalai, Muthiah; Lakoba, Taras I; Vasilyev, Michael

2017-10-12

One of the main reasons why nonlinear-optical signal processing (regeneration, logic, etc.) has not yet become a practical alternative to electronic processing is that the all-optical elements with nonlinear input-output relationship have remained inherently single-channel devices (just like their electronic counterparts) and, hence, cannot fully utilise the parallel processing potential of optical fibres and amplifiers. The nonlinear input-output transfer function requires strong optical nonlinearity, e.g. self-phase modulation, which, for fundamental reasons, is always accompanied by cross-phase modulation and four-wave mixing. In processing multiple wavelength-division-multiplexing channels, large cross-phase modulation and four-wave mixing crosstalks among the channels destroy signal quality. Here we describe a solution to this problem: an optical signal processor employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without such nonlinear crosstalk. We demonstrate, for the first time to our knowledge, simultaneous all-optical regeneration of up to 16 wavelength-division-multiplexing channels by one device. This multi-channel concept can be extended to other nonlinear-optical processing schemes.Nonlinear optical processing devices are not yet fully practical as they are single channel. Here the authors demonstrate all-optical regeneration of up to 16 channels by one device, employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without nonlinear inter-channel crosstalk.

Interaction of external n = 1 magnetic fields with the sawtooth instability in low- q RFX-mod and DIII-D tokamaks

DOE PAGES

Piron, C.; Martin, P.; Bonfiglio, D.; ...

2016-08-11

External n = 1 magnetic fields are applied in RFX-mod and DIII-D low safety factor Tokamak plasmas to investigate their interaction with the internal MHD dynamics and in particular with the sawtooth instability. In these experiments the applied magnetic fields cause a reduction of both the sawtooth amplitude and period, leading to an overall stabilizing effect on the oscillations. In RFX-mod sawteeth eventually disappear and are replaced by a stationary m = 1, n = 1 helical equilibrium without an increase in disruptivity. However toroidal rotation is significantly reduced in these plasmas, thus it is likely that the sawtooth mitigationmore » in these experiments is due to the combination of the helically deformed core and the reduced rotation. The former effect is qualitatively well reproduced by nonlinear MHD simulations performed with the PIXIE3D code. The results obtained in these RFX-mod experiments motivated similar ones in DIII-D L-mode diverted Tokamak plasmas at low q 95. These experiments succeeded in reproducing the sawtooth mitigation with the approach developed in RFX-mod. In DIII-D this effect is correlated with a clear increase of the n = 1 plasma response, that indicates an enhancement of the coupling to the marginally stable n = 1 external kink, as simulations with the linear MHD code IPEC suggest. A significant rotation braking in the plasma core is also observed in DIII-D. Finally, numerical calculations of the neoclassical toroidal viscosity (NTV) carried out with PENT identify this torque as a possible contributor for this effect.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, S. Y.; Yuan, Z. G.; Hadid, L. Z.

In the solar wind, power spectral density (PSD) of the magnetic field fluctuations generally follow the so-called Kolmogorov spectrum f {sup −5/3} in the inertial range, where the dynamics is thought to be dominated by nonlinear interactions between counter-propagating incompressible Alfvén wave parquets. These features are thought to be ubiquitous in space plasmas. The present study gives a new and more complex picture of magnetohydrodynamic (MHD) turbulence as observed in the terrestrial magnetosheath. The study uses three years of in situ data from the Cluster mission to explore the nature of the magnetic fluctuations at MHD scales in different locationsmore » within the magnetosheath, including flanks and subsolar regions. It is found that the magnetic field fluctuations at MHD scales generally have a PSD close to f {sup −1} (shallower than the Kolmogorov one f {sup −5/3}) down to the ion characteristic scale, which recalls the energy-containing scales of solar wind turbulence. The Kolmogorov spectrum is observed only away from the bow shock toward the flank and the magnetopause regions in 17% of the analyzed time intervals. Measuring the magnetic compressibility, it is shown that only a fraction (35%) of the observed Kolmogorov spectra was populated by shear Alfvénic fluctuations, whereas the majority of the events (65%) was found to be dominated by compressible magnetosonic-like fluctuations, which contrasts with well-known turbulence properties in the solar wind. This study gives a first comprehensive view of the origin of the f {sup −1} and the transition to the Kolmogorov inertial range; both questions remain controversial in solar wind turbulence.« less

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

DOE PAGES

Makwana, K. D.; Zhdankin, V.; Li, H.; ...

2015-04-10

We performed simulations of decaying magnetohydrodynamic (MHD) turbulence with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k-1.3⊥k⊥-1.3. The kinetic code shows a spectral slope of k-1.5⊥k⊥-1.5 for smallermore » simulation domain, and k-1.3⊥k⊥-1.3 for larger domain. We then estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. Finally, this work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.« less

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makwana, K. D.; Zhdankin, V.; Li, H.

We performed simulations of decaying magnetohydrodynamic (MHD) turbulence with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k-1.3⊥k⊥-1.3. The kinetic code shows a spectral slope of k-1.5⊥k⊥-1.5 for smallermore » simulation domain, and k-1.3⊥k⊥-1.3 for larger domain. We then estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. Finally, this work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.« less

Metallurgical technologies, energy conversion, and magnetohydrodynamic flows

NASA Astrophysics Data System (ADS)

Branover, Herman; Unger, Yeshajahu

The present volume discusses metallurgical applications of MHD, R&D on MHD devices employing liquid working medium for process applications, electromagnetic (EM) modulation of molten metal flow, EM pump performance of superconducting MHD devices, induction EM alkali-metal pumps, a physical model for EM-driven flow in channel-induction furnaces, grain refinement in Al alloys via EM vibrational method, dendrite growth of solidifying metal in dc magnetic field, MHD for mass and heat transfer in single-crystal melt growth, inverse EM shaping, and liquid-metal MHD development in Israel. Also discussed are the embrittlement of steel by lead, an open cycle MHD disk generator, the acceleration of gas-liquid piston flows for molten-metal MHD generators, MHD flow around a cylinder, new MHD drag coefficients, liquid-metal MHD two-phase flow, and two-phase liquid gas mixers for MHD energy conversion. (No individual items are abstracted in this volume)

Control of polarization rotation in nonlinear propagation of fully structured light

NASA Astrophysics Data System (ADS)

Gibson, Christopher J.; Bevington, Patrick; Oppo, Gian-Luca; Yao, Alison M.

2018-03-01

Knowing and controlling the spatial polarization distribution of a beam is of importance in applications such as optical tweezing, imaging, material processing, and communications. Here we show how the polarization distribution is affected by both linear and nonlinear (self-focusing) propagation. We derive an analytical expression for the polarization rotation of fully structured light (FSL) beams during linear propagation and show that the observed rotation is due entirely to the difference in Gouy phase between the two eigenmodes comprising the FSL beams, in excellent agreement with numerical simulations. We also explore the effect of cross-phase modulation due to a self-focusing (Kerr) nonlinearity and show that polarization rotation can be controlled by changing the eigenmodes of the superposition, and physical parameters such as the beam size, the amount of Kerr nonlinearity, and the input power. Finally, we show that by biasing cylindrical vector beams to have elliptical polarization, we can vary the polarization state from radial through spiral to azimuthal using nonlinear propagation.

Towards Integrated Pulse Detonation Propulsion and MHD Power

NASA Technical Reports Server (NTRS)

Litchford, Ron J.; Thompson, Bryan R.; Lineberry, John T.

1999-01-01

The interest in pulse detonation engines (PDE) arises primarily from the advantages that accrue from the significant combustion pressure rise that is developed in the detonation process. Conventional rocket engines, for example, must obtain all of their compression from the turbopumps, while the PDE provides additional compression in the combustor. Thus PDE's are expected to achieve higher I(sub sp) than conventional rocket engines and to require smaller turbopumps. The increase in I(sub sp) and the decrease in turbopump capacity must be traded off against each other. Additional advantages include the ability to vary thrust level by adjusting the firing rate rather than throttling the flow through injector elements. The common conclusion derived from these aggregated performance attributes is that PDEs should result in engines which are smaller, lower in cost, and lighter in weight than conventional engines. Unfortunately, the analysis of PDEs is highly complex due to their unsteady operation and non-ideal processes. Although the feasibility of the basic PDE concept has been proven in several experimental and theoretical efforts, the implied performance improvements have yet to be convincingly demonstrated. Also, there are certain developmental issues affecting the practical application of pulse detonation propulsion systems which are yet to be fully resolved. Practical detonation combustion engines, for example, require a repetitive cycle of charge induction, mixing, initiation/propagation of the detonation wave, and expulsion/scavenging of the combustion product gases. Clearly, the performance and power density of such a device depends upon the maximum rate at which this cycle can be successfully implemented. In addition, the electrical energy required for direct detonation initiation can be significant, and a means for direct electrical power production is needed to achieve self-sustained engine operation. This work addresses the technological issues associated with PDEs for integrated aerospace propulsion and MHD power. An effort is made to estimate the energy requirements for direct detonation initiation of potential fuel/oxidizer mixtures and to determine the electrical power requirements. This requirement is evaluated in terms of the possibility for MHD power generation using the combustion detonation wave. Small scale laboratory experiments were conducted using stoichiometric mixtures of acetylene and oxygen with an atomized spray of cesium hydroxide dissolved in alcohol as an ionization seed in the active MHD region. Time resolved thrust and MHD power generation measurements were performed. These results show that PDEs yield higher I(sub sp) levels than a comparable rocket engine and that MHD power generation is viable candidate for achieving self-excited engine operation.

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pincha)

NASA Astrophysics Data System (ADS)

King, J. R.; Sovinec, C. R.; Mirnov, V. V.

2012-05-01

Drift and Hall effects on magnetic tearing, island evolution, and relaxation in pinch configurations are investigated using a non-reduced first-order finite-Larmor-radius (FLR) fluid model with the nonideal magnetohydrodynamics (MHD) with rotation, open discussion (NIMROD) code [C.R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)]. An unexpected result with a uniform pressure profile is a drift effect that reduces the growth rate when the ion sound gyroradius (ρs) is smaller than the tearing-layer width. This drift is present only with warm-ion FLR modeling, and analytics show that it arises from ∇B and poloidal curvature represented in the Braginskii gyroviscous stress. Nonlinear single-helicity computations with experimentally relevant ρs values show that the warm-ion gyroviscous effects reduce saturated-island widths. Computations with multiple nonlinearly interacting tearing fluctuations find that m = 1 core-resonant-fluctuation amplitudes are reduced by a factor of two relative to single-fluid modeling by the warm-ion effects. These reduced core-resonant-fluctuation amplitudes compare favorably to edge coil measurements in the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. The computations demonstrate that fluctuations induce both MHD- and Hall-dynamo emfs during relaxation events. The presence of a Hall-dynamo emf implies a fluctuation-induced Maxwell stress, and the simulation results show net transport of parallel momentum. The computed magnitude of force densities from the Maxwell and competing Reynolds stresses, and changes in the parallel flow profile, are qualitatively and semi-quantitatively similar to measurements during relaxation in MST.

Explosive Magnetic Reconnection in Double-current Sheet Systems: Ideal versus Resistive Tearing Mode

NASA Astrophysics Data System (ADS)

Baty, Hubert

2017-03-01

Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of resistive magnetohydrodynamics (MHD) in a two-dimensional Cartesian geometry. A special emphasis on the existence of fast and explosive phases is taken. First, we extend the recent theory on the ideal tearing mode of a single-current sheet to a double-current layer configuration. A linear stability analysis shows that, in long and thin systems with (length to shear layer thickness) aspect ratios scaling as {S}L9/29 (S L being the Lundquist number based on the length scale L), tearing modes can develop on a fast Alfvénic timescale in the asymptotic limit {S}L\\to ∞ . The linear results are confirmed by means of compressible resistive MHD simulations at relatively high S L values (up to 3× {10}6) for different current sheet separations. Moreover, the nonlinear evolution of the ideal double tearing mode (IDTM) exhibits a richer dynamical behavior than its single-tearing counterpart, as a nonlinear explosive growth violently ends up with a disruption when the two current layers interact trough the merging of plasmoids. The final outcome of the system is a relaxation toward a new state, free of magnetic field reversal. The IDTM dynamics is also compared to the resistive double tearing mode dynamics, which develops in similar systems with smaller aspect ratios, ≳ 2π , and exhibits an explosive secondary reconnection, following an initial slow resistive growth phase. Finally, our results are used to discuss the flaring activity in astrophysical magnetically dominated plasmas, with a particular emphasis on pulsar systems.

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, J. R.; Tech-X Corporation, 5621 Arapahoe Ave., Suite A Boulder, Colorado 80303; Sovinec, C. R.

Drift and Hall effects on magnetic tearing, island evolution, and relaxation in pinch configurations are investigated using a non-reduced first-order finite-Larmor-radius (FLR) fluid model with the nonideal magnetohydrodynamics (MHD) with rotation, open discussion (NIMROD) code [C.R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)]. An unexpected result with a uniform pressure profile is a drift effect that reduces the growth rate when the ion sound gyroradius ({rho}{sub s}) is smaller than the tearing-layer width. This drift is present only with warm-ion FLR modeling, and analytics show that it arises from {nabla}B and poloidal curvature represented in themore » Braginskii gyroviscous stress. Nonlinear single-helicity computations with experimentally relevant {rho}{sub s} values show that the warm-ion gyroviscous effects reduce saturated-island widths. Computations with multiple nonlinearly interacting tearing fluctuations find that m = 1 core-resonant-fluctuation amplitudes are reduced by a factor of two relative to single-fluid modeling by the warm-ion effects. These reduced core-resonant-fluctuation amplitudes compare favorably to edge coil measurements in the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. The computations demonstrate that fluctuations induce both MHD- and Hall-dynamo emfs during relaxation events. The presence of a Hall-dynamo emf implies a fluctuation-induced Maxwell stress, and the simulation results show net transport of parallel momentum. The computed magnitude of force densities from the Maxwell and competing Reynolds stresses, and changes in the parallel flow profile, are qualitatively and semi-quantitatively similar to measurements during relaxation in MST.« less

Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

NASA Astrophysics Data System (ADS)

Hirakawa, Tomoaki; Okamura, Makoto

2018-04-01

We directly calculate fully nonlinear traveling waves that are periodic in two independent horizontal directions (biperiodic) in shallow water. Based on the Riemann theta function, we also calculate exact periodic solutions to the Kadomtsev-Petviashvili (KP) equation, which can be obtained by assuming weakly-nonlinear, weakly-dispersive, weakly-two-dimensional waves. To clarify how the accuracy of the biperiodic KP solution is affected when some of the KP approximations are not satisfied, we compare the fully- and weakly-nonlinear periodic traveling waves of various wave amplitudes, wave depths, and interaction angles. As the interaction angle θ decreases, the wave frequency and the maximum wave height of the biperiodic KP solution both increase, and the central peak sharpens and grows beyond the height of the corresponding direct numerical solutions, indicating that the biperiodic KP solution cannot qualitatively model direct numerical solutions for θ ≲ 45^\\circ . To remedy the weak two-dimensionality approximation, we apply the correction of Yeh et al (2010 Eur. Phys. J. Spec. Top. 185 97-111) to the biperiodic KP solution, which substantially improves the solution accuracy and results in wave profiles that are indistinguishable from most other cases.

3D Hall MHD-EPIC Simulations of Ganymede's Magnetosphere

NASA Astrophysics Data System (ADS)

Zhou, H.; Toth, G.; Jia, X.

2017-12-01

Fully kinetic modeling of a complete 3D magnetosphere is still computationally expensive and not feasible on current computers. While magnetohydrodynamic (MHD) models have been successfully applied to a wide range of plasma simulation, they cannot capture some important kinetic effects. We have recently developed a new modeling tool to embed the implicit particle-in-cell (PIC) model iPIC3D into the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US) magnetohydrodynamic model. This results in a kinetic model of the regions where kinetic effects are important. In addition to the MHD-EPIC modeling of the magnetosphere, the improved model presented here is now able to represent the moon as a resistive body. We use a stretched spherical grid with adaptive mesh refinement (AMR) to capture the resistive body and its boundary. A semi-implicit scheme is employed for solving the magnetic induction equation to allow time steps that are not limited by the resistivity. We have applied the model to Ganymede, the only moon in the solar system known to possess a strong intrinsic magnetic field, and included finite resistivity beneath the moon`s surface to model the electrical properties of the interior in a self-consistent manner. The kinetic effects of electrons and ions on the dayside magnetopause and tail current sheet are captured with iPIC3D. Magnetic reconnections under different upstream background conditions of several Galileo flybys are simulated to study the global reconnection rate and the magnetospheric dynamics

Global plasma oscillations in electron internal transport barriers in TCV

NASA Astrophysics Data System (ADS)

Udintsev, V. S.; Sauter, O.; Asp, E.; Fable, E.; Goodman, T. P.; Turri, G.; Graves, J. P.; Scarabosio, A.; Zhuang, G.; Zucca, C.; TCV Team

2008-12-01

In the Tokamak à Configuration Variable (TCV) (Hofmann F et al1994 Plasma Phys. Control. Fusion 36 B277), global plasma oscillations have been discovered in fully non-inductively driven plasmas featuring electron internal transport barriers (ITB) with strong ECRH/ECCD. These oscillations are linked to the destabilization and stabilization of MHD modes near the foot of the ITB and can lead to large oscillations of the total plasma current and line-averaged density, among others. They are intrinsically related to the fact that ITBs have large pressure gradients in a region of low magnetic shear. Therefore, the ideal MHD limit is relatively low and infernal modes can be unstable. Depending on the proximity to the ideal limit, small crashes or resistive modes can appear which affect the time evolution of the discharge. Being near marginal stability, the modes can self-stabilize due to the modification of the pressure gradient and local q-profile. The plasma recovers good confinement, reverses shear and the ITB builds up, until a new MHD mode is destabilized. TCV results show that this cycling behaviour can be controlled by modifying the current density or the pressure profiles, either with Ohmic current density perturbation or by modifying the ECH/ECCD power. It is demonstrated that many observations such as q >= 2 sawteeth, beta collapses, minor disruptions and oscillation regimes in ITBs can be assigned to the same physics origin: the proximity to the infernal mode stability limit.

High-resolution hybrid simulations of turbulence from inertial to sub-proton scales

NASA Astrophysics Data System (ADS)

Franci, Luca; Hellinger, Petr; Landi, Simone; Matteini, Lorenzo; Verdini, Andrea

2015-04-01

We investigate properties of turbulence from MHD scales to ion scales by means of two-dimensional, large-scale, high-resolution hybrid particle-in-cell simulations, which to our knowledge constitute the most accurate hybrid simulations of ion scale turbulence ever presented so far. We impose an initial ambient magnetic field perpendicular to the simulation box, and we add a spectrum of large-scale, linearly polarized Alfvén waves, balanced and Alfvénically equipartitioned, on average. When turbulence is fully developed, we observe an inertial range which is characterized by the power spectrum of perpendicular magnetic field fluctuations following a Kolmogorov law with spectral index close to -5/3, while the proton bulk velocity fluctuations exhibit a less steeper slope with index close to -3/2. Both these trends hold over a full decade. A definite transition is observed at a scale of the order of the proton inertial length, above which both spectra steepen, with the perpendicular magnetic field still exhibiting a power law with spectral index about -3 over another full decade. The spectrum of perpendicular electric fluctuations follows the one of the proton bulk velocity at MHD scales and reaches a sort of plateau at small scales. The turbulent nature of our data is also supported by the presence of intermittency. This is revealed by the non-Gaussianity of the probability distribution functions of MHD primitive variables increasing as approaching kinetic scales. All these features are in good agreement with solar wind observations.

EXTENSION OF THE MURAM RADIATIVE MHD CODE FOR CORONAL SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rempel, M., E-mail: rempel@ucar.edu

2017-01-01

We present a new version of the MURaM radiative magnetohydrodynamics (MHD) code that allows for simulations spanning from the upper convection zone into the solar corona. We implement the relevant coronal physics in terms of optically thin radiative loss, field aligned heat conduction, and an equilibrium ionization equation of state. We artificially limit the coronal Alfvén and heat conduction speeds to computationally manageable values using an approximation to semi-relativistic MHD with an artificially reduced speed of light (Boris correction). We present example solutions ranging from quiet to active Sun in order to verify the validity of our approach. We quantifymore » the role of numerical diffusivity for the effective coronal heating. We find that the (numerical) magnetic Prandtl number determines the ratio of resistive to viscous heating and that owing to the very large magnetic Prandtl number of the solar corona, heating is expected to happen predominantly through viscous dissipation. We find that reasonable solutions can be obtained with values of the reduced speed of light just marginally larger than the maximum sound speed. Overall this leads to a fully explicit code that can compute the time evolution of the solar corona in response to photospheric driving using numerical time steps not much smaller than 0.1 s. Numerical simulations of the coronal response to flux emergence covering a time span of a few days are well within reach using this approach.« less

Covariant and 3 + 1 Equations for Dynamo-Chiral General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Del Zanna, L.; Bucciantini, N.

2018-06-01

The exponential amplification of initial seed magnetic fields in relativistic plasmas is a very important topic in astrophysics, from the conditions in the early Universe to the interior of neutron stars. While dynamo action in a turbulent plasma is often invoked, in the last years a novel mechanism of quantum origin has gained increasingly more attention, namely the Chiral Magnetic Effect (CME). This has been recognized in semi-metals and it is most likely at work in the quark-gluon plasma formed in heavy-ion collision experiments, where the highest magnetic fields in nature, up to B ˜ 1018 G, are produced. This effect is expected to survive even at large hydrodynamical/MHD scales and it is based on the chiral anomaly due to an imbalance between left- and right-handed relativistic fermions in the constituent plasma. Such imbalance leads to an electric current parallel to an external magnetic field, which is precisely the same mechanism of an α-dynamo action in classical MHD. Here we extend the close parallelism between the chiral and the dynamo effects to relativistic plasmas and we propose a unified, fully covariant formulation of the generalized Ohm's law. Moreover, we derive for the first time the 3 + 1 general relativistic MHD equations for a chiral plasma both in flat and curved spacetimes, in view of numerical investigation of the CME in compact objects, especially magnetars, or of the interplay among the non-ideal magnetic effects of dynamo, the CME and reconnection.

Skeletal muscle tensile strain dependence: hyperviscoelastic nonlinearity

PubMed Central

Wheatley, Benjamin B; Morrow, Duane A; Odegard, Gregory M; Kaufman, Kenton R; Donahue, Tammy L Haut

2015-01-01

Introduction Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. Materials and Methods Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. Results Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. Conclusions Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model. PMID:26409235

Experimental investigation of material nonlinearity using the Rayleigh surface waves excited and detected by angle beam wedge transducers.

PubMed

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo; Hu, Hongwei

2018-05-12

Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method. Copyright © 2018. Published by Elsevier B.V.

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Brain shift computation using a fully nonlinear biomechanical model.

PubMed

Wittek, Adam; Kikinis, Ron; Warfield, Simon K; Miller, Karol

2005-01-01

In the present study, fully nonlinear (i.e. accounting for both geometric and material nonlinearities) patient specific finite element brain model was applied to predict deformation field within the brain during the craniotomy-induced brain shift. Deformation of brain surface was used as displacement boundary conditions. Application of the computed deformation field to align (i.e. register) the preoperative images with the intraoperative ones indicated that the model very accurately predicts the displacements of gravity centers of the lateral ventricles and tumor even for very limited information about the brain surface deformation. These results are sufficient to suggest that nonlinear biomechanical models can be regarded as one possible way of complementing medical image processing techniques when conducting nonrigid registration. Important advantage of such models over the linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain tissue stress-strain relationship is linear.

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Reply to Comments by Tsurutani et al. on "Modeling Extreme `Carrington-Type' Space Weather Events Using Three-Dimensional Global MHD Simulations"

NASA Astrophysics Data System (ADS)

Ngwira, Chigomezyo M.; Pulkkinen, Antti; Kuznetsova, Maria M.; Glocer, Alex

2018-02-01

In this response, we address the three main comments by Tsurutani et al. (2018, http://doi.org/10.1002/2017JA024779) namely, unusually high plasma density, interplanetary magnetic field intensity, and fast storm recovery phase. The authors agree that there is room to improve the modeling by taking into account these comments and other aspects that were not fully explored during our initial work. We are already in the process of undertaking a more comprehensive modeling project.

Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

DOE PAGES

Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.; ...

2017-03-10

We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.

We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

Nonlinear ideal magnetohydrodynamics instabilities

NASA Astrophysics Data System (ADS)

Pfirsch, D.; Sudan, R. N.

1993-07-01

Explosive phenomena such as internal disruptions in toroidal discharges and solar flares are difficult to explain in terms of linear instabilities. A plasma approaching a linear stability limit can, however, become nonlinearly and explosively unstable, with noninfinitesimal perturbations even before the marginal state is reached. For such investigations, a nonlinear extension of the usual MHD (magnetohydrodynamic) energy principle is helpful. (This was obtained by Merkel and Schlüter, Sitzungsberichted. Bayer. Akad. Wiss., Munich, 1976, No. 7, for Cartesian coordinate systems.) A coordinate system independent Eulerian formulation for the Lagrangian allowing for equilibria with flow and with built-in conservation laws for mass, magnetic flux, and entropy is developed in this paper which is similar to Newcomb's Lagrangian method of 1962 [Nucl. Fusion, Suppl., Pt. II, 452 (1962)]. For static equilibria nonlinear stability is completely determined by the potential energy. For a potential energy which contains second- and nth order or some more general contributions only, it is shown in full generality that linearly unstable and marginally stable systems are explosively unstable even for infinitesimal perturbations; linearly absolutely stable systems require finite initial perturbations. For equilibria with Abelian symmetries symmetry breaking initial perturbations are needed, which should be observed in numerical simulations. Nonlinear stability is proved for two simple examples, m=0 perturbations of a Bennet Z-pinch and z-independent perturbations of a θ pinch. The algebra for treating these cases reduces considerably if symmetries are taken into account from the outset, as suggested by M. N. Rosenbluth (private communication, 1992).

Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

NASA Astrophysics Data System (ADS)

Abdelkhalek, M. M.

2009-05-01

Numerical results are presented for heat and mass transfer effect on hydromagnetic flow of a moving permeable vertical surface. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a moving permeable surface. The surface is maintained at linear temperature and concentration variations. The non-linear coupled boundary layer equations were transformed and the resulting ordinary differential equations were solved by perturbation technique [Aziz A, Na TY. Perturbation methods in heat transfer. Berlin: Springer-Verlag; 1984. p. 1-184; Kennet Cramer R, Shih-I Pai. Magneto fluid dynamics for engineers and applied physicists 1973;166-7]. The solution is found to be dependent on several governing parameter, including the magnetic field strength parameter, Prandtl number, Schmidt number, buoyancy ratio and suction/blowing parameter, a parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Numerical results for the dimensionless velocity profiles, the temperature profiles, the concentration profiles, the local friction coefficient and the local Nusselt number are presented for various combinations of parameters.

Boundary layer flow of MHD tangent hyperbolic nanofluid over a stretching sheet: A numerical investigation

NASA Astrophysics Data System (ADS)

Khan, Mair; Hussain, Arif; Malik, M. Y.; Salahuddin, T.; Khan, Farzana

This article presents the two-dimensional flow of MHD hyperbolic tangent fluid with nanoparticles towards a stretching surface. The mathematical modelling of current flow analysis yields the nonlinear set of partial differential equations which then are reduce to ordinary differential equations by using suitable scaling transforms. Then resulting equations are solved by using shooting technique. The behaviour of the involved physical parameters (Weissenberg number We , Hartmann number M , Prandtl number Pr , Brownian motion parameter Nb , Lewis number Le and thermophoresis number Nt) on velocity, temperature and concentration are interpreted in detail. Additionally, local skin friction, local Nusselt number and local Sherwood number are computed and analyzed. It has been explored that Weissenberg number and Hartmann number are decelerate fluid motion. Brownian motion and thermophoresis both enhance the fluid temperature. Local Sherwood number is increasing function whereas Nusselt number is reducing function for increasing values of Brownian motion parameter Nb , Prandtl number Pr , thermophoresis parameter Nt and Lewis number Le . Additionally, computed results are compared with existing literature to validate the accuracy of solution, one can see that present results have quite resemblance with reported data.

Global Simulations of Dynamo and Magnetorotational Instability in Madison Plasma Experiments and Astrophysical Disks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ebrahimi, Fatima

2014-07-31

Large-scale magnetic fields have been observed in widely different types of astrophysical objects. These magnetic fields are believed to be caused by the so-called dynamo effect. Could a large-scale magnetic field grow out of turbulence (i.e. the alpha dynamo effect)? How could the topological properties and the complexity of magnetic field as a global quantity, the so called magnetic helicity, be important in the dynamo effect? In addition to understanding the dynamo mechanism in astrophysical accretion disks, anomalous angular momentum transport has also been a longstanding problem in accretion disks and laboratory plasmas. To investigate both dynamo and momentum transport,more » we have performed both numerical modeling of laboratory experiments that are intended to simulate nature and modeling of configurations with direct relevance to astrophysical disks. Our simulations use fluid approximations (Magnetohydrodynamics - MHD model), where plasma is treated as a single fluid, or two fluids, in the presence of electromagnetic forces. Our major physics objective is to study the possibility of magnetic field generation (so called MRI small-scale and large-scale dynamos) and its role in Magneto-rotational Instability (MRI) saturation through nonlinear simulations in both MHD and Hall regimes.« less

Three-dimensional rotating flow of MHD single wall carbon nanotubes over a stretching sheet in presence of thermal radiation

NASA Astrophysics Data System (ADS)

Nasir, Saleem; Islam, Saeed; Gul, Taza; Shah, Zahir; Khan, Muhammad Altaf; Khan, Waris; Khan, Aurang Zeb; Khan, Saima

2018-05-01

In this article the modeling and computations are exposed to introduce the new idea of MHD three-dimensional rotating flow of nanofluid through a stretching sheet. Single wall carbon nanotubes (SWCNTs) are utilized as a nano-sized materials while water is used as a base liquid. Single-wall carbon nanotubes (SWNTs) parade sole assets due to their rare structure. Such structure has significant optical and electronics features, wonderful strength and elasticity, and high thermal and chemical permanence. The heat exchange phenomena are deliberated subject to thermal radiation and moreover the impact of nanoparticles Brownian motion and thermophoresis are involved in the present investigation. For the nanofluid transport mechanism, we implemented the Xue model (Xue, Phys B Condens Matter 368:302-307, 2005). The governing nonlinear formulation based upon the law of conservation of mass, quantity of motion, thermal field and nanoparticles concentrations is first modeled and then solved by homotopy analysis method (HAM). Moreover, the graphical result has been exposed to investigate that in what manner the velocities, heat and nanomaterial concentration distributions effected through influential parameters. The mathematical facts of skin friction, Nusselt number and Sherwood number are presented through numerical data for SWCNTs.

Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

NASA Astrophysics Data System (ADS)

Bai, Yu; Jiang, Yuehua; Liu, Fawang; Zhang, Yan

2017-12-01

This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

Residual Energy Spectrum of Solar Wind Turbulence

NASA Astrophysics Data System (ADS)

Chen, C. H. K.; Bale, S. D.; Salem, C. S.; Maruca, B. A.

2013-06-01

It has long been known that the energy in velocity and magnetic field fluctuations in the solar wind is not in equipartition. In this paper, we present an analysis of 5 yr of Wind data at 1 AU to investigate the reason for this. The residual energy (difference between energy in velocity and magnetic field fluctuations) was calculated using both the standard magnetohydrodynamic (MHD) normalization for the magnetic field and a kinetic version, which includes temperature anisotropies and drifts between particle species. It was found that with the kinetic normalization, the fluctuations are closer to equipartition, with a mean normalized residual energy of σr = -0.19 and mean Alfvén ratio of r A = 0.71. The spectrum of residual energy, in the kinetic normalization, was found to be steeper than both the velocity and magnetic field spectra, consistent with some recent MHD turbulence predictions and numerical simulations, having a spectral index close to -1.9. The local properties of residual energy and cross helicity were also investigated, showing that globally balanced intervals with small residual energy contain local patches of larger imbalance and larger residual energy at all scales, as expected for nonlinear turbulent interactions.

Modeling resistive wall modes and disruptive instabilities with M3D-C1

NASA Astrophysics Data System (ADS)

Ferraro, Nm; Jardin, Sc; Pfefferle, D.

2016-10-01

Disruptive instabilities pose a significant challenge to the tokamak approach to magnetic fusion energy, and must be reliably avoided in a successful reactor. These instabilities generally involve rapid, global changes to the magnetic field, and electromagnetic interaction with surrounding conducting structures. Here we apply the extended-MHD code M3D-C1 to calculate the stability and evolution of disruptive modes, including their interaction with external conducting structures. The M3D-C1 model includes the effects of resistivity, equilibrium rotation, and resistive walls of arbitrary thickness, each of which may play important roles in the stability and evolution of disruptive modes. The strong stabilizing effect of rotation on resistive wall modes is explored and compared with analytic theory. The nonlinear evolution of vertical displacement events is also considered, including the evolution of non-axisymmetric instabilities that may arise during the current-quench phase of the disruption. It is found that the non-axisymmetric stability of the plasma during a VDE depends strongly on the thermal history of the plasma. This work is supported by US DOE Grant DE-AC02-09CH11466 and the SciDAC Center for Extended MHD Modeling.

Are current sheets the boundary of fluxtubes in the solar wind? -- A study from multiple spacecraft observation

NASA Astrophysics Data System (ADS)

Li, G.; Arnold, L.; Miao, B.; Yan, Y.

2011-12-01

G. Li (1,2), L. Arnold (1), B. Miao (3) and Y. Yan (4) (1) Department of Physics, University of Alabama in Huntsville Huntsville, AL, 35899 (2) CSPAR, University of Alabama in Huntsville Huntsville, AL, 35899 (3) School of Earth and Space Sciences, University of Science and Technology of CHINA, Hefei, China (4) Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Science, Beijing 100012, China Current sheets is a common structure in the solar wind and is a significant source of solar wind MHD turbulence intermittency. The origin of these structure is presently unknown. Non-linear interactions of the solar wind MHD turbulence can spontaneously generate these structures. On the other hand, there are proposals that these structures may represent relic structures having solar origins. Using a technique developed in [1], we examine current sheets in the solar wind from multiple spacecraft. We identify the "single-peak" and "double-peak" events in the solar wind and discuss possible scenarios for these events and its implication of the origin of the current sheets. [1] Li, G., "Identify current-sheet-like structures in the solar wind", ApJL 672, L65, 2008.

Ideal MHD Stability and Characteristics of Edge Localized Modes on CFETR

NASA Astrophysics Data System (ADS)

Li, Zeyu; Chan, Vincent; Xu, Xueqiao; Wang, Xiaogang; Cfetr Physics Team

2017-10-01

Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario derived from multi-code integrated modeling, with key parameters varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for engineering design. The linear stabilities of low-n and intermediate-n peeling-ballooning modes for CFETR baseline scenario are analyzed. Multi-code benchmarking, including GATO, ELITE, BOUT + + and NIMROD, demonstrated good agreement in predicting instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT + + . Instabilities are found both at the pedestal top and inside the pedestal region, which lead to a mix of grassy and type I ELMs. Pedestal structures extending inward beyond the pedestal top are also varied to study the influence on ELM characteristic. Preliminary results on the dependence of the Type-I ELM divertor heat load scaling on machine size and pedestal pressure will also be presented. Prepared by LLNL under Contract DE-AC52-07NA27344 and National Magnetic Confinement Fusion Research Program of China (Grant No. 2014GB110003 and 2014GB107004).

Impact of ideal MHD stability limits on high-beta hybrid operation

NASA Astrophysics Data System (ADS)

Piovesan, P.; Igochine, V.; Turco, F.; Ryan, D. A.; Cianciosa, M. R.; Liu, Y. Q.; Marrelli, L.; Terranova, D.; Wilcox, R. S.; Wingen, A.; Angioni, C.; Bock, A.; Chrystal, C.; Classen, I.; Dunne, M.; Ferraro, N. M.; Fischer, R.; Gude, A.; Holcomb, C. T.; Lebschy, A.; Luce, T. C.; Maraschek, M.; McDermott, R.; Odstrčil, T.; Paz-Soldan, C.; Reich, M.; Sertoli, M.; Suttrop, W.; Taylor, N. Z.; Weiland, M.; Willensdorfer, M.; The ASDEX Upgrade Team; The DIII-D Team; The EUROfusion MST1 Team

2017-01-01

The hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressure {βN} must be maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX Upgrade error fields are amplified and their effects become visible. To quantify such effects, ASDEX Upgrade measured the response to 3D fields applied by 8× 2 non-axisymmetric coils as {βN} approaches the no-wall limit. The full n  =  1 response profile and poloidal structure were measured by a suite of diagnostics and compared with linear MHD simulations, revealing a characteristic feature of hybrids: the n  =  1 response is due to a global, marginally-stable n  =  1 kink characterized by a large m  =  1, n  =  1 core harmonic due to q min being just above 1. A helical core distortion of a few cm forms and affects various core quantities, including plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments, DIII-D also measured the effect of this helical core on the internal current profile, providing information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous current redistribution by MHD modes that keeps {{q}\\text{min}}>1 . Thanks to flux pumping, a broad current profile is maintained in DIII-D even with large on-axis current drive, enabling fully non-inductive operation at high {βN} up to 3.5-4.

Impact of ideal MHD stability limits on high-beta hybrid operation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piovesan, Paolo; Igochine, V.; Turco, F.

Here, the hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressuremore » $${{\\beta}_{N}}$$ must be maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX Upgrade error fields are amplified and their effects become visible. To quantify such effects, ASDEX Upgrade measured the response to 3D fields applied by $$8\\times 2$$ non-axisymmetric coils as $${{\\beta}_{N}}$$ approaches the no-wall limit. The full n = 1 response profile and poloidal structure were measured by a suite of diagnostics and compared with linear MHD simulations, revealing a characteristic feature of hybrids: the n = 1 response is due to a global, marginally-stable n = 1 kink characterized by a large m = 1, n = 1 core harmonic due to q min being just above 1. A helical core distortion of a few cm forms and affects various core quantities, including plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments, DIII-D also measured the effect of this helical core on the internal current profile, providing information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous current redistribution by MHD modes that keeps $${{q}_{\\text{min}}}>1$$ . Thanks to flux pumping, a broad current profile is maintained in DIII-D even with large on-axis current drive, enabling fully non-inductive operation at high $${{\\beta}_{N}}$$ up to 3.5–4.« less

Validation of numerical solvers for liquid metal flow in a complex geometry in the presence of a strong magnetic field

NASA Astrophysics Data System (ADS)

Patel, Anita; Pulugundla, Gautam; Smolentsev, Sergey; Abdou, Mohamed; Bhattacharyay, Rajendraprasad

2018-04-01

Following the magnetohydrodynamic (MHD) code validation and verification proposal by Smolentsev et al. (Fusion Eng Des 100:65-72, 2015), we perform code to code and code to experiment comparisons between two computational solvers, FLUIDYN and HIMAG, which are presently considered as two of the prospective CFD tools for fusion blanket applications. In such applications, an electrically conducting breeder/coolant circulates in the blanket ducts in the presence of a strong plasma-confining magnetic field at high Hartmann numbers, it{Ha} (it{Ha}^2 is the ratio between electromagnetic and viscous forces) and high interaction parameters, it{N} (it{N} is the ratio of electromagnetic to inertial forces). The main objective of this paper is to provide the scientific and engineering community with common references to assist fusion researchers in the selection of adequate computational means to be used for blanket design and analysis. As an initial validation case, the two codes are applied to the classic problem of a laminar fully developed MHD flows in a rectangular duct. Both codes demonstrate a very good agreement with the analytical solution for it{Ha} up to 15, 000. To address the capabilities of the two codes to properly resolve complex geometry flows, we consider a case of three-dimensional developing MHD flow in a geometry comprising of a series of interconnected electrically conducting rectangular ducts. The computed electric potential distributions for two flows (Case A) it{Ha}=515, it{N}=3.2 and (Case B) it{Ha}=2059, it{N}=63.8 are in very good agreement with the experimental data, while the comparisons for the MHD pressure drop are still unsatisfactory. To better interpret the observed differences, the obtained numerical data are analyzed against earlier theoretical and experimental studies for flows that involve changes in the relative orientation between the flow and the magnetic field.

Impact of ideal MHD stability limits on high-beta hybrid operation

DOE PAGES

Piovesan, Paolo; Igochine, V.; Turco, F.; ...

2016-10-27

Here, the hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressuremore » $${{\\beta}_{N}}$$ must be maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even if hybrids are mainly limited by tearing modes, proximity to the no-wall limit leads to 3D field amplification that affects plasma profiles, e.g. rotation braking is observed in ASDEX Upgrade throughout the plasma and peaks in the core. As a result, even the small ASDEX Upgrade error fields are amplified and their effects become visible. To quantify such effects, ASDEX Upgrade measured the response to 3D fields applied by $$8\\times 2$$ non-axisymmetric coils as $${{\\beta}_{N}}$$ approaches the no-wall limit. The full n = 1 response profile and poloidal structure were measured by a suite of diagnostics and compared with linear MHD simulations, revealing a characteristic feature of hybrids: the n = 1 response is due to a global, marginally-stable n = 1 kink characterized by a large m = 1, n = 1 core harmonic due to q min being just above 1. A helical core distortion of a few cm forms and affects various core quantities, including plasma rotation, electron and ion temperature, and intrinsic W density. In similar experiments, DIII-D also measured the effect of this helical core on the internal current profile, providing information useful to understanding of the physics of magnetic flux pumping, i.e. anomalous current redistribution by MHD modes that keeps $${{q}_{\\text{min}}}>1$$ . Thanks to flux pumping, a broad current profile is maintained in DIII-D even with large on-axis current drive, enabling fully non-inductive operation at high $${{\\beta}_{N}}$$ up to 3.5–4.« less

Turbulence scaling study in an MHD wind tunnel on the Swarthmore Spheromak Experiment

NASA Astrophysics Data System (ADS)

Schaffner, D. A.; Brown, M. R.; Wan, A.

2013-12-01

The turbulence of colliding plasmas is explored in an MHD wind tunnel on the SSX in an effort to understand solar wind physics in a laboratory setting. Fully ionized hydrogen plasma is produced by two plasma guns on opposite sides of a 1m by 15cm copper cylinder creating plasma with L/ρi ~ 75-150, β ~ 0.1-0.2 and Lundquist number ~ 1000. Modification of B-field, Ti and β are made through stuffing flux variation of the plasma guns. Presented here are turbulent f-/k-spectra and correlation times and lengths of B-field fluctuations as measured by a 16 channel B-dot radial probe array at the chamber midplane using both FFT and wavelet analysis techniques. Power-law behavior is observed spanning about two decades of frequencies [100kHz-10MHz] and about one decade of wavelength [10cm-1cm]. Power-law fits to spectra show scaling in these regions to be robust to changes in stuffing flux; fits are on the order of f-4 and k-2 for all flux variations. Low frequency fluctuations [<100kHz] can vary significantly suggesting a range of energy injection at large scales. Evidence for dissipation range modification of the spectra is also observed; divergence from power-law behavior is seen in f-spectra for frequencies around f=fci while changes in k-spectra slopes appear around 1/k ~ 5ρi. Dissipation range fits are made with an exponentially modified power-law model [Terry et al, PoP 2012]. Fluctuation measurements in axial velocity are made using a Mach probe with edge flows reaching M ~ 0.4. Both B-field and velocity fluctuations persist on the same timescale in these experiments, though Mach velocity f-spectra show power-laws slightly shallower than those for B-field. Comparison of spectra from MHD and Hall MHD simulations of SSX performed within the HiFi modeling framework are made to the experimental results.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

Effect of resonant magnetic perturbations on microturbulence in DIII-D pedestal

DOE PAGES

Holod, I.; Lin, Z.; Taimourzadeh, S.; ...

2016-10-03

Vacuum resonant magnetic perturbations (RMP) applied to otherwise axisymmetric tokamak plasmas produce in general a combination of non-resonant effects that preserve closed flux surfaces (kink response) and resonant effects that introduce magnetic islands and/or stochasticity (tearing response). The effect of the plasma kink response on the linear stability and nonlinear transport of edge turbulence is studied using the gyrokinetic toroidal code GTC for a DIII-D plasma with applied n = 2 vacuum RMP. GTC simulations use the 3D equilibrium of DIII-D discharge 158103 (Nazikian et al 2015 Phys. Rev. Lett. 114 105002), which is provided by nonlinear ideal MHD VMECmore » equilibrium solver in order to include the effect of the plasma kink response to the external field but to exclude island formation at rational surfaces. Analysis using the GTC simulation results reveal no increase of growth rates for the electrostatic drift wave instability and for the electromagnetic kinetic-ballooning mode in the presence of the plasma kink response to the RMP. Moreover, nonlinear electrostatic simulations show that the effect of the 3D equilibrium on zonal flow damping is very weak and found to be insufficient to modify turbulent transport in the electrostatic turbulence.« less

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

Initial Flow Matching Results of MHD Energy Bypass on a Supersonic Turbojet Engine Using the Numerical Propulsion System Simulation (NPSS) Environment

NASA Technical Reports Server (NTRS)

Benyo, Theresa L.

2010-01-01

Preliminary flow matching has been demonstrated for a MHD energy bypass system on a supersonic turbojet engine. The Numerical Propulsion System Simulation (NPSS) environment was used to perform a thermodynamic cycle analysis to properly match the flows from an inlet to a MHD generator and from the exit of a supersonic turbojet to a MHD accelerator. Working with various operating conditions such as the enthalpy extraction ratio and isentropic efficiency of the MHD generator and MHD accelerator, interfacing studies were conducted between the pre-ionizers, the MHD generator, the turbojet engine, and the MHD accelerator. This paper briefly describes the NPSS environment used in this analysis and describes the NPSS analysis of a supersonic turbojet engine with a MHD generator/accelerator energy bypass system. Results from this study have shown that using MHD energy bypass in the flow path of a supersonic turbojet engine increases the useful Mach number operating range from 0 to 3.0 Mach (not using MHD) to an explored and desired range of 0 to 7.0 Mach.

Energetic-particle-modified global Alfvén eigenmodes

NASA Astrophysics Data System (ADS)

Lestz, J. B.; Belova, E. V.; Gorelenkov, N. N.

2018-04-01

Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function—the normalized injection velocity v0/vA and central pitch—are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v0/vA . This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE. Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.

Energetic-particle-modified global Alfven eigenmodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lestz, J. B.; Belova, E. V.; Gorelenkov, N. N.

Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function—the normalized injection velocity v 0/v A and central pitch—are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v 0/v A. This unexpected result is present for both counter-propagating GAEs, which aremore » routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE. In conclusion, additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.« less

A General Computational Approach for Magnetohydrodynamic Flows Using the CFX Code: Buoyant Flow Through a Vertical Square Channel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Piazza, Ivan; Buehler, Leo

2000-09-15

The buoyancy-driven magnetoconvection in the cross section of an infinitely long vertical square duct is investigated numerically using the CFX code package. The implementation of a magnetohydrodynamic (MHD) problem in CFX is discussed, with particular reference to the Lorentz forces and the electric potential boundary conditions for arbitrary electrical conductivity of the walls. The method proposed is general and applies to arbitrary geometries with an arbitrary orientation of the magnetic field. Results for fully developed flow under various thermal boundary conditions are compared with asymptotic analytical solutions. The comparison shows that the asymptotic analysis is confirmed for highly conducting wallsmore » as high velocity jets occur at the side walls. For weakly conducting walls, the side layers become more conducting than the side walls, and strong electric currents flow within these layers parallel to the magnetic field. As a consequence, the velocity jets are suppressed, and the core solution is only corrected by the viscous forces near the wall. The implementation of MHD in CFX is achieved.« less

Energetic-particle-modified global Alfven eigenmodes

DOE PAGES

Lestz, J. B.; Belova, E. V.; Gorelenkov, N. N.

2018-04-30

Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function—the normalized injection velocity v 0/v A and central pitch—are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v 0/v A. This unexpected result is present for both counter-propagating GAEs, which aremore » routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE. In conclusion, additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.« less

Numerical MHD study for plasmoid instability in uniform resistivity

NASA Astrophysics Data System (ADS)

Shimizu, Tohru; Kondoh, Koji; Zenitani, Seiji

2017-11-01

The plasmoid instability (PI) caused in uniform resistivity is numerically studied with a MHD numerical code of HLLD scheme. It is shown that the PI observed in numerical studies may often include numerical (non-physical) tearing instability caused by the numerical dissipations. By increasing the numerical resolutions, the numerical tearing instability gradually disappears and the physical tearing instability remains. Hence, the convergence of the numerical results is observed. Note that the reconnection rate observed in the numerical tearing instability can be higher than that of the physical tearing instability. On the other hand, regardless of the numerical and physical tearing instabilities, the tearing instability can be classified into symmetric and asymmetric tearing instability. The symmetric tearing instability tends to occur when the thinning of current sheet is stopped by the physical or numerical dissipations, often resulting in the drastic changes in plasmoid chain's structure and its activity. In this paper, by eliminating the numerical tearing instability, we could not specify the critical Lundquist number Sc beyond which PI is fully developed. It suggests that Sc does not exist, at least around S = 105.

Transverse thermopherotic MHD Oldroyd-B fluid with Newtonian heating

NASA Astrophysics Data System (ADS)

Mehmood, R.; Rana, S.; Nadeem, S.

2018-03-01

Hydromagnetic transverse flow of an Oldroyd-B type fluid with suspension of nanoparticles and Newtonian heating effects is conferred in this article. Relaxation and Retardation time effects are taken into consideration. Using suitable transformations physical problem is converted into non-linear ordinary differential equations which are tackled numerically via Runge-Kutta Fehlberg integration scheme. Illustration of embedded constraints on flow characteristics are extracted through graphs. The physical response of velocity, temperature and concentration are investigated computationally. Momentum boundary layer thickness decreases but local heat and mass flux rises for Deborah number and Hartman number. The results provide interesting insights into certain applicable transport phenomena involving hydromagnetic rheological fluids.

Properties of the edge plasma in the rebuilt Extrap-T2R reversed field pinch experiment

NASA Astrophysics Data System (ADS)

Vianello, N.; Spolaore, M.; Serianni, G.; Bergsåker, H.; Antoni, V.; Drake, J. R.

2002-12-01

The edge region of the rebuilt Extrap-T2R reversed field pinch experiment has been investigated using Langmuir probes. Radial profiles of main plasma parameters are obtained and compared with those of the previous device Extrap-T2. The spontaneous setting up of a double shear layer of E×B toroidal velocity is confirmed. The particle flux induced by electrostatic fluctuations is calculated and the resulting effective diffusion coefficient is consistent with the Bohm estimate. A close relationship between electrostatic fluctuations at the edge and non-linear coupling of MHD modes in the core is found.

Asymmetry of nonlinear interactions of solar MHD discontinuities with the bow shock

NASA Astrophysics Data System (ADS)

Grib, S. A.; Pushkar, E. A.

2006-07-01

Oblique interaction between the solar fast shock wave, which is a typical nonstationary strong discontinuity in the interplanetary space, and the bow shock front upstream of an Earth-type planetary magnetosphere is studied. Attention has been paid to the qualitative and quantitative (with respect to the proton density distribution) dawn-dusk (or morning-evening) asymmetry of the discontinuities refracted into the magnetosheath, which originates in the ecliptic plane on different sides of the Sun-Earth line. The results under discussion have been corroborated experimentally by the gas-kinetic pattern of the bow-shock front and the WIND and ISEE 3 spacecraft measurements of the plasma density.

DOE Office of Scientific and Technical Information (OSTI.GOV)

L. Delgado-Aparicio, et. al.

New observations of the formation and dynamics of long-lived impurity-induced helical "snake" modes in tokamak plasmas have recently been carried-out on Alcator C-Mod. The snakes form as an asymmetry in the impurity ion density that undergoes a seamless transition from a small helically displaced density to a large crescent-shaped helical structure inside q < 1, with a regularly sawtoothing core. The observations show that the conditions for the formation and persistence of a snake cannot be explained by plasma pressure alone. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma densitymore » and temperature« less

Formation and stability of impurity "snakes" in tokamak plasmas.

PubMed

Delgado-Aparicio, L; Sugiyama, L; Granetz, R; Gates, D A; Rice, J E; Reinke, M L; Bitter, M; Fredrickson, E; Gao, C; Greenwald, M; Hill, K; Hubbard, A; Hughes, J W; Marmar, E; Pablant, N; Podpaly, Y; Scott, S; Wilson, R; Wolfe, S; Wukitch, S

2013-02-08

New observations of the formation and dynamics of long-lived impurity-induced helical "snake" modes in tokamak plasmas have recently been carried out on Alcator C-Mod. The snakes form as an asymmetry in the impurity ion density that undergoes a seamless transition from a small helically displaced density to a large crescent-shaped helical structure inside q<1, with a regularly sawtoothing core. The observations show that the conditions for the formation and persistence of a snake cannot be explained by plasma pressure alone. Instead, many features arise naturally from nonlinear interactions in a 3D MHD model that separately evolves the plasma density and temperature.

Development of an Implicit, Charge and Energy Conserving 2D Electromagnetic PIC Code on Advanced Architectures

NASA Astrophysics Data System (ADS)

Payne, Joshua; Taitano, William; Knoll, Dana; Liebs, Chris; Murthy, Karthik; Feltman, Nicolas; Wang, Yijie; McCarthy, Colleen; Cieren, Emanuel

2012-10-01

In order to solve problems such as the ion coalescence and slow MHD shocks fully kinetically we developed a fully implicit 2D energy and charge conserving electromagnetic PIC code, PlasmaApp2D. PlasmaApp2D differs from previous implicit PIC implementations in that it will utilize advanced architectures such as GPUs and shared memory CPU systems, with problems too large to fit into cache. PlasmaApp2D will be a hybrid CPU-GPU code developed primarily to run on the DARWIN cluster at LANL utilizing four 12-core AMD Opteron CPUs and two NVIDIA Tesla GPUs per node. MPI will be used for cross-node communication, OpenMP will be used for on-node parallelism, and CUDA will be used for the GPUs. Development progress and initial results will be presented.

Nonlinear Viscoelastic Characterization of the Porcine Spinal Cord

PubMed Central

Shetye, Snehal; Troyer, Kevin; Streijger, Femke; Lee, Jae H. T.; Kwon, Brian K.; Cripton, Peter; Puttlitz, Christian M.

2014-01-01

Although quasi-static and quasi-linear viscoelastic properties of the spinal cord have been reported previously, there are no published studies that have investigated the fully (strain-dependent) nonlinear viscoelastic properties of the spinal cord. In this study, stress relaxation experiments and dynamic cycling were performed on six fresh porcine lumbar cord specimens to examine their viscoelastic mechanical properties. The stress relaxation data were fitted to a modified superposition formulation and a novel finite ramp time correction technique was applied. The parameters obtained from this fitting methodology were used to predict the average dynamic cyclic viscoelastic behavior of the porcine cord. The data indicate that the porcine spinal cord exhibited fully nonlinear viscoelastic behavior. The average weighted RMSE for a Heaviside ramp fit was 2.8kPa, which was significantly greater (p < 0.001) than that of the nonlinear (comprehensive viscoelastic characterization (CVC) method) fit (0.365kPa). Further, the nonlinear mechanical parameters obtained were able to accurately predict the dynamic behavior, thus exemplifying the reliability of the obtained nonlinear parameters. These parameters will be important for future studies investigating various damage mechanisms of the spinal cord and studies developing high resolution finite elements models of the spine. PMID:24211612

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

PubMed

Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.

Magnetohydrodynamic dissipative flow across the slendering stretching sheet with temperature dependent variable viscosity

NASA Astrophysics Data System (ADS)

Jayachandra Babu, M.; Sandeep, N.; Ali, M. E.; Nuhait, Abdullah O.

The boundary layer flow across a slendering stretching sheet has gotten awesome consideration due to its inexhaustible pragmatic applications in nuclear reactor technology, acoustical components, chemical and manufacturing procedures, for example, polymer extrusion, and machine design. By keeping this in view, we analyzed the two-dimensional MHD flow across a slendering stretching sheet within the sight of variable viscosity and viscous dissipation. The sheet is thought to be convectively warmed. Convective boundary conditions through heat and mass are employed. Similarity transformations used to change over the administering nonlinear partial differential equations as a group of nonlinear ordinary differential equations. Runge-Kutta based shooting technique is utilized to solve the converted equations. Numerical estimations of the physical parameters involved in the problem are calculated for the friction factor, local Nusselt and Sherwood numbers. Viscosity variation parameter and chemical reaction parameter shows the opposite impact to each other on the concentration profile. Heat and mass transfer Biot numbers are helpful to enhance the temperature and concentration respectively.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beresnyak, Andrey; Li, Hui

Nonresonant current instability was identified by Bell as an important mechanism for magnetic field amplification in supernova remnants. In this paper we focus on studying the nonlinear stage of this instability using the incompressible MHD formulation. We demonstrate that the evolution of magnetic turbulence driven by the Bell instability resembles turbulence driven on large scales. More importantly, we demonstrate that the energy-containing scale for magnetic fields is proportional to the square root of the magnetic energy density. Given the observational constraints of the possible field amplification, this new relation allows us to directly estimate the maximum energy of particles scatteredmore » by such fields, and this estimate is normally below the average particle energy. This implies that, without taking into account the feedback to cosmic rays (CRs), the typical scales of Bell fields, in either the linear or nonlinear regime, will be too small to affect high-energy particle acceleration. We mention several scenarios of back reaction to CRs that could be important.« less

Double stratified radiative Jeffery magneto nanofluid flow along an inclined stretched cylinder with chemical reaction and slip condition

NASA Astrophysics Data System (ADS)

Ramzan, M.; Gul, Hina; Dong Chung, Jae

2017-11-01

A mathematical model is designed to deliberate the flow of an MHD Jeffery nanofluid past a vertically inclined stretched cylinder near a stagnation point. The flow analysis is performed in attendance of thermal radiation, mixed convection and chemical reaction. Influence of thermal and solutal stratification with slip boundary condition is also considered. Apposite transformations are engaged to convert the nonlinear partial differential equations to differential equations with high nonlinearity. Convergent series solutions of the problem are established via the renowned Homotopy Analysis Method (HAM). Graphical illustrations are plotted to depict the effects of prominent arising parameters against all involved distributions. Numerically erected tables of important physical parameters like Skin friction, Nusselt and Sherwood numbers are also give. Comparative studies (with a previously examined work) are also included to endorse our results. It is noticed that the thermal stratification parameter has diminishing effect on temperature distribution. Moreover, the velocity field is a snowballing and declining function of curvature and slip parameters respectively.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lazerson, Samuel A.; Loizu, Joaquim; Hirshman, Steven

The VMEC nonlinear ideal MHD equilibrium code [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like configuration. The focus of such analysis is to verify the ideal MHD response at magnetic surfaces which possess magnetic transform (ι) which is resonant with spectral values of the perturbed boundary harmonics. A large aspect ratio circular cross section zero-beta equilibrium is considered. This equilibrium possess a rational surface with safety factor q = 2 at a normalized flux value of 0.5. A small resonant boundary perturbation is introduced, excitingmore » a response at the resonant rational surface. The code is found to capture the plasma response as predicted by a newly developed analytic theory that ensures the existence of nested flux surfaces by allowing for a jump in rotational transform (ι=1/q). The VMEC code satisfactorily reproduces these theoretical results without the necessity of an explicit transform discontinuity (Δι) at the rational surface. It is found that the response across the rational surfaces depends upon both radial grid resolution and local shear (dι/dΦ, where ι is the rotational transform and Φ the enclosed toroidal flux). Calculations of an implicit Δι suggest that it does not arise due to numerical artifacts (attributed to radial finite differences in VMEC) or existence conditions for flux surfaces as predicted by linear theory (minimum values of Δι). Scans of the rotational transform profile indicate that for experimentally relevant levels of transform shear the response becomes increasing localised. Furthermore, careful examination of a large experimental tokamak equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu Zhaohuan; Stone, James M.; Rafikov, Roman R., E-mail: zhzhu@astro.princeton.edu, E-mail: jstone@astro.princeton.edu, E-mail: rrr@astro.princeton.edu

Some regions in protoplanetary disks are turbulent, while some regions are quiescent (e.g. the dead zone). In order to study how planets open gaps in both inviscid hydrodynamic disk (e.g. the dead zone) and the disk subject to magnetorotational instability (MRI), we carried out both shearing box two-dimensional inviscid hydrodynamical simulations and three-dimensional unstratified magnetohydrodynamical (MHD) simulations (having net vertical magnetic fields) with a planet at the box center. We found that, due to the nonlinear wave steepening, even a low mass planet can open gaps in both cases, in contradiction to the ''thermal criterion'' for gap opening. In ordermore » to understand if we can represent the MRI turbulent stress with the viscous {alpha} prescription for studying gap opening, we compare gap properties in MRI-turbulent disks to those in viscous HD disks having the same stress, and found that the same mass planet opens a significantly deeper and wider gap in net vertical flux MHD disks than in viscous HD disks. This difference arises due to the efficient magnetic field transport into the gap region in MRI disks, leading to a larger effective {alpha} within the gap. Thus, across the gap, the Maxwell stress profile is smoother than the gap density profile, and a deeper gap is needed for the Maxwell stress gradient to balance the planetary torque density. Comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. We also found that long-lived density features (termed zonal flows) produced by the MRI can affect planet migration. Overall, our results suggest that gaps can be commonly produced by low mass planets in realistic protoplanetary disks, and caution the use of a constant {alpha}-viscosity to model gaps in protoplanetary disks.« less

Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code

DOE PAGES

Lazerson, Samuel A.; Loizu, Joaquim; Hirshman, Steven; ...

2016-01-13

The VMEC nonlinear ideal MHD equilibrium code [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like configuration. The focus of such analysis is to verify the ideal MHD response at magnetic surfaces which possess magnetic transform (ι) which is resonant with spectral values of the perturbed boundary harmonics. A large aspect ratio circular cross section zero-beta equilibrium is considered. This equilibrium possess a rational surface with safety factor q = 2 at a normalized flux value of 0.5. A small resonant boundary perturbation is introduced, excitingmore » a response at the resonant rational surface. The code is found to capture the plasma response as predicted by a newly developed analytic theory that ensures the existence of nested flux surfaces by allowing for a jump in rotational transform (ι=1/q). The VMEC code satisfactorily reproduces these theoretical results without the necessity of an explicit transform discontinuity (Δι) at the rational surface. It is found that the response across the rational surfaces depends upon both radial grid resolution and local shear (dι/dΦ, where ι is the rotational transform and Φ the enclosed toroidal flux). Calculations of an implicit Δι suggest that it does not arise due to numerical artifacts (attributed to radial finite differences in VMEC) or existence conditions for flux surfaces as predicted by linear theory (minimum values of Δι). Scans of the rotational transform profile indicate that for experimentally relevant levels of transform shear the response becomes increasing localised. Furthermore, careful examination of a large experimental tokamak equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.« less

Temporal evolution of a Current Sheet with Initial Finite Perturbations by Three-dimensional MHD Simulations

NASA Astrophysics Data System (ADS)

Yokoyama, Takaaki

Temporal evolution of a current sheet with initial perturbations is studied by using the threedimensional resistive magnetohydrodynamic (MHD) simulations. The magnetic reconnection is considered to be the main engine of the energy rele ase in solar flares. The structure of the diffusion region is, however, not stil l understood under the circumstances with enormously large magnetic Reynolds num ber as the solar corona. In particular, the relationship between the flare's macroscopic physics and the microscopic ones are unclear. It is generally believed that the MHD turbulence s hould play a role in the intermediate scale. The initial current sheet is in an approximately hydromagnetic equilibrium with anti-parallel magnetic field in the y-direction. We imposed a finite-amplitude perturbations (=50ee what happens. Special attention is paid upon the evolution of a three-dimens ional structure in the direction along the initial electric current (z-direction ). Our preliminary results are as follows: (1) In the early phase of the evolut ion, high wavenumber modes in the z-direction are excited and grow. (2) Many "X "-type neutral points (lines) are generated along the magnetic neutral line (pla ne) in the current sheet. When they evolve into the non-linear phase, three-dime nsional structures in the z-direction also evolve. The spatial scale in the z-di rection seems to be almost comparable with that in the xy-plane. (3) The energy release rate is reduced in case of 3D simulations compared with 2D ones probably because of the reduction of the inflow cross sections by the formation of pattc hy structures in the current sheet.

Interaction of external n  =  1 magnetic fields with the sawtooth instability in low-q RFX-mod and DIII-D tokamaks

NASA Astrophysics Data System (ADS)

Piron, C.; Martin, P.; Bonfiglio, D.; Hanson, J.; Logan, N. C.; Paz-Soldan, C.; Piovesan, P.; Turco, F.; Bialek, J.; Franz, P.; Jackson, G.; Lanctot, M. J.; Navratil, G. A.; Okabayashi, M.; Strait, E.; Terranova, D.; Turnbull, A.

2016-10-01

External n  =  1 magnetic fields are applied in RFX-mod and DIII-D low safety factor Tokamak plasmas to investigate their interaction with the internal MHD dynamics and in particular with the sawtooth instability. In these experiments the applied magnetic fields cause a reduction of both the sawtooth amplitude and period, leading to an overall stabilizing effect on the oscillations. In RFX-mod sawteeth eventually disappear and are replaced by a stationary m  =  1, n  =  1 helical equilibrium without an increase in disruptivity. However toroidal rotation is significantly reduced in these plasmas, thus it is likely that the sawtooth mitigation in these experiments is due to the combination of the helically deformed core and the reduced rotation. The former effect is qualitatively well reproduced by nonlinear MHD simulations performed with the PIXIE3D code. The results obtained in these RFX-mod experiments motivated similar ones in DIII-D L-mode diverted Tokamak plasmas at low q 95. These experiments succeeded in reproducing the sawtooth mitigation with the approach developed in RFX-mod. In DIII-D this effect is correlated with a clear increase of the n  =  1 plasma response, that indicates an enhancement of the coupling to the marginally stable n  =  1 external kink, as simulations with the linear MHD code IPEC suggest. A significant rotation braking in the plasma core is also observed in DIII-D. Numerical calculations of the neoclassical toroidal viscosity (NTV) carried out with PENT identify this torque as a possible contributor for this effect.

Casting the Coronal Magnetic Field Reconstruction Tools in 3D Using the MHD Bifrost Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fleishman, Gregory D.; Loukitcheva, Maria; Anfinogentov, Sergey

Quantifying the coronal magnetic field remains a central problem in solar physics. Nowadays, the coronal magnetic field is often modeled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as π -disambiguation, photospheric field preprocessing, and volume reconstruction methods, using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model, we know the magnetic field vector in the entire 3D domain, which enables us to perform a “voxel-by-voxel” comparison of the restored and the true magnetic fieldsmore » in the 3D model volume. Our tests show that the available π -disambiguation methods often fail in the quiet-Sun areas dominated by small-scale magnetic elements, while they work well in the active region (AR) photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although it does produce a more force-free boundary condition, also results in some effective “elevation” of the magnetic field components. This “elevation” height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from the actual AR photospheric magnetogram are free from this systematic error, while other metrics are comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results than those from a photospheric boundary.« less

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

NASA Astrophysics Data System (ADS)

Duan, Aiying; Jiang, Chaowei; Hu, Qiang; Zhang, Huai; Gary, G. Allen; Wu, S. T.; Cao, Jinbin

2017-06-01

Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field, which is difficult to directly measure. Various analytic models and numerical codes exist, but their results often drastically differ. Thus, a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a nonlinear force-free field code (CESE-MHD-NLFFF) and a non-force-free field (NFFF) code, in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from the region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO/AIA. It is found that the CESE-MHD-NLFFF code with preprocessed magnetogram performs the best, outputting a field that matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ˜10°. This suggests that the CESE-MHD-NLFFF code, even without using the information of the coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential field give comparable results of the mean misalignment angle (˜30°). Thus, further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region.

2-D modelling and simulation of EM brake for liquid steel

NASA Astrophysics Data System (ADS)

Aslan, Necdet; Senturk, Kenan; Tessarotto, Massimo

2003-11-01

The problem of EM control of bottom tapping in steelmaking metallurgy is an old and well known challenge not only from the technological viewpoint but also, potentially, an interesting and still open theoretical problem, from the viewpoint of the investigation of the detailed MHD phenomena occurring in EM braking devices [1]. Purpose of the present work is the formulation of a 2-D MHD model for a DC EM braking device, which includes the consistent modelization of inductive EM fields produced by the conductive fluid, large scale turbulence, boundary conditions for the EM fields and thermal effects. The mathematical model has been implemented in a new 2-D MHD code developed for this purpose [2], based on the so-called fluctuation splitting and dual-time stepping methods, respectively, to advance in time the fluid fields and satisfy the relevant incompressibility-solenoidality conditions for the fluid mass velocity and the magnetic field. Main goal of the investigation is the analysis of the nonlinear phenomena occurring in the process of slowing down of a column of liquid steel under the action of the EM brake, and in particular the detailed description of the effects of large scale turbulence produced by the action of Lorentz force on the fluid, their influence on the magnitude of the inductive EM fields and the performance of the EM brake itself. REFERENCES [1] A.Codutti, A.Martinis, M.Pavlicevic, M.Tessarotto and D.Batic, Proc. 3rd International Symposium on EMP (Nagoya, Japan, April 2000), p.530 (2000). [2] N.Aslan, K.Senturk and M.Tessarotto, Efficient 2-D solver for incompressible magnefluids, communication at this Conference (2003).

Numerical and Experimental Dynamic Characteristics of Thin-Film Membranes

NASA Technical Reports Server (NTRS)

Young, Leyland G.; Ramanathan, Suresh; Hu, Jia-Zhu; Pai, P. Frank

2004-01-01

Presented is a total-Lagrangian displacement-based non-linear finite-element model of thin-film membranes for static and dynamic large-displacement analyses. The membrane theory fully accounts for geometric non-linearities. Fully non-linear static analysis followed by linear modal analysis is performed for an inflated circular cylindrical Kapton membrane tube under different pressures, and for a rectangular membrane under different tension loads at four comers. Finite element results show that shell modes dominate the dynamics of the inflated tube when the inflation pressure is low, and that vibration modes localized along four edges dominate the dynamics of the rectangular membrane. Numerical dynamic characteristics of the two membrane structures were experimentally verified using a Polytec PI PSV-200 scanning laser vibrometer and an EAGLE-500 8-camera motion analysis system.

Reference Models for Multi-Layer Tissue Structures

DTIC Science & Technology

2016-09-01

simulation,  finite   element  analysis 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC...Physiologically realistic, fully specimen-specific, nonlinear reference models. Tasks. Finite element analysis of non-linear mechanics of cadaver...models. Tasks. Finite element analysis of non-linear mechanics of multi-layer tissue regions of human subjects. Deliverables. Partially subject- and

The initial instability and finite-amplitude stability of alternate bars in straight channels

USGS Publications Warehouse

Nelson, J.M.

1990-01-01

The initial instability and fully developed stability of alternate bars in straight channels are investigated using linearized and nonlinear analyses. The fundamental instability leading to these features is identified through a linear stability analysis of the equations governing the flow and sediment transport fields. This instability is explained in terms of topographically induced steering of the flow and the associated pattern of erosion and deposition on the bed. While the linear theory is useful for examining the instability mechanism, this approach is shown to yield relatively little information about well-developed alternate bars and, specifically, the linear analysis is shown to yield poor predictions of the fully developed bar wavelength. A fully nonlinear approach is presented that permits computation of the evolution of these bed features from an initial perturbation to their fully developed morphology. This analysis indicates that there is typically substantial elongation of the bar wavelength during the evolution process, a result that is consistent with observations of bar development in flumes and natural channels. The nonlinear approach demonstrates that the eventual stability of these features is a result of the interplay between topographic steering effects, secondary flow production as a result of streamline curvature, and gravitationally induced modifications of sediment fluxes over a sloping bed. ?? 1990.

Evolution of the magnetized, neutrino-cooled accretion disk in the aftermath of a black hole-neutron star binary merger

NASA Astrophysics Data System (ADS)

Hossein Nouri, Fatemeh; Duez, Matthew D.; Foucart, Francois; Deaton, M. Brett; Haas, Roland; Haddadi, Milad; Kidder, Lawrence E.; Ott, Christian D.; Pfeiffer, Harald P.; Scheel, Mark A.; Szilagyi, Bela

2018-04-01

Black hole-torus systems from compact binary mergers are possible engines for gamma-ray bursts (GRBs). During the early evolution of the postmerger remnant, the state of the torus is determined by a combination of neutrino cooling and magnetically driven heating processes, so realistic models must include both effects. In this paper, we study the postmerger evolution of a magnetized black hole-neutron star binary system using the Spectral Einstein Code (SpEC) from an initial postmerger state provided by previous numerical relativity simulations. We use a finite-temperature nuclear equation of state and incorporate neutrino effects in a leakage approximation. To achieve the needed accuracy, we introduce improvements to SpEC's implementation of general-relativistic magnetohydrodynamics (MHD), including the use of cubed-sphere multipatch grids and an improved method for dealing with supersonic accretion flows where primitive variable recovery is difficult. We find that a seed magnetic field triggers a sustained source of heating, but its thermal effects are largely cancelled by the accretion and spreading of the torus from MHD-related angular momentum transport. The neutrino luminosity peaks at the start of the simulation, and then drops significantly over the first 20 ms but in roughly the same way for magnetized and nonmagnetized disks. The heating rate and disk's luminosity decrease much more slowly thereafter. These features of the evolution are insensitive to grid structure and resolution, formulation of the MHD equations, and seed field strength, although turbulent effects are not fully converged.

Dynamo action and magnetic activity during the pre-main sequence: Influence of rotation and structural changes

NASA Astrophysics Data System (ADS)

Emeriau-Viard, Constance; Brun, Allan Sacha

2017-10-01

During the PMS, structure and rotation rate of stars evolve significantly. We wish to assess the consequences of these drastic changes on stellar dynamo, internal magnetic field topology and activity level by mean of HPC simulations with the ASH code. To answer this question, we develop 3D MHD simulations that represent specific stages of stellar evolution along the PMS. We choose five different models characterized by the radius of their radiative zone following an evolutionary track, from 1 Myr to 50 Myr, computed by a 1D stellar evolution code. We introduce a seed magnetic field in the youngest model and then we spread it through all simulations. First of all, we study the consequences that the increase of rotation rate and the change of geometry of the convective zone have on the dynamo field that exists in the convective envelop. The magnetic energy increases, the topology of the magnetic field becomes more complex and the axisymmetric magnetic field becomes less predominant as the star ages. The computation of the fully convective MHD model shows that a strong dynamo develops with a ratio of magnetic to kinetic energy reaching equipartition and even super-equipartition states in the faster rotating cases. Magnetic fields resulting from our MHD simulations possess a mixed poloidal-toroidal topology with no obvious dominant component. We also study the relaxation of the vestige dynamo magnetic field within the radiative core and found that it satisfies stability criteria. Hence it does not experience a global reconfiguration and instead slowly relaxes by retaining its mixed poloidal-toroidal topology.

Coronal magnetohydrodynamic waves and oscillations: observations and quests.

PubMed

Aschwanden, Markus J

2006-02-15

Coronal seismology, a new field of solar physics that emerged over the last 5 years, provides unique information on basic physical properties of the solar corona. The inhomogeneous coronal plasma supports a variety of magnetohydrodynamics (MHD) wave modes, which manifest themselves as standing waves (MHD oscillations) and propagating waves. Here, we briefly review the physical properties of observed MHD oscillations and waves, including fast kink modes, fast sausage modes, slow (acoustic) modes, torsional modes, their diagnostics of the coronal magnetic field, and their physical damping mechanisms. We discuss the excitation mechanisms of coronal MHD oscillations and waves: the origin of the exciter, exciter propagation, and excitation in magnetic reconnection outflow regions. Finally, we consider the role of coronal MHD oscillations and waves for coronal heating, the detectability of various MHD wave types, and we estimate the energies carried in the observed MHD waves and oscillations: Alfvénic MHD waves could potentially provide sufficient energy to sustain coronal heating, while acoustic MHD waves fall far short of the required coronal heating rates.

Flow Matching Results of an MHD Energy Bypass System on a Supersonic Turbojet Engine Using the Numerical Propulsion System Simulation (NPSS) Environment

NASA Technical Reports Server (NTRS)

Benyo, Theresa L.

2011-01-01

Flow matching has been successfully achieved for an MHD energy bypass system on a supersonic turbojet engine. The Numerical Propulsion System Simulation (NPSS) environment helped perform a thermodynamic cycle analysis to properly match the flows from an inlet employing a MHD energy bypass system (consisting of an MHD generator and MHD accelerator) on a supersonic turbojet engine. Working with various operating conditions (such as the applied magnetic field, MHD generator length and flow conductivity), interfacing studies were conducted between the MHD generator, the turbojet engine, and the MHD accelerator. This paper briefly describes the NPSS environment used in this analysis. This paper further describes the analysis of a supersonic turbojet engine with an MHD generator/accelerator energy bypass system. Results from this study have shown that using MHD energy bypass in the flow path of a supersonic turbojet engine increases the useful Mach number operating range from 0 to 3.0 Mach (not using MHD) to a range of 0 to 7.0 Mach with specific net thrust range of 740 N-s/kg (at ambient Mach = 3.25) to 70 N-s/kg (at ambient Mach = 7). These results were achieved with an applied magnetic field of 2.5 Tesla and conductivity levels in a range from 2 mhos/m (ambient Mach = 7) to 5.5 mhos/m (ambient Mach = 3.5) for an MHD generator length of 3 m.