Proceedings of the US-Japan Workshop on Advanced Plasma Modeling II Held in Nagoya, Japan on March 23-27, 1987

DTIC Science & Technology

1988-03-01

Ogino : An MHD Simulation Of the Solar Wind and romer -, Piasma (Nagoya Univ.) (An MHD Model with Plasma Production) C.Z.Cheng( PPPL ) : NOVA-2: A Kinetic...and Massless Fluid Electrons W.W. Lee( PPPL ) : Gyrokinetic Particle Simulation of Finite-Beta Plasma Coffee Break (10:50-11:00) Morning Session D (11

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

Kinetic simulation of edge instability in fusion plasmas

NASA Astrophysics Data System (ADS)

Fulton, Daniel Patrick

In this work, gyrokinetic simulations in edge plasmas of both tokamaks and field reversed. configurations (FRC) have been carried out using the Gyrokinetic Toroidal Code (GTC) and A New Code (ANC) has been formulated for cross-separatrix FRC simulation. In the tokamak edge, turbulent transport in the pedestal of an H-mode DIII-D plasma is. studied via simulations of electrostatic driftwaves. Annulus geometry is used and simulations focus on two radial locations corresponding to the pedestal top with mild pressure gradient and steep pressure gradient. A reactive trapped electron instability with typical ballooning mode structure is excited in the pedestal top. At the steep gradient, the electrostatic instability exhibits unusual mode structure, peaking at poloidal angles theta=+- pi/2. Simulations find this unusual mode structure is due to steep pressure gradients in the pedestal but not due to the particular DIII-D magnetic geometry. Realistic DIII-D geometry has a stabilizing effect compared to a simple circular tokamak geometry. Driftwave instability in FRC is studied for the first time using gyrokinetic simulation. GTC. is upgraded to treat realistic equilibrium calculated by an MHD equilibrium code. Electrostatic local simulations in outer closed flux surfaces find ion-scale modes are stable due to the large ion gyroradius and that electron drift-interchange modes are excited by electron temperature gradient and bad magnetic curvature. In the scrape-off layer (SOL) ion-scale modes are excited by density gradient and bad curvature. Collisions have weak effects on instabilities both in the core and SOL. Simulation results are consistent with density fluctuation measurements in the C-2 experiment using Doppler backscattering (DBS). The critical density gradients measured by the DBS qualitatively agree with the linear instability threshold calculated by GTC simulations. One outstanding critical issue in the FRC is the interplay between turbulence in the FRC. core and SOL regions. While the magnetic flux coordinates used by GTC provide a number of computational advantages, they present unique challenges at the magnetic field separatrix. To address this limitation, a new code, capable of coupled core-SOL simulations, is formulated, implemented, and successfully verified.

Second order gyrokinetic theory for particle-in-cell codes

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

Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric

2016-08-15

The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell–Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell–Vlasov system issuedmore » from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell–Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.« less

5D Tempest simulations of kinetic edge turbulence

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Cohen, B. I.; Cohen, R. H.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G. D.; Nevins, W. M.; Rognlien, T. D.; Umansky, M. V.; Qin, H.

2006-10-01

Results are presented from the development and application of TEMPEST, a nonlinear five dimensional (3d2v) gyrokinetic continuum code. The simulation results and theoretical analysis include studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry and its relationship to plasma flow generation with zero external momentum input, including the important orbit-squeezing effect due to the large electric field flow-shear in the edge. In order to extend the code to 5D, we have formulated a set of fully nonlinear electrostatic gyrokinetic equations and a fully nonlinear gyrokinetic Poisson's equation which is valid for both neoclassical and turbulence simulations. Our 5D gyrokinetic code is built on 4D version of Tempest neoclassical code with extension to a fifth dimension in binormal direction. The code is able to simulate either a full torus or a toroidal segment. Progress on performing 5D turbulence simulations will be reported.

Analysis of JT-60SA operational scenarios

NASA Astrophysics Data System (ADS)

Garzotti, L.; Barbato, E.; Garcia, J.; Hayashi, N.; Voitsekhovitch, I.; Giruzzi, G.; Maget, P.; Romanelli, M.; Saarelma, S.; Stankiewitz, R.; Yoshida, M.; Zagórski, R.

2018-02-01

Reference scenarios for the JT-60SA tokamak have been simulated with one-dimensional transport codes to assess the stationary state of the flat-top phase and provide a profile database for further physics studies (e.g. MHD stability, gyrokinetic analysis) and diagnostics design. The types of scenario considered vary from pulsed standard H-mode to advanced non-inductive steady-state plasmas. In this paper we present the results obtained with the ASTRA, CRONOS, JINTRAC and TOPICS codes equipped with the Bohm/gyro-Bohm, CDBM and GLF23 transport models. The scenarios analysed here are: a standard ELMy H-mode, a hybrid scenario and a non-inductive steady state plasma, with operational parameters from the JT-60SA research plan. Several simulations of the scenarios under consideration have been performed with the above mentioned codes and transport models. The results from the different codes are in broad agreement and the main plasma parameters generally agree well with the zero dimensional estimates reported previously. The sensitivity of the results to different transport models and, in some cases, to the ELM/pedestal model has been investigated.

A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma

NASA Astrophysics Data System (ADS)

Kawazura, Y.; Barnes, M.

2018-05-01

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) Schekochihin et al. (2009) [9]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into AstroGK, an Eulerian δf gyrokinetics code specialized to a slab geometry Numata et al. (2010) [41]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant-Friedrichs-Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs ∼ 2√{mi /me } ∼ 100 times faster than AstroGK with a single ion species and kinetic electrons where mi /me is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron-ion temperature ratio and plasma beta.

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.

Gyrokinetic analysis of pedestal transport

NASA Astrophysics Data System (ADS)

Kotschenreuther, Mike; Liu, X.; Hatch, Dr; Zheng, Lj; Mahajan, S.; Diallo, A.; Groebner, Rj; Hubbard, Ae; Hughes, Jw; Maggi, Cf; Saarelma, S.; JET Contributors

2017-10-01

Surprisingly, basic considerations can determine which modes are responsible for pedestal energy transport (e.g., KBM, ETG, ITG, MTM etc.). Gyrokinetic simulations of experiments, and analysis of the Gyrokinetic-Maxwell equations, find that each mode type produces characteristic ratios of transport in the various channels: density, heat and impurities. This, together with the relative size of the driving sources of each channel, can strongly constrain or determine the dominant modes causing energy transport. MHD-like modes are not the dominant agent of energy transport - when the density source is weak as is often expected. Drift modes must fill this role. Detailed examination of experimental observations, including frequency and transport channel behavior, with simulations, demonstrates these points. Also see related posters by X. Liu, D.R. Hatch, and A. Blackmon. Work supported by US DOE under DE-FC02-04ER54698, DE-FG02-04ER54742 and DE-FC02-99ER54512 and by Eurofusion under Grant No. 633053.

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.

Global linear gyrokinetic particle-in-cell simulations including electromagnetic effects in shaped plasmas

NASA Astrophysics Data System (ADS)

Mishchenko, A.; Borchardt, M.; Cole, M.; Hatzky, R.; Fehér, T.; Kleiber, R.; Könies, A.; Zocco, A.

2015-05-01

We give an overview of recent developments in electromagnetic simulations based on the gyrokinetic particle-in-cell codes GYGLES and EUTERPE. We present the gyrokinetic electromagnetic models implemented in the codes and discuss further improvements of the numerical algorithm, in particular the so-called pullback mitigation of the cancellation problem. The improved algorithm is employed to simulate linear electromagnetic instabilities in shaped tokamak and stellarator plasmas, which was previously impossible for the parameters considered.

M3D-K Simulations of Beam-Driven Alfven Eigenmodes in ASDEX-U

NASA Astrophysics Data System (ADS)

Wang, Ge; Fu, Guoyong; Lauber, Philipp; Schneller, Mirjam

2013-10-01

Core-localized Alfven eigenmodes are often observed in neutral beam-heated plasma in ASDEX-U tokamak. In this work, hybrid simulations with the global kinetic/MHD hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven Alfven eigenmodes using experimental parameters and profiles of an ASDEX-U discharge. The safety factor q profile is weakly reversed with minimum q value about qmin = 3.0. The simulation results show that the n = 3 mode transits from a reversed shear Alfven eigenmode (RSAE) to a core-localized toroidal Alfven eigenmode (TAE) as qmin drops from 3.0 to 2.79, consistent with results from the stability code NOVA as well as the experimental measurement. The M3D-K results are being compared with those of the linear gyrokinetic stability code LIGKA for benchmark. The simulation results will also be compared with the measured mode frequency and mode structure. This work was funded by the Max-Planck/Princeton Center for Plasma Physics.

GTC Turbulence Simulations near H-mode Pedestal with Resonant Magnetic Perturbations

NASA Astrophysics Data System (ADS)

Shi, Lei; Ferraro, Nathaniel; Taimourzadeh, Sam; Fu, Jingyuan; Lin, Zhihong; Nazikian, Raffi

2017-10-01

Full plasma responses to Resonant Magnetic Perturbations (RMPs) as provided by the resistive MHD code M3D-C1 are implemented into Gyrokinetic Toroidal Code (GTC) to study the effect of magnetic islands and stochastic field regions on microturbulence in realistic DIII-D geometry. Electrostatic turbulence simulations with adiabatic electrons show no significant increase of the saturated ion heat conductivity in the presence of RMP-induced islands. However, electron response to zonal flow in the presence of magnetic islands and stochastic fields can drastically increase zonal flow dielectric constant for long wavelength fluctuations. Zonal flow generation can then be reduced and the microturbulence can be enhanced greatly. Furthermore, because the RMP magnetic island size is comparable to the ion banana width, electron and ion responses to these islands may be fundamentally different, which could drive non-ambipolar particles fluxes leading to changes of the radial electric field shear. This work is supported by General Atomics subcontract.

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

NASA Astrophysics Data System (ADS)

Rogers, Barrett N.; Zhu, Ben; Francisquez, Manaure

2018-05-01

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi˜1 and vanish in the long wavelength k⊥→0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ=√{β/[2 (1 +β)] }Cs/|Lp| with Cs2=p0/ρ0 for k⊥→0 and is universally unstable for 1 /Lp≠0 . We show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B02/(8 π)=constant , which renders the assumption B0'=0 inconsistent if p0'≠0 .

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Intercode comparison of gyrokinetic global electromagnetic modes

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

Görler, T., E-mail: tobias.goerler@ipp.mpg.de; Tronko, N.; Hornsby, W. A.

Aiming to fill a corresponding lack of sophisticated test cases for global electromagnetic gyrokinetic codes, a new hierarchical benchmark is proposed. Starting from established test sets with adiabatic electrons, fully gyrokinetic electrons, and electrostatic fluctuations are taken into account before finally studying the global electromagnetic micro-instabilities. Results from up to five codes involving representatives from different numerical approaches as particle-in-cell methods, Eulerian and Semi-Lagrangian are shown. By means of spectrally resolved growth rates and frequencies and mode structure comparisons, agreement can be confirmed on ion-gyro-radius scales, thus providing confidence in the correct implementation of the underlying equations.

Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence

NASA Astrophysics Data System (ADS)

Belli, Emily Ann

Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the enhancement of zonal flows with shaping, which is observed with the GS2 simulations. Finally, a local linear trial function-based gyrokinetic code is developed to aid in fast scoping studies of gyrokinetic linear stability. This code is successfully benchmarked with the full GS2 code in the collisionless, electrostatic limit, as well as in the more general electromagnetic description with higher-order Hermite basis functions.

A verification of the gyrokinetic microstability codes GEM, GYRO, and GS2

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

Bravenec, R. V.; Chen, Y.; Wan, W.

2013-10-15

A previous publication [R. V. Bravenec et al., Phys. Plasmas 18, 122505 (2011)] presented favorable comparisons of linear frequencies and nonlinear fluxes from the Eulerian gyrokinetic codes gyro[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and gs2[W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)]. The motivation was to verify the codes, i.e., demonstrate that they correctly solve the gyrokinetic-Maxwell equations. The premise was that it is highly unlikely for both codes to yield the same incorrect results. In this work, we add the Lagrangian particle-in-cell code gem[Y. Chen and S. Parker, J. Comput. Phys.more » 220, 839 (2007)] to the comparisons, not simply to add another code, but also to demonstrate that the codes' algorithms do not matter. We find good agreement of gem with gyro and gs2 for the plasma conditions considered earlier, thus establishing confidence that the codes are verified and that ongoing validation efforts for these plasma parameters are warranted.« less

Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2013-01-25

The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy.more » Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.« less

Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. I. Internal kink mode

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

McClenaghan, J.; Lin, Z.; Holod, I.

The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface.

CICART Center For Integrated Computation And Analysis Of Reconnection And Turbulence

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

Bhattacharjee, Amitava

CICART is a partnership between the University of New Hampshire (UNH) and Dartmouth College. CICART addresses two important science needs of the DoE: the basic understanding of magnetic reconnection and turbulence that strongly impacts the performance of fusion plasmas, and the development of new mathematical and computational tools that enable the modeling and control of these phenomena. The principal participants of CICART constitute an interdisciplinary group, drawn from the communities of applied mathematics, astrophysics, computational physics, fluid dynamics, and fusion physics. It is a main premise of CICART that fundamental aspects of magnetic reconnection and turbulence in fusion devices, smaller-scalemore » laboratory experiments, and space and astrophysical plasmas can be viewed from a common perspective, and that progress in understanding in any of these interconnected fields is likely to lead to progress in others. The establishment of CICART has strongly impacted the education and research mission of a new Program in Integrated Applied Mathematics in the College of Engineering and Applied Sciences at UNH by enabling the recruitment of a tenure-track faculty member, supported equally by UNH and CICART, and the establishment of an IBM-UNH Computing Alliance. The proposed areas of research in magnetic reconnection and turbulence in astrophysical, space, and laboratory plasmas include the following topics: (A) Reconnection and secondary instabilities in large high-Lundquist-number plasmas, (B) Particle acceleration in the presence of multiple magnetic islands, (C) Gyrokinetic reconnection: comparison with fluid and particle-in-cell models, (D) Imbalanced turbulence, (E) Ion heating, and (F) Turbulence in laboratory (including fusion-relevant) experiments. These theoretical studies make active use of three high-performance computer simulation codes: (1) The Magnetic Reconnection Code, based on extended two-fluid (or Hall MHD) equations, in an Adaptive Mesh Refinement (AMR) framework, (2) the Particle Simulation Code, a fully electromagnetic 3D Particle-In-Cell (PIC) code that includes a collision operator, and (3) GS2, an Eulerian, electromagnetic, kinetic code that is widely used in the fusion program, and simulates the nonlinear gyrokinetic equations, together with a self-consistent set of Maxwell’s equations.« less

Global linear gyrokinetic simulations for LHD including collisions

NASA Astrophysics Data System (ADS)

Kauffmann, K.; Kleiber, R.; Hatzky, R.; Borchardt, M.

2010-11-01

The code EUTERPE uses a Particle-In-Cell (PIC) method to solve the gyrokinetic equation globally (full radius, full flux surface) for three-dimensional equilibria calculated with VMEC. Recently this code has been extended to include multiple kinetic species and electromagnetic effects. Additionally, a pitch-angle scattering operator has been implemented in order to include collisional effects in the simulation of instabilities and to be able to simulate neoclassical transport. As a first application of this extended code we study the effects of collisions on electrostatic ion-temperature-gradient (ITG) instabilities in LHD.

Non-Maxwellian fast particle effects in gyrokinetic GENE simulations

NASA Astrophysics Data System (ADS)

Di Siena, A.; Görler, T.; Doerk, H.; Bilato, R.; Citrin, J.; Johnson, T.; Schneider, M.; Poli, E.; JET Contributors

2018-04-01

Fast ions have recently been found to significantly impact and partially suppress plasma turbulence both in experimental and numerical studies in a number of scenarios. Understanding the underlying physics and identifying the range of their beneficial effect is an essential task for future fusion reactors, where highly energetic ions are generated through fusion reactions and external heating schemes. However, in many of the gyrokinetic codes fast ions are, for simplicity, treated as equivalent-Maxwellian-distributed particle species, although it is well known that to rigorously model highly non-thermalised particles, a non-Maxwellian background distribution function is needed. To study the impact of this assumption, the gyrokinetic code GENE has recently been extended to support arbitrary background distribution functions which might be either analytical, e.g., slowing down and bi-Maxwellian, or obtained from numerical fast ion models. A particular JET plasma with strong fast-ion related turbulence suppression is revised with these new code capabilities both with linear and nonlinear gyrokinetic simulations. It appears that the fast ion stabilization tends to be less strong but still substantial with more realistic distributions, and this improves the quantitative power balance agreement with experiments.

H-mode pedestal stability and ELMs in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Mossessian, Dmitri

2002-11-01

For steady state H-mode operation, a relaxation mechanism is required to limit build-up of the edge gradient and impurity accumulation. The major relaxation mechanism seen on most of the existing tokamaks - large type I ELMs - drive high particle and energy fluxes that present a significant power load on the divertor plates. On Alcator C-Mod, however, type I ELMs are not observed. Instead, more benign mechanisms - EDA and small grassy ELMs - appear to drive enhanced particle transport at the edge of H-mode plasmas. Both have good energy confinement, no impurity accumulation, and are steady state. In EDA the edge relaxation mechanism is provided by a quasicoherent electromagnetic mode localized in the outer part of the pedestal. Non-linear gyrofluid and linear gyrokinetic simulations, as well as real geometry fluctuation modeling based on fluid equations show the presence of a coherent mode. Based on those results the observed mode is tentatively identified as resistive ballooning. At higher edge pressure gradient the mode is replaced by broadband fluctuations and small irregular ELMs are observed. Based on ideal MHD calculations that include effects of bootstrap current, these ELMs are identified as medium n coupled ideal peeling/ballooning modes. The stability threshold and modes structure of these modes are studied with recently developed linear MHD stability code ELITE and the results are compared with the observed dependence of the ELMs' character on pedestal parameters and plasma shape.

Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas (GPS - TTBP) Final Report

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

Chame, Jacqueline

2011-05-27

The goal of this project is the development of the Gyrokinetic Toroidal Code (GTC) Framework and its applications to problems related to the physics of turbulence and turbulent transport in tokamaks,. The project involves physics studies, code development, noise effect mitigation, supporting computer science efforts, diagnostics and advanced visualizations, verification and validation. Its main scientific themes are mesoscale dynamics and non-locality effects on transport, the physics of secondary structures such as zonal flows, and strongly coherent wave-particle interaction phenomena at magnetic precession resonances. Special emphasis is placed on the implications of these themes for rho-star and current scalings and formore » the turbulent transport of momentum. GTC-TTBP also explores applications to electron thermal transport, particle transport; ITB formation and cross-cuts such as edge-core coupling, interaction of energetic particles with turbulence and neoclassical tearing mode trigger dynamics. Code development focuses on major initiatives in the development of full-f formulations and the capacity to simulate flux-driven transport. In addition to the full-f -formulation, the project includes the development of numerical collision models and methods for coarse graining in phase space. Verification is pursued by linear stability study comparisons with the FULL and HD7 codes and by benchmarking with the GKV, GYSELA and other gyrokinetic simulation codes. Validation of gyrokinetic models of ion and electron thermal transport is pursed by systematic stressing comparisons with fluctuation and transport data from the DIII-D and NSTX tokamaks. The physics and code development research programs are supported by complementary efforts in computer sciences, high performance computing, and data management.« less

Detailed study of spontaneous rotation generation in diverted H-mode plasma using the full-f gyrokinetic code XGC1

NASA Astrophysics Data System (ADS)

Seo, Janghoon; Chang, C. S.; Ku, S.; Kwon, J. M.; Yoon, E. S.

2013-10-01

The Full-f gyrokinetic code XGC1 is used to study the details of toroidal momentum generation in H-mode plasma. Diverted DIII-D geometry is used, with Monte Carlo neutral particles that are recycled at the limiter wall. Nonlinear Coulomb collisions conserve particle, momentum, and energy. Gyrokinetic ions and adiabatic electrons are used in the present simulation to include the effects from ion gyrokinetic turbulence and neoclassical physics, under self-consistent radial electric field generation. Ion orbit loss physics is automatically included. Simulations show a strong co-Ip flow in the H-mode layer at outside midplane, similarly to the experimental observation from DIII-D and ASDEX-U. The co-Ip flow in the edge propagates inward into core. It is found that the strong co-Ip flow generation is mostly from neoclassical physics. On the other hand, the inward momentum transport is from turbulence physics, consistently with the theory of residual stress from symmetry breaking. Therefore, interaction between the neoclassical and turbulence physics is a key factor in the spontaneous momentum generation.

Study of no-man's land physics in the total-f gyrokinetic code XGC1

NASA Astrophysics Data System (ADS)

Ku, Seung Hoe; Chang, C. S.; Lang, J.

2014-10-01

While the ``transport shortfall'' in the ``no-man's land'' has been observed often in delta-f codes, it has not yet been observed in the global total-f gyrokinetic particle code XGC1. Since understanding the interaction between the edge and core transport appears to be a critical element in the prediction for ITER performance, understanding the no-man's land issue is an important physics research topic. Simulation results using the Holland case will be presented and the physics causing the shortfall phenomenon will be discussed. Nonlinear nonlocal interaction of turbulence, secondary flows, and transport appears to be the key.

Simulation of ion-temperature-gradient turbulence in tokamaks

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

Cohen, B I; Dimits, A M; Kim, C

Results are presented from nonlinear gyrokinetic simulations of toroidal ion temperature gradient (ITG) turbulence and transport. The gyrokinetic simulations are found to yield values of the thermal diffusivity significantly lower than gyrofluid or IFS-PPPL-model predictions. A new phenomenon of nonlinear effective critical gradients larger than the linear instability threshold gradients is observed, and is associated with undamped flux-surface-averaged shear flows. The nonlinear gyrokineic codes have passed extensive validity tests which include comparison against independent linear calculations, a series of nonlinear convergence tests, and a comparison between two independent nonlinear gyrokinetic codes. Our most realistic simulations to date have actual reconstructedmore » equilibria from experiments and a model for dilution by impurity and beam ions. These simulations highlight the need for still more physics to be included in the simulations« less

Gyrokinetic particle simulation of a field reversed configuration

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

Fulton, D. P., E-mail: dfulton@uci.edu; Lau, C. K.; Holod, I.

2016-01-15

Gyrokinetic particle simulation of the field-reversed configuration (FRC) has been developed using the gyrokinetic toroidal code (GTC). The magnetohydrodynamic equilibrium is mapped from cylindrical coordinates to Boozer coordinates for the FRC core and scrape-off layer (SOL), respectively. A field-aligned mesh is constructed for solving self-consistent electric fields using a semi-spectral solver in a partial torus FRC geometry. This new simulation capability has been successfully verified and driftwave instability in the FRC has been studied using the gyrokinetic simulation for the first time. Initial GTC simulations find that in the FRC core, the ion-scale driftwave is stabilized by the large ionmore » gyroradius. In the SOL, the driftwave is unstable on both ion and electron scales.« less

A Systematic Method for Verification and Validation of Gyrokinetic Microstability Codes

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

Bravenec, Ronald

My original proposal for the period Feb. 15, 2014 through Feb. 14, 2017 called for an integrated validation and verification effort carried out by myself with collaborators. The validation component would require experimental profile and power-balance analysis. In addition, it would require running the gyrokinetic codes varying the input profiles within experimental uncertainties to seek agreement with experiment before discounting a code as invalidated. Therefore, validation would require a major increase of effort over my previous grant periods which covered only code verification (code benchmarking). Consequently, I had requested full-time funding. Instead, I am being funded at somewhat less thanmore » half time (5 calendar months per year). As a consequence, I decided to forego the validation component and to only continue the verification efforts.« less

The next-generation ESL continuum gyrokinetic edge code

NASA Astrophysics Data System (ADS)

Cohen, R.; Dorr, M.; Hittinger, J.; Rognlien, T.; Collela, P.; Martin, D.

2009-05-01

The Edge Simulation Laboratory (ESL) project is developing continuum-based approaches to kinetic simulation of edge plasmas. A new code is being developed, based on a conservative formulation and fourth-order discretization of full-f gyrokinetic equations in parallel-velocity, magnetic-moment coordinates. The code exploits mapped multiblock grids to deal with the geometric complexities of the edge region, and utilizes a new flux limiter [P. Colella and M.D. Sekora, JCP 227, 7069 (2008)] to suppress unphysical oscillations about discontinuities while maintaining high-order accuracy elsewhere. The code is just becoming operational; we will report initial tests for neoclassical orbit calculations in closed-flux surface and limiter (closed plus open flux surfaces) geometry. It is anticipated that the algorithmic refinements in the new code will address the slow numerical instability that was observed in some long simulations with the existing TEMPEST code. We will also discuss the status and plans for physics enhancements to the new code.

Continuum Edge Gyrokinetic Theory and Simulations

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

Xu, X Q; Xiong, Z; Dorr, M R

The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regimemore » with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are for both neoclassical and turbulence simulations.« less

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

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

Xu, X Q

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. Withmore » our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.« less

Gyrokinetic projection of the divertor heat-flux width from present tokamaks to ITER

DOE PAGES

Chang, Choong Seock; Ku, Seung -Hoe; Loarte, Alberto; ...

2017-07-11

Here, the XGC1 edge gyrokinetic code is used to study the width of the heat-flux to divertor plates in attached plasma condition. The flux-driven simulation is performed until an approximate power balance is achieved between the heat-flux across the steep pedestal pressure gradient and the heat-flux on the divertor plates.

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.

Overview of Edge Simulation Laboratory (ESL)

NASA Astrophysics Data System (ADS)

Cohen, R. H.; Dorr, M.; Hittinger, J.; Rognlien, T.; Umansky, M.; Xiong, A.; Xu, X.; Belli, E.; Candy, J.; Snyder, P.; Colella, P.; Martin, D.; Sternberg, T.; van Straalen, B.; Bodi, K.; Krasheninnikov, S.

2006-10-01

The ESL is a new collaboration to build a full-f electromagnetic gyrokinetic code for tokamak edge plasmas using continuum methods. Target applications are edge turbulence and transport (neoclassical and anomalous), and edge-localized modes. Initially the project has three major threads: (i) verification and validation of TEMPEST, the project's initial (electrostatic) edge code which can be run in 4D (neoclassical and transport-timescale applications) or 5D (turbulence); (ii) design of the next generation code, which will include more complete physics (electromagnetics, fluid equation option, improved collisions) and advanced numerics (fully conservative, high-order discretization, mapped multiblock grids, adaptivity), and (iii) rapid-prototype codes to explore the issues attached to solving fully nonlinear gyrokinetics with steep radial gradiens. We present a brief summary of the status of each of these activities.

Numerical simulation support to the ESA/THOR mission

NASA Astrophysics Data System (ADS)

Valentini, F.; Servidio, S.; Perri, S.; Perrone, D.; De Marco, R.; Marcucci, M. F.; Daniele, B.; Bruno, R.; Camporeale, E.

2016-12-01

THOR is a spacecraft concept currently undergoing study phase as acandidate for the next ESA medium size mission M4. THOR has been designedto solve the longstanding physical problems of particle heating andenergization in turbulent plasmas. It will provide high resolutionmeasurements of electromagnetic fields and particle distribution functionswith unprecedented resolution, with the aim of exploring the so-calledkinetic scales. We present the numerical simulation framework which is supporting the THOR mission during the study phase. The THOR teamincludes many scientists developing and running different simulation codes(Eulerian-Vlasov, Particle-In-Cell, Gyrokinetics, Two-fluid, MHD, etc.),addressing the physics of plasma turbulence, shocks, magnetic reconnectionand so on.These numerical codes are being used during the study phase, mainly withthe aim of addressing the following points:(i) to simulate the response of real particle instruments on board THOR, byemploying an electrostatic analyser simulator which mimics the response ofthe CSW, IMS and TEA instruments to the particle velocity distributions ofprotons, alpha particle and electrons, as obtained from kinetic numericalsimulations of plasma turbulence.(ii) to compare multi-spacecraft with single-spacecraft configurations inmeasuring current density, by making use of both numerical models ofsynthetic turbulence and real data from MMS spacecraft.(iii) to investigate the validity of the Taylor hypothesis indifferent configurations of plasma turbulence

A gyrokinetic one-dimensional scrape-off layer model of an edge-localized mode heat pulse

DOE PAGES

Shi, E. L.; Hakim, A. H.; Hammett, G. W.

2015-02-03

An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. We focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode in JET. Previous work has used direct particle-in-cellequations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheathboundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. Finally, this test problem also helps illustratemore » some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.« less

Finite Larmor radius effects on the (m = 2, n = 1) cylindrical tearing mode

NASA Astrophysics Data System (ADS)

Chen, Y.; Chowdhury, J.; Parker, S. E.; Wan, W.

2015-04-01

New field solvers are developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate low-n modes. A novel discretization is developed for the ion polarization term in the gyrokinetic vorticity equation. An eigenmode analysis with finite Larmor radius effects is developed to study the linear resistive tearing mode. The mode growth rate is shown to scale with resistivity as γ ˜ η1/3, the same as the semi-collisional regime in previous kinetic treatments [Drake and Lee, Phys. Fluids 20, 1341 (1977)]. Tearing mode simulations with gyrokinetic ions are verified with the eigenmode calculation.

Toroidal Alfvénic Eigenmodes Driven by Energetic Particles with Maxwell and Slowing-down Distributions

NASA Astrophysics Data System (ADS)

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

2016-10-01

The energetic-particle (EP) driven toroidal Alfvén eigenmodes (TAEs) in a circular-shaped large aspect ratio tokamak are studied using the hybrid kinetic-MHD model in the NIMROD code, where the EPs are advanced using the δf particle-in-cell (PIC) method and their kinetic effects are coupled to the bulk plasma through moment closures. Two initial distributions of EPs, Maxwell and slowing-down, are considered. The influence of EP parameters, including density, temperature and density gradient, on the frequency and the growth rate of TAEs are obtained and benchmarked with theory and gyrokinetic simulations for the Maxwell distribution with good agreement. When the density and temperature of EPs are above certain thresholds, the transition from TAE to energetic particle modes (EPM) occurs and the mode structure also changes. Comparisons between Maxwell and slowing-down distributions in terms of EP-driven TAEs and EPMs will also be presented and discussed. Supported by the National Magnetic Confinement Fusion Science Program of China Grant Nos. 2014GB124002 and 2015GB101004, and the Natural Science Foundation of China Grant No. 11205194.

Development of a Grid-Based Gyro-Kinetic Simulation Code

NASA Astrophysics Data System (ADS)

Lapillonne, Xavier; Brunetti, Maura; Tran, Trach-Minh; Brunner, Stephan

2006-10-01

A grid-based semi-Lagrangian code using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)] in a cylindrical system. This 4-dim code, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this code are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-Lagrangian frame. On the other hand, fully Eulerian schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the E xB drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.

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

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

Implementation of non-axisymmetric mesh system in the gyrokinetic PIC code (XGC) for Stellarators

NASA Astrophysics Data System (ADS)

Moritaka, Toseo; Hager, Robert; Cole, Micheal; Chang, Choong-Seock; Lazerson, Samuel; Ku, Seung-Hoe; Ishiguro, Seiji

2017-10-01

Gyrokinetic simulation is a powerful tool to investigate turbulent and neoclassical transports based on the first-principles of plasma kinetics. The gyrokinetic PIC code XGC has been developed for integrated simulations that cover the entire region of Tokamaks. Complicated field line and boundary structures should be taken into account to demonstrate edge plasma dynamics under the influence of X-point and vessel components. XGC employs gyrokinetic Poisson solver on unstructured triangle mesh to deal with this difficulty. We introduce numerical schemes newly developed for XGC simulation in non-axisymmetric Stellarator geometry. Triangle meshes in each poloidal plane are defined by PEST poloidal angle in the VMEC equilibrium so that they have the same regular structure in the straight field line coordinate. Electric charge of marker particle is distributed to the triangles specified by the field-following projection to the neighbor poloidal planes. 3D spline interpolation in a cylindrical mesh is also used to obtain equilibrium magnetic field at the particle position. These schemes capture the anisotropic plasma dynamics and resulting potential structure with high accuracy. The triangle meshes can smoothly connect to unstructured meshes in the edge region. We will present the validation test in the core region of Large Helical Device and discuss about future challenges toward edge simulations.

Investigation of the transport shortfall in Alcator C-Mod L-mode plasmas

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

Howard, N. T.; White, A. E.; Greenwald, M.

2013-03-15

A so-called 'transport shortfall,' where ion and electron heat fluxes and turbulence are underpredicted by gyrokinetic codes, has been robustly identified in DIII-D L-mode plasmas for {rho}>0.55[T. L. Rhodes et al., Nucl. Fusion 51(6), 063022 (2011); and C. Holland et al., Phys. Plasmas 16(5), 052301 (2009)]. To probe the existence of a transport shortfall across different tokamaks, a dedicated scan of auxiliary heated L-mode discharges in Alcator C-Mod are studied in detail with nonlinear gyrokinetic simulations for the first time. Two discharges, only differing by the amount of auxiliary heating are investigated using both linear and nonlinear simulation of themore » GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)]. Nonlinear gyrokinetic simulation of the low and high input power discharges reveals a discrepancy between simulation and experiment in only the electron heat flux channel of the low input power discharge. However, both discharges demonstrate excellent agreement in the ion heat flux channel, and the high input power discharge demonstrates simultaneous agreement with experiment in both the electron and ion heat flux channels. A summary of linear and nonlinear gyrokinetic results and a discussion of possible explanations for the agreement/disagreement in each heat flux channel is presented.« less

Advances in stellarator gyrokinetics

NASA Astrophysics Data System (ADS)

Helander, P.; Bird, T.; Jenko, F.; Kleiber, R.; Plunk, G. G.; Proll, J. H. E.; Riemann, J.; Xanthopoulos, P.

2015-05-01

Recent progress in the gyrokinetic theory of stellarator microinstabilities and turbulence simulations is summarized. The simulations have been carried out using two different gyrokinetic codes, the global particle-in-cell code EUTERPE and the continuum code GENE, which operates in the geometry of a flux tube or a flux surface but is local in the radial direction. Ion-temperature-gradient (ITG) and trapped-electron modes are studied and compared with their counterparts in axisymmetric tokamak geometry. Several interesting differences emerge. Because of the more complicated structure of the magnetic field, the fluctuations are much less evenly distributed over each flux surface in stellarators than in tokamaks. Instead of covering the entire outboard side of the torus, ITG turbulence is localized to narrow bands along the magnetic field in regions of unfavourable curvature, and the resulting transport depends on the normalized gyroradius ρ* even in radially local simulations. Trapped-electron modes can be significantly more stable than in typical tokamaks, because of the spatial separation of regions with trapped particles from those with bad magnetic curvature. Preliminary non-linear simulations in flux-tube geometry suggest differences in the turbulence levels in Wendelstein 7-X and a typical tokamak.

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.

Four-Dimensional Continuum Gyrokinetic Code: Neoclassical Simulation of Fusion Edge Plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2005-10-01

We are developing a continuum gyrokinetic code, TEMPEST, to simulate edge plasmas. Our code represents velocity space via a grid in equilibrium energy and magnetic moment variables, and configuration space via poloidal magnetic flux and poloidal angle. The geometry is that of a fully diverted tokamak (single or double null) and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The 4-dimensional code includes kinetic electrons and ions, and electrostatic field-solver options, and simulates neoclassical transport. The present implementation is a Method of Lines approach where spatial finite-differences (higher order upwinding) and implicit time advancement are used. We present results of initial verification and validation studies: transition from collisional to collisionless limits of parallel end-loss in the scrape-off layer, self-consistent electric field, and the effect of the real X-point geometry and edge plasma conditions on the standard neoclassical theory, including a comparison of our 4D code with other kinetic neoclassical codes and experiments.

Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations

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

Deng, Zhao, E-mail: zhao.deng@foxmail.com; Waltz, R. E.

2015-05-15

This paper presents numerical simulations of the nonlinear cyclokinetic equations in the cyclotron harmonic representation [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Simulations are done with a local flux-tube geometry and with the parallel motion and variation suppressed using a newly developed rCYCLO code. Cyclokinetic simulations dynamically follow the high-frequency ion gyro-phase motion which is nonlinearly coupled into the low-frequency drift-waves possibly interrupting and suppressing gyro-averaging and increasing the transport over gyrokinetic levels. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the breakdown of gyrokinetics at high turbulence levels is quantitatively testedmore » over a range of relative ion cyclotron frequency 10 < Ω*{sup  }< 100 where Ω*{sup  }= 1/ρ*, and ρ* is the relative ion gyroradius. The gyrokinetic linear mode rates closely match the cyclokinetic low-frequency rates for Ω*{sup  }> 5. Gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω*{sup  }≥ 50) and low turbulence level as required. Cyclokinetic transport is found to be lower than gyrokinetic transport at high turbulence levels and low-Ω* values with stable ion cyclotron (IC) modes. The gyrokinetic approximation is found to break down when the density perturbations exceed 20%. For cyclokinetic simulations with sufficiently unstable IC modes and sufficiently low Ω*{sup  }∼ 10, the high-frequency component of cyclokinetic transport level can exceed the gyrokinetic transport level. However, the low-frequency component of the cyclokinetic transport and turbulence level does not exceed that of gyrokinetics. At higher and more physically relevant Ω*{sup  }≥ 50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport and turbulence level is still smaller than that of gyrokinetics. Thus, the cyclokinetic simulations do not account for the so-called “L-mode near edge short fall” seen in some low-frequency gyrokinetic transport and turbulence simulations.« less

A basic plasma test for gyrokinetics: GDC turbulence in LAPD

NASA Astrophysics Data System (ADS)

Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.

2017-02-01

Providing an important step towards validating gyrokinetics under comparatively little-explored conditions, simulations of pressure-gradient-driven plasma turbulence in the Large Plasma Device (LAPD) are compared with experimental observations. The corresponding signatures confirm the existence of a novel regime of turbulence, based on the recently-discovered gradient-driven drift coupling (GDC) instability, which is thus confirmed as a candidate mechanism for turbulence in basic, space and astrophysical plasmas. Despite the limitations of flux-tube gyrokinetics for this scenario, when accounting for box size scaling by applying a scalar factor η =6, agreement between simulations and experiment improves to within a factor of two for key observables: compressional magnetic, density, and temperature fluctuations, both in amplitude and structure. Thus, a first, strong indication is presented that the GDC instability seen in gyrokinetics appears to operate in the experiment and that the essential instability physics is present in the numerical model. Overall, the gyrokinetic framework and its numerical implementation in the Gene code therefore perform well for LAPD plasmas very different from their brethren in fusion experiments.

Mode Analyses of Gyrokinetic Simulations of Plasma Microturbulence

NASA Astrophysics Data System (ADS)

Hatch, David R.

This thesis presents analysis of the excitation and role of damped modes in gyrokinetic simulations of plasma microturbulence. In order to address this question, mode decompositions are used to analyze gyrokinetic simulation data. A mode decomposition can be constructed by projecting a nonlinearly evolved gyrokinetic distribution function onto a set of linear eigenmodes, or alternatively by constructing a proper orthogonal decomposition of the distribution function. POD decompositions are used to examine the role of damped modes in saturating ion temperature gradient driven turbulence. In order to identify the contribution of different modes to the energy sources and sinks, numerical diagnostics for a gyrokinetic energy quantity were developed for the GENE code. The use of these energy diagnostics in conjunction with POD mode decompositions demonstrates that ITG turbulence saturates largely through dissipation by damped modes at the same perpendicular spatial scales as those of the driving instabilities. This defines a picture of turbulent saturation that is very different from both traditional hydrodynamic scenarios and also many common theories for the saturation of plasma turbulence. POD mode decompositions are also used to examine the role of subdominant modes in causing magnetic stochasticity in electromagnetic gyrokinetic simulations. It is shown that the magnetic stochasticity, which appears to be ubiquitous in electromagnetic microturbulence, is caused largely by subdominant modes with tearing parity. The application of higher-order singular value decomposition (HOSVD) to the full distribution function from gyrokinetic simulations is presented. This is an effort to demonstrate the ability to characterize and extract insight from a very large, complex, and high-dimensional data-set - the 5-D (plus time) gyrokinetic distribution function.

Finite Larmor radius effects on the (m = 2, n = 1) cylindrical tearing mode

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

Chen, Y.; Chowdhury, J.; Parker, S. E.

2015-04-15

New field solvers are developed in the gyrokinetic code GEM [Chen and Parker, J. Comput. Phys. 220, 839 (2007)] to simulate low-n modes. A novel discretization is developed for the ion polarization term in the gyrokinetic vorticity equation. An eigenmode analysis with finite Larmor radius effects is developed to study the linear resistive tearing mode. The mode growth rate is shown to scale with resistivity as γ ∼ η{sup 1∕3}, the same as the semi-collisional regime in previous kinetic treatments [Drake and Lee, Phys. Fluids 20, 1341 (1977)]. Tearing mode simulations with gyrokinetic ions are verified with the eigenmode calculation.

PREFACE: Theory of Fusion Plasmas, 13th Joint Varenna-Lausanne International Workshop (2012)

NASA Astrophysics Data System (ADS)

Garbet, Xavier; Sauter, Olivier

2012-12-01

The 2012 joint Varenna-Lausanne international workshop on the theory of fusion plasmas has been very fruitful. A broad variety of topics were addressed, as usual covering turbulence, MHD, edge physic, RF wave heating and a taste of astrophysics. Moreover the scope of the meeting was extended this year to include the physics of materials and diagnostics for burning plasmas. This evolution reflects the complexity of problems at hand in fusion, in particular in the context of ITER construction. Long-standing problems without immediate consequences have sometimes become an urgent matter in that context. One may quote for instance the choice of plasma facing components or the design of control systems. Another characteristic of the meeting is the interplay between various domains of plasma physics. For instance MHD modes are now currently investigated with gyrokinetic codes, kinetic effects are more and more included in MHD stability analysis, and turbulence is now accounted for in wave propagation problems. This is the proof of cross-fertilization and it is certainly a healthy sign in our community. Finally introducing some novelty in the programme does not prevent us from respecting the traditions of the meeting. As usual a good deal of the presentations were dedicated to numerical simulations. Combining advanced numerical techniques with elaborated analytical theory is certainly a trademark of the Varenna-Lausanne conference, which was respected again this year. The quality and size of the scientific production is illustrated by the 26 papers which appear in the present volume of Journal of Physics: Conference Series, all refereed. We would also like to mention another set of 20 papers to be published in Plasma Physics and Controlled Fusion. We hope the readers will enjoy this special issue of JPCS and the one to come in PPCF. Xavier Garbet and Olivier Sauter October 26, 2012

Coupling MHD and PIC models in 2 dimensions

NASA Astrophysics Data System (ADS)

Daldorff, L.; Toth, G.; Sokolov, I.; Gombosi, T. I.; Lapenta, G.; Brackbill, J. U.; Markidis, S.; Amaya, J.

2013-12-01

Even for extended fluid plasma models, like Hall, anisotropic ion pressure and multi fluid MHD, there are still many plasma phenomena that are not well captured. For this reason, we have coupled the Implicit Particle-In-Cell (iPIC3D) code with the BATSRUS global MHD code. The PIC solver is applied in a part of the computational domain, for example, in the vicinity of reconnection sites, and overwrites the MHD solution. On the other hand, the fluid solver provides the boundary conditions for the PIC code. To demonstrate the use of the coupled codes for magnetospheric applications, we perform a 2D magnetosphere simulation, where BATSRUS solves for Hall MHD in the whole domain except for the tail reconnection region, which is handled by iPIC3D.

Verification of a magnetic island in gyro-kinetics by comparison with analytic theory

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

Zarzoso, D., E-mail: david.zarzoso-fernandez@polytechnique.org; Casson, F. J.; Poli, E.

A rotating magnetic island is imposed in the gyrokinetic code GKW, when finite differences are used for the radial direction, in order to develop the predictions of analytic tearing mode theory and understand its limitations. The implementation is verified against analytics in sheared slab geometry with three numerical tests that are suggested as benchmark cases for every code that imposes a magnetic island. The convergence requirements to properly resolve physics around the island separatrix are investigated. In the slab geometry, at low magnetic shear, binormal flows inside the island can drive Kelvin-Helmholtz instabilities which prevent the formation of the steadymore » state for which the analytic theory is formulated.« less

A fast low-to-high confinement mode bifurcation dynamics in the boundary-plasma gyrokinetic code XGC1

NASA Astrophysics Data System (ADS)

Ku, S.; Chang, C. S.; Hager, R.; Churchill, R. M.; Tynan, G. R.; Cziegler, I.; Greenwald, M.; Hughes, J.; Parker, S. E.; Adams, M. F.; D'Azevedo, E.; Worley, P.

2018-05-01

A fast edge turbulence suppression event has been simulated in the electrostatic version of the gyrokinetic particle-in-cell code XGC1 in a realistic diverted tokamak edge geometry under neutral particle recycling. The results show that the sequence of turbulent Reynolds stress followed by neoclassical ion orbit-loss driven together conspire to form the sustaining radial electric field shear and to quench turbulent transport just inside the last closed magnetic flux surface. The main suppression action is located in a thin radial layer around ψN≃0.96 -0.98 , where ψN is the normalized poloidal flux, with the time scale ˜0.1 ms.

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.

Fully-kinetic Ion Simulation of Global Electrostatic Turbulent Transport in C-2U

NASA Astrophysics Data System (ADS)

Fulton, Daniel; Lau, Calvin; Bao, Jian; Lin, Zhihong; Tajima, Toshiki; TAE Team

2017-10-01

Understanding the nature of particle and energy transport in field-reversed configuration (FRC) plasmas is a crucial step towards an FRC-based fusion reactor. The C-2U device at Tri Alpha Energy (TAE) achieved macroscopically stable plasmas and electron energy confinement time which scaled favorably with electron temperature. This success led to experimental and theoretical investigation of turbulence in C-2U, including gyrokinetic ion simulations with the Gyrokinetic Toroidal Code (GTC). A primary objective of TAE's new C-2W device is to explore transport scaling in an extended parameter regime. In concert with the C-2W experimental campaign, numerical efforts have also been extended in A New Code (ANC) to use fully-kinetic (FK) ions and a Vlasov-Poisson field solver. Global FK ion simulations are presented. Future code development is also discussed.

Simulations of 4D edge transport and dynamics using the TEMPEST gyro-kinetic code

NASA Astrophysics Data System (ADS)

Rognlien, T. D.; Cohen, B. I.; Cohen, R. H.; Dorr, M. R.; Hittinger, J. A. F.; Kerbel, G. D.; Nevins, W. M.; Xiong, Z.; Xu, X. Q.

2006-10-01

Simulation results are presented for tokamak edge plasmas with a focus on the 4D (2r,2v) option of the TEMPEST continuum gyro-kinetic code. A detailed description of a variety of kinetic simulations is reported, including neoclassical radial transport from Coulomb collisions, electric field generation, dynamic response to perturbations by geodesic acoustic modes, and parallel transport on open magnetic-field lines. Comparison is made between the characteristics of the plasma solutions on closed and open magnetic-field line regions separated by a magnetic separatrix, and simple physical models are used to qualitatively explain the differences observed in mean flow and electric-field generation. The status of extending the simulations to 5D turbulence will be summarized. The code structure used in this ongoing project is also briefly described, together with future plans.

Progress with the COGENT Edge Kinetic Code: Collision operator options

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Compton, J. C.; ...

2012-06-27

In this study, COGENT is a continuum gyrokinetic code for edge plasmas being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of the fourth order conservative discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. It is written in v∥-μ (parallel velocity – magnetic moment) velocity coordinates, and making use of the gyrokinetic Poisson equation for the calculation of a self-consistent electric potential. In the present manuscript we report on the implementation and initial testing of a succession of increasingly detailed collision operator options, including a simple drag-diffusion operatormore » in the parallel velocity space, Lorentz collisions, and a linearized model Fokker-Planck collision operator conserving momentum and energy (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

Comparisons of 'Identical' Simulations by the Eulerian Gyrokinetic Codes GS2 and GYRO

NASA Astrophysics Data System (ADS)

Bravenec, R. V.; Ross, D. W.; Candy, J.; Dorland, W.; McKee, G. R.

2003-10-01

A major goal of the fusion program is to be able to predict tokamak transport from first-principles theory. To this end, the Eulerian gyrokinetic code GS2 was developed years ago and continues to be improved [1]. Recently, the Eulerian code GYRO was developed [2]. These codes are not subject to the statistical noise inherent to particle-in-cell (PIC) codes, and have been very successful in treating electromagnetic fluctuations. GS2 is fully spectral in the radial coordinate while GYRO uses finite-differences and ``banded" spectral schemes. To gain confidence in nonlinear simulations of experiment with these codes, ``apples-to-apples" comparisons (identical profile inputs, flux-tube geometry, two species, etc.) are first performed. We report on a series of linear and nonlinear comparisons (with overall agreement) including kinetic electrons, collisions, and shaped flux surfaces. We also compare nonlinear simulations of a DIII-D discharge to measurements of not only the fluxes but also the turbulence parameters. [1] F. Jenko, et al., Phys. Plasmas 7, 1904 (2000) and refs. therein. [2] J. Candy, J. Comput. Phys. 186, 545 (2003).

Simulating the effects of stellarator geometry on gyrokinetic drift-wave turbulence

NASA Astrophysics Data System (ADS)

Baumgaertel, Jessica Ann

Nuclear fusion is a clean, safe form of energy with abundant fuel. In magnetic fusion energy (MFE) experiments, the plasma fuel is confined by magnetic fields at very high temperatures and densities. One fusion reactor design is the non-axisymmetric, torus-shaped stellarator. Its fully-3D fields have advantages over the simpler, better-understood axisymmetric tokamak, including the ability to optimize magnetic configurations for desired properties, such as lower transport (longer confinement time). Turbulence in the plasma can break MFE confinement. While turbulent transport is known to cause a significant amount of heat loss in tokamaks, it is a new area of research in stellarators. Gyrokinetics is a good mathematical model of the drift-wave instabilities that cause turbulence. Multiple gyrokinetic turbulence codes that had great success comparing to tokamak experiments are being converted for use with stellarator geometry. This thesis describes such adaptations of the gyrokinetic turbulence code, GS2. Herein a new computational grid generator and upgrades to GS2 itself are described, tested, and benchmarked against three other gyrokinetic codes. Using GS2, detailed linear studies using the National Compact Stellarator Experiment (NCSX) geometry were conducted. The first compares stability in two equilibria with different β=(plasma pressure)/(magnetic pressure). Overall, the higher β case was more stable than the lower β case. As high β is important for MFE experiments, this is encouraging. The second compares NCSX linear stability to a tokamak case. NCSX was more stable with a 20% higher critical temperature gradient normalized by the minor radius, suggesting that the fusion power might be enhanced by ˜ 50%. In addition, the first nonlinear, non-axisymmetric GS2 simulations are presented. Finally, linear stability of two locations in a W7-AS plasma were compared. The experimentally-measured parameters used were from a W7-AS shot in which measured heat fluxes match neoclassical theory predictions at inner radii, but are too large for neoclassical predictions at outer radii. Results from GS2 linear simulations show that the outer location has higher gyrokinetic instability growth rates than at the inner one. Mixing-length estimates of the heat flux are within a factor of 3 of the experimental measurements, indicating that gyrokinetic turbulence may be responsible for the higher transport measured by the experiment in the outer regions. Future nonlinear simulations can explore this question in more detail. This work is supported by the Princeton Plasma Physics Laboratory, which is operated by Princeton University for the U.S. Department of Energy under Contract No. DE-AC02-09CH11466, and the SciDAC Center for the Study of Plasma Microturbulence.

Parametric study of potential early commercial power plants Task 3-A MHD cost analysis

NASA Technical Reports Server (NTRS)

1983-01-01

The development of costs for an MHD Power Plant and the comparison of these costs to a conventional coal fired power plant are reported. The program is divided into three activities: (1) code of accounts review; (2) MHD pulverized coal power plant cost comparison; (3) operating and maintenance cost estimates. The scope of each NASA code of account item was defined to assure that the recently completed Task 3 capital cost estimates are consistent with the code of account scope. Improvement confidence in MHD plant capital cost estimates by identifying comparability with conventional pulverized coal fired (PCF) power plant systems is undertaken. The basis for estimating the MHD plant operating and maintenance costs of electricity is verified.

A fast low-to-high confinement mode bifurcation dynamics in the boundary-plasma gyrokinetic code XGC1

DOE PAGES

Ku, S.; Chang, C. S.; Hager, R.; ...

2018-04-18

Here, a fast edge turbulence suppression event has been simulated in the electrostatic version of the gyrokinetic particle-in-cell code XGC1 in a realistic diverted tokamak edge geometry under neutral particle recycling. The results show that the sequence of turbulent Reynolds stress followed by neoclassical ion orbit-loss driven together conspire to form the sustaining radial electric field shear and to quench turbulent transport just inside the last closed magnetic flux surface. As a result, the main suppression action is located in a thin radial layer around ψ N≃0.96–0.98, where ψ N is the normalized poloidal flux, with the time scale ~0.1more » ms.« less

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

DOE PAGES

Dorf, M. A.; Cohen, R. H.; Dorr, M.; ...

2014-06-20

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas.more » The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)« less

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

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.

Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations

NASA Astrophysics Data System (ADS)

Hause, Benjamin; Parker, Scott

2012-10-01

We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the GPU accelerator compiler directives. We have implemented the GPU acceleration on a Core I7 gaming PC with a NVIDIA GTX 580 GPU. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. Optimization strategies and comparisons between DIRAC and the gaming PC will be presented. We will also discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.

An Efficient Method for Verifying Gyrokinetic Microstability Codes

NASA Astrophysics Data System (ADS)

Bravenec, R.; Candy, J.; Dorland, W.; Holland, C.

2009-11-01

Benchmarks for gyrokinetic microstability codes can be developed through successful ``apples-to-apples'' comparisons among them. Unlike previous efforts, we perform the comparisons for actual discharges, rendering the verification efforts relevant to existing experiments and future devices (ITER). The process requires i) assembling the experimental analyses at multiple times, radii, discharges, and devices, ii) creating the input files ensuring that the input parameters are faithfully translated code-to-code, iii) running the codes, and iv) comparing the results, all in an organized fashion. The purpose of this work is to automate this process as much as possible: At present, a python routine is used to generate and organize GYRO input files from TRANSP or ONETWO analyses. Another routine translates the GYRO input files into GS2 input files. (Translation software for other codes has not yet been written.) Other python codes submit the multiple GYRO and GS2 jobs, organize the results, and collect them into a table suitable for plotting. (These separate python routines could easily be consolidated.) An example of the process -- a linear comparison between GYRO and GS2 for a DIII-D discharge at multiple radii -- will be presented.

Sharp Interface Algorithm for Large Density Ratio Incompressible Multiphase Magnetohydrodynamic Flows

DTIC Science & Technology

2013-01-01

experiments on liquid metal jets . The FronTier-MHD code has been used for simulations of liquid mercury targets for the proposed muon collider...validated through the comparison with experiments on liquid metal jets . The FronTier-MHD code has been used for simulations of liquid mercury targets...FronTier-MHD code have been performed using experimental and theoretical studies of liquid mercury jets in magnetic fields. Experimental studies of a

Extension of the XGC code for global gyrokinetic simulations in stellarator geometry

NASA Astrophysics Data System (ADS)

Cole, Michael; Moritaka, Toseo; White, Roscoe; Hager, Robert; Ku, Seung-Hoe; Chang, Choong-Seock

2017-10-01

In this work, the total-f, gyrokinetic particle-in-cell code XGC is extended to treat stellarator geometries. Improvements to meshing tools and the code itself have enabled the first physics studies, including single particle tracing and flux surface mapping in the magnetic geometry of the heliotron LHD and quasi-isodynamic stellarator Wendelstein 7-X. These have provided the first successful test cases for our approach. XGC is uniquely placed to model the complex edge physics of stellarators. A roadmap to such a global confinement modeling capability will be presented. Single particle studies will include the physics of energetic particles' global stochastic motions and their effect on confinement. Good confinement of energetic particles is vital for a successful stellarator reactor design. These results can be compared in the core region with those of other codes, such as ORBIT3d. In subsequent work, neoclassical transport and turbulence can then be considered and compared to results from codes such as EUTERPE and GENE. After sufficient verification in the core region, XGC will move into the stellarator edge region including the material wall and neutral particle recycling.

Full-f version of GENE for turbulence in open-field-line systems

NASA Astrophysics Data System (ADS)

Pan, Q.; Told, D.; Shi, E. L.; Hammett, G. W.; Jenko, F.

2018-06-01

Unique properties of plasmas in the tokamak edge, such as large amplitude fluctuations and plasma-wall interactions in the open-field-line regions, require major modifications of existing gyrokinetic codes originally designed for simulating core turbulence. To this end, the global version of the 3D2V gyrokinetic code GENE, so far employing a δf-splitting technique, is extended to simulate electrostatic turbulence in straight open-field-line systems. The major extensions are the inclusion of the velocity-space nonlinearity, the development of a conducting-sheath boundary, and the implementation of the Lenard-Bernstein collision operator. With these developments, the code can be run as a full-f code and can handle particle loss to and reflection from the wall. The extended code is applied to modeling turbulence in the Large Plasma Device (LAPD), with a reduced mass ratio and a much lower collisionality. Similar to turbulence in a tokamak scrape-off layer, LAPD turbulence involves collisions, parallel streaming, cross-field turbulent transport with steep profiles, and particle loss at the parallel boundary.

Gyrokinetic Simulations of Transport Scaling and Structure

NASA Astrophysics Data System (ADS)

Hahm, Taik Soo

2001-10-01

There is accumulating evidence from global gyrokinetic particle simulations with profile variations and experimental fluctuation measurements that microturbulence, with its time-averaged eddy size which scales with the ion gyroradius, can cause ion thermal transport which deviates from the gyro-Bohm scaling. The physics here can be best addressed by large scale (rho* = rho_i/a = 0.001) full torus gyrokinetic particle-in-cell turbulence simulations using our massively parallel, general geometry gyrokinetic toroidal code with field-aligned mesh. Simulation results from device-size scans for realistic parameters show that ``wave transport'' mechanism is not the dominant contribution for this Bohm-like transport and that transport is mostly diffusive driven by microscopic scale fluctuations in the presence of self-generated zonal flows. In this work, we analyze the turbulence and zonal flow statistics from simulations and compare to nonlinear theoretical predictions including the radial decorrelation of the transport events by zonal flows and the resulting probability distribution function (PDF). In particular, possible deviation of the characteristic radial size of transport processes from the time-averaged radial size of the density fluctuation eddys will be critically examined.

A new method for computing the gyrocenter orbit in the tokamak configuration

NASA Astrophysics Data System (ADS)

Xu, Yingfeng

2013-10-01

Gyrokinetic theory is an important tool for studying the long-time behavior of magnetized plasmas in Tokamaks. The gyrocenter trajectory determined by the gyrocenter equations of motion can be computed by using a special kind of the Lie-transform perturbation method. The corresponding Lie-transform called I-transform makes that the transformed equations of motion have the same form as the unperturbed ones. The gyrocenter trajectory in short time is divided into two parts. One is along the unperturbed orbit. The other one, which is related to perturbation, is determined by the I-transform generating vector. The numerical gyrocenter orbit code based on this new method has been developed in the tokamak configuration and benchmarked with the other orbit code in some simple cases. Furthermore, it is clearly demonstrated that this new method for computing gyrocenter orbit is equivalent to the gyrocenter Hamilton equations of motion up to the second order in timestep. The new method can be applied to the gyrokinetic simulation. The gyrocenter orbit of the unperturbed part determined by the equilibrium fields can be computed previously in the gyrokinetic simulation, and the corresponding time consumption is neglectable.

Impact of centrifugal drifts on ion turbulent transport

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

Belli, Emily A.; Candy, J.

Here, the influence of sonic toroidal rotation on gyrokinetic stability and transport is studied, with important implications for heavy impurity dynamics. When centrifugal drifts and electrostatic trapping corrections are included, significant modifications to the calculated transport of heavy impurities are observed. These high-rotation corrections add to the standard Coriolis drift and toroidal rotation shear drive which are normally included in gyrokinetics. Yet, because of their complexity, centrifugal and electrostatic trapping terms (quadratic in the main ion Mach number) are not generally included in gyrokinetic codes. In this work, we explore the implications of using reduced descriptions of the rotational physics.more » For heavy impurities such as tungsten, cross terms due to the centrifugal force can dominate the rotation dynamics, and neglecting them is shown to lead to large errors in the impurity particle flux.« less

Impact of centrifugal drifts on ion turbulent transport

DOE PAGES

Belli, Emily A.; Candy, J.

2018-03-01

Here, the influence of sonic toroidal rotation on gyrokinetic stability and transport is studied, with important implications for heavy impurity dynamics. When centrifugal drifts and electrostatic trapping corrections are included, significant modifications to the calculated transport of heavy impurities are observed. These high-rotation corrections add to the standard Coriolis drift and toroidal rotation shear drive which are normally included in gyrokinetics. Yet, because of their complexity, centrifugal and electrostatic trapping terms (quadratic in the main ion Mach number) are not generally included in gyrokinetic codes. In this work, we explore the implications of using reduced descriptions of the rotational physics.more » For heavy impurities such as tungsten, cross terms due to the centrifugal force can dominate the rotation dynamics, and neglecting them is shown to lead to large errors in the impurity particle flux.« less

Influence of a large-scale field on energy dissipation in magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Zhdankin, Vladimir; Boldyrev, Stanislav; Mason, Joanne

2017-07-01

In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimension kinetic models, gyrokinetics, etc., which make theoretical calculations easier and numerical computations cheaper. Recently, however, it has become clear that the turbulent energy dissipation is concentrated in the regions of strong magnetic field variations. A significant fraction of the energy dissipation may be localized in very small volumes corresponding to the boundaries between strongly magnetized domains. In these regions, the reduced models are not applicable. This has important implications for studies of particle heating and acceleration in magnetic plasma turbulence. The goal of this work is to systematically investigate the relationship between local magnetic field variations and magnetic energy dissipation, and to understand its implications for modelling energy dissipation in realistic turbulent plasmas.

Tempest simulations of kinetic GAM mode and neoclassical turbulence

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Dimits, A. M.

2007-11-01

TEMPEST is a nonlinear five dimensional (3d2v) gyrokinetic continuum code for studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry. The 4D TEMPEST code correctly produces frequency, collisionless damping of GAM and zonal flow with fully nonlinear Boltzmann electrons in homogeneous plasmas. For large q=4 to 9, the Tempest simulations show that a series of resonance at higher harmonics v||=φGqR0/n with n=4 become effective. The TEMPEST simulation also shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual with neoclassical transport, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude. Our 5D gyrokinetic code is built on 4D Tempest neoclassical code with extension to a fifth dimension in toroidal direction and with 3D domain decompositions. Progress on performing 5D neoclassical turbulence simulations will be reported.

Calculations of key magnetospheric parameters using the isotropic and anisotropic SPSU global MHD code

NASA Astrophysics Data System (ADS)

Samsonov, Andrey; Gordeev, Evgeny; Sergeev, Victor

2017-04-01

As it was recently suggested (e.g., Gordeev et al., 2015), the global magnetospheric configuration can be characterized by a set of key parameters, such as the magnetopause distance at the subsolar point and on the terminator plane, the magnetic field in the magnetotail lobe and the plasma sheet thermal pressure, the cross polar cap electric potential drop and the total field-aligned current. For given solar wind conditions, the values of these parameters can be obtained from both empirical models and global MHD simulations. We validate the recently developed global MHD code SPSU-16 using the key magnetospheric parameters mentioned above. The code SPSU-16 can calculate both the isotropic and anisotropic MHD equations. In the anisotropic version, we use the modified double-adiabatic equations in which the T⊥/T∥ (the ratio of perpendicular to parallel thermal pressures) has been bounded from above by the mirror and ion-cyclotron thresholds and from below by the firehose threshold. The results of validation for the SPSU-16 code well agree with the previously published results of other global codes. Some key parameters coincide in the isotropic and anisotropic MHD simulations, but some are different.

Collisional tests and an extension of the TEMPEST continuum gyrokinetic code

NASA Astrophysics Data System (ADS)

Cohen, R. H.; Dorr, M.; Hittinger, J.; Kerbel, G.; Nevins, W. M.; Rognlien, T.; Xiong, Z.; Xu, X. Q.

2006-04-01

An important requirement of a kinetic code for edge plasmas is the ability to accurately treat the effect of colllisions over a broad range of collisionalities. To test the interaction of collisions and parallel streaming, TEMPEST has been compared with published analytic and numerical (Monte Carlo, bounce-averaged Fokker-Planck) results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential and mirror ratio, and the required velocity space resolution is modest. We also describe progress toward extension of (4-dimensional) TEMPEST into a ``kinetic edge transport code'' (a kinetic counterpart of UEDGE). The extension includes averaging of the gyrokinetic equations over fast timescales and approximating the averaged quadratic terms by diffusion terms which respect the boundaries of inaccessable regions in phase space. F. Najmabadi, R.W. Conn and R.H. Cohen, Nucl. Fusion 24, 75 (1984); T.D. Rognlien and T.A. Cutler, Nucl. Fusion 20, 1003 (1980).

Tempest Neoclassical Simulation of Fusion Edge Plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Cohen, B. I.; Cohen, R. H.; Dorr, M.; Hittinger, J.; Kerbel, G. D.; Nevins, W. M.; Rognlien, T. D.

2006-04-01

We are developing a continuum gyrokinetic full-F code, TEMPEST, to simulate edge plasmas. The geometry is that of a fully diverted tokamak and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The code, presently 4-dimensional (2D2V), includes kinetic ions and electrons, a gyrokinetic Poisson solver for electric field, and the nonlinear Fokker-Planck collision operator. Here we present the simulation results of neoclassical transport with Boltzmann electrons. In a large aspect ratio circular geometry, excellent agreement is found for neoclassical equilibrium with parallel flows in the banana regime without a temperature gradient. In divertor geometry, it is found that the endloss of particles and energy induces pedestal-like density and temperature profiles inside the magnetic separatrix and parallel flow stronger than the neoclassical predictions in the SOL. The impact of the X-point divertor geometry on the self-consistent electric field and geo-acoustic oscillations will be reported. We will also discuss the status of extending TEMPEST into a 5-D code.

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma

DOE PAGES

Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.; ...

2017-05-29

Here, five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currentsmore » to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.« less

Gyrokinetic particle simulations of the effects of compressional magnetic perturbations on drift-Alfvenic instabilities in tokamaks

DOE PAGES

Dong, Ge; Bao, Jian; Bhattacharjee, Amitava; ...

2017-08-10

The compressional component of magnetic perturbation δB- || to can play an important role in drift-Alfvenic instabilities in tokamaks, especially as the plasma β increases (β is the ratio of kinetic pressure to magnetic pressure). In this work, we have formulated a gyrokinetic particle simulation model incorporating δB- ||, and verified the model in kinetic Alfven wave simulations using the Gyrokinetic Toroidal Code in slab geometry. Simulations of drift-Alfvenic instabilities in tokamak geometry shows that the kinetic ballooning mode (KBM) growth rate decreases more than 20% when δB- || is neglected for β e = 0.02, and that δB- ||more » to has stabilizing effects on the ion temperature gradient instability, but negligible effects on the collisionless trapped electron mode. Lastly, the KBM growth rate decreases about 15% when equilibrium current is neglected.« less

Transport and discrete particle noise in gyrokinetic simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Lee, W. W.

2006-10-01

We present results from our recent investigations regarding the effects of discrete particle noise on the long-time behavior and transport properties of gyrokinetic particle-in-cell simulations. It is found that the amplitude of nonlinearly saturated drift waves is unaffected by discreteness-induced noise in plasmas whose behavior is dominated by a single mode in the saturated state. We further show that the scaling of this noise amplitude with particle count is correctly predicted by the fluctuation-dissipation theorem, even though the drift waves have driven the plasma from thermal equilibrium. As well, we find that the long-term behavior of the saturated system is unaffected by discreteness-induced noise even when multiple modes are included. Additional work utilizing a code with both total-f and δf capabilities is also presented, as part of our efforts to better understand the long- time balance between entropy production, collisional dissipation, and particle/heat flux in gyrokinetic plasmas.

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

DOE PAGES

Mikkelsen, D. R.; Howard, N. T.; White, A. E.; ...

2018-04-25

Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

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

Mikkelsen, D. R.; Howard, N. T.; White, A. E.

Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

Modified NASA-Lewis chemical equilibrium code for MHD applications

NASA Technical Reports Server (NTRS)

Sacks, R. A.; Geyer, H. K.; Grammel, S. J.; Doss, E. D.

1979-01-01

A substantially modified version of the NASA-Lewis Chemical Equilibrium Code was recently developed. The modifications were designed to extend the power and convenience of the Code as a tool for performing combustor analysis for MHD systems studies. The effect of the programming details is described from a user point of view.

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.

Gyrokinetic simulations and experiment

NASA Astrophysics Data System (ADS)

Ross, David W.; Bravenec, R. V.; Dorland, W.

2002-11-01

Nonlinear gyrokinetic simulations with the code GS2 have been carried out in an effort to predict transport fluxes and fluctuation levels in the tokamaks DIII-D and Alcator C-Mod.(W. Dorland et al. in Fusion Energy 2000 (International Atomic Energy Agency, Vienna, 2000).)^,( W. Ross and W. Dorland, submitted to Phys. Plasmas (2002).) These simulations account for full electron dynamics and, in some instances, electromagnetic waves.( D. W. Ross, W. Dorland, and B. N. Rogers, Bull. Am. Phys. Soc. 46, 115 (2001).) Here, some issues of the necessary resolution, precision and wave number range are examined in connection with the experimental comparisons and parameter scans.

Analysis and optimization of gyrokinetic toroidal simulations on homogenous and heterogenous platforms

DOE PAGES

Ibrahim, Khaled Z.; Madduri, Kamesh; Williams, Samuel; ...

2013-07-18

The Gyrokinetic Toroidal Code (GTC) uses the particle-in-cell method to efficiently simulate plasma microturbulence. This paper presents novel analysis and optimization techniques to enhance the performance of GTC on large-scale machines. We introduce cell access analysis to better manage locality vs. synchronization tradeoffs on CPU and GPU-based architectures. Finally, our optimized hybrid parallel implementation of GTC uses MPI, OpenMP, and NVIDIA CUDA, achieves up to a 2× speedup over the reference Fortran version on multiple parallel systems, and scales efficiently to tens of thousands of cores.

MHD code using multi graphical processing units: SMAUG+

NASA Astrophysics Data System (ADS)

Gyenge, N.; Griffiths, M. K.; Erdélyi, R.

2018-01-01

This paper introduces the Sheffield Magnetohydrodynamics Algorithm Using GPUs (SMAUG+), an advanced numerical code for solving magnetohydrodynamic (MHD) problems, using multi-GPU systems. Multi-GPU systems facilitate the development of accelerated codes and enable us to investigate larger model sizes and/or more detailed computational domain resolutions. This is a significant advancement over the parent single-GPU MHD code, SMAUG (Griffiths et al., 2015). Here, we demonstrate the validity of the SMAUG + code, describe the parallelisation techniques and investigate performance benchmarks. The initial configuration of the Orszag-Tang vortex simulations are distributed among 4, 16, 64 and 100 GPUs. Furthermore, different simulation box resolutions are applied: 1000 × 1000, 2044 × 2044, 4000 × 4000 and 8000 × 8000 . We also tested the code with the Brio-Wu shock tube simulations with model size of 800 employing up to 10 GPUs. Based on the test results, we observed speed ups and slow downs, depending on the granularity and the communication overhead of certain parallel tasks. The main aim of the code development is to provide massively parallel code without the memory limitation of a single GPU. By using our code, the applied model size could be significantly increased. We demonstrate that we are able to successfully compute numerically valid and large 2D MHD problems.

Core turbulence behavior moving from ion-temperature-gradient regime towards trapped-electron-mode regime in the ASDEX Upgrade tokamak and comparison with gyrokinetic simulation

NASA Astrophysics Data System (ADS)

Happel, T.; Navarro, A. Bañón; Conway, G. D.; Angioni, C.; Bernert, M.; Dunne, M.; Fable, E.; Geiger, B.; Görler, T.; Jenko, F.; McDermott, R. M.; Ryter, F.; Stroth, U.

2015-03-01

Additional electron cyclotron resonance heating (ECRH) is used in an ion-temperature-gradient instability dominated regime to increase R / L Te in order to approach the trapped-electron-mode instability regime. The radial ECRH deposition location determines to a large degree the effect on R / L Te . Accompanying scale-selective turbulence measurements at perpendicular wavenumbers between k⊥ = 4-18 cm-1 (k⊥ρs = 0.7-4.2) show a pronounced increase of large-scale density fluctuations close to the ECRH radial deposition location at mid-radius, along with a reduction in phase velocity of large-scale density fluctuations. Measurements are compared with results from linear and non-linear flux-matched gyrokinetic (GK) simulations with the gyrokinetic code GENE. Linear GK simulations show a reduction of phase velocity, indicating a pronounced change in the character of the dominant instability. Comparing measurement and non-linear GK simulation, as a central result, agreement is obtained in the shape of radial turbulence level profiles. However, the turbulence intensity is increasing with additional heating in the experiment, while gyrokinetic simulations show a decrease.

Development of a fully implicit particle-in-cell scheme for gyrokinetic electromagnetic turbulence simulation in XGC1

NASA Astrophysics Data System (ADS)

Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team

2016-10-01

The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.

Nonlinear 3D visco-resistive MHD modeling of fusion plasmas: a comparison between numerical codes

NASA Astrophysics Data System (ADS)

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

2008-11-01

Fluid plasma models (and, in particular, the MHD model) are extensively used in the theoretical description of laboratory and astrophysical plasmas. We present here a successful benchmark between two nonlinear, three-dimensional, compressible visco-resistive MHD codes. One is the fully implicit, finite volume code PIXIE3D [1,2], which is characterized by many attractive features, notably the generalized curvilinear formulation (which makes the code applicable to different geometries) and the possibility to include in the computation the energy transport equation and the extended MHD version of Ohm's law. In addition, the parallel version of the code features excellent scalability properties. Results from this code, obtained in cylindrical geometry, are compared with those produced by the semi-implicit cylindrical code SpeCyl, which uses finite differences radially, and spectral formulation in the other coordinates [3]. Both single and multi-mode simulations are benchmarked, regarding both reversed field pinch (RFP) and ohmic tokamak magnetic configurations. [1] L. Chacon, Computer Physics Communications 163, 143 (2004). [2] L. Chacon, Phys. Plasmas 15, 056103 (2008). [3] S. Cappello, Plasma Phys. Control. Fusion 46, B313 (2004) & references therein.

Numerical Analysis of 2-D and 3-D MHD Flows Relevant to Fusion Applications

DOE PAGES

Khodak, Andrei

2017-08-21

Here, the analysis of many fusion applications such as liquid-metal blankets requires application of computational fluid dynamics (CFD) methods for electrically conductive liquids in geometrically complex regions and in the presence of a strong magnetic field. A current state of the art general purpose CFD code allows modeling of the flow in complex geometric regions, with simultaneous conjugated heat transfer analysis in liquid and surrounding solid parts. Together with a magnetohydrodynamics (MHD) capability, the general purpose CFD code will be a valuable tool for the design and optimization of fusion devices. This paper describes an introduction of MHD capability intomore » the general purpose CFD code CFX, part of the ANSYS Workbench. The code was adapted for MHD problems using a magnetic induction approach. CFX allows introduction of user-defined variables using transport or Poisson equations. For MHD adaptation of the code three additional transport equations were introduced for the components of the magnetic field, in addition to the Poisson equation for electric potential. The Lorentz force is included in the momentum transport equation as a source term. Fusion applications usually involve very strong magnetic fields, with values of the Hartmann number of up to tens of thousands. In this situation a system of MHD equations become very rigid with very large source terms and very strong variable gradients. To increase system robustness, special measures were introduced during the iterative convergence process, such as linearization using source coefficient for momentum equations. The MHD implementation in general purpose CFD code was tested against benchmarks, specifically selected for liquid-metal blanket applications. Results of numerical simulations using present implementation closely match analytical solutions for a Hartmann number of up to 1500 for a 2-D laminar flow in the duct of square cross section, with conducting and nonconducting walls. Results for a 3-D test case are also included.« less

Numerical Analysis of 2-D and 3-D MHD Flows Relevant to Fusion Applications

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

Khodak, Andrei

Here, the analysis of many fusion applications such as liquid-metal blankets requires application of computational fluid dynamics (CFD) methods for electrically conductive liquids in geometrically complex regions and in the presence of a strong magnetic field. A current state of the art general purpose CFD code allows modeling of the flow in complex geometric regions, with simultaneous conjugated heat transfer analysis in liquid and surrounding solid parts. Together with a magnetohydrodynamics (MHD) capability, the general purpose CFD code will be a valuable tool for the design and optimization of fusion devices. This paper describes an introduction of MHD capability intomore » the general purpose CFD code CFX, part of the ANSYS Workbench. The code was adapted for MHD problems using a magnetic induction approach. CFX allows introduction of user-defined variables using transport or Poisson equations. For MHD adaptation of the code three additional transport equations were introduced for the components of the magnetic field, in addition to the Poisson equation for electric potential. The Lorentz force is included in the momentum transport equation as a source term. Fusion applications usually involve very strong magnetic fields, with values of the Hartmann number of up to tens of thousands. In this situation a system of MHD equations become very rigid with very large source terms and very strong variable gradients. To increase system robustness, special measures were introduced during the iterative convergence process, such as linearization using source coefficient for momentum equations. The MHD implementation in general purpose CFD code was tested against benchmarks, specifically selected for liquid-metal blanket applications. Results of numerical simulations using present implementation closely match analytical solutions for a Hartmann number of up to 1500 for a 2-D laminar flow in the duct of square cross section, with conducting and nonconducting walls. Results for a 3-D test case are also included.« less

Parallel filtering in global gyrokinetic simulations

NASA Astrophysics Data System (ADS)

Jolliet, S.; McMillan, B. F.; Villard, L.; Vernay, T.; Angelino, P.; Tran, T. M.; Brunner, S.; Bottino, A.; Idomura, Y.

2012-02-01

In this work, a Fourier solver [B.F. McMillan, S. Jolliet, A. Bottino, P. Angelino, T.M. Tran, L. Villard, Comp. Phys. Commun. 181 (2010) 715] is implemented in the global Eulerian gyrokinetic code GT5D [Y. Idomura, H. Urano, N. Aiba, S. Tokuda, Nucl. Fusion 49 (2009) 065029] and in the global Particle-In-Cell code ORB5 [S. Jolliet, A. Bottino, P. Angelino, R. Hatzky, T.M. Tran, B.F. McMillan, O. Sauter, K. Appert, Y. Idomura, L. Villard, Comp. Phys. Commun. 177 (2007) 409] in order to reduce the memory of the matrix associated with the field equation. This scheme is verified with linear and nonlinear simulations of turbulence. It is demonstrated that the straight-field-line angle is the coordinate that optimizes the Fourier solver, that both linear and nonlinear turbulent states are unaffected by the parallel filtering, and that the k∥ spectrum is independent of plasma size at fixed normalized poloidal wave number.

Gyrofluid theory and simulation of electromagnetic turbulence and transport in tokamak plasmas

NASA Astrophysics Data System (ADS)

Snyder, Philip Benjamin

1999-11-01

Turbulence and transport in toroidal plasmas is studied via the development of an electromagnetic gyrofluid model, and its implementation in realistic nonlinear simulations. This work extends earlier electrostatic gyrofluid models to include magnetic fluctuations and non-adiabatic passing electron dynamics. A new set of electron fluid equations is derived from the drift kinetic equation, via an expansion in the electron-ion mass ratio. These electron equations include descriptions of linear and nonlinear drift motion, Landau damping, and electron-ion collisions. Ion moment equations are derived from the electromagnetic gyrokinetic equation, and the gyrokinetic Poisson's Equation and Ampere's Law close the system. The model is benchmarked with linear gyrokinetic calculations, and good agreement is found for both the finite-β ion temperature gradient (ITG) and kinetic Alfvén ballooning (KBM) instabilities. Nonlinear simulations of ITG and KBM-driven turbulence are performed in toroidal flux tube geometry at a range of values of plasma β, and electromagnetic effects are found to significantly impact turbulent heat and particle transport. At low values of β, transport is reduced, as expected due to the finite-β stabilization of the ITG mode. However, as β approaches the Ideal-MHD stability threshold, transport can increase. In the presence of dissipation provided by a model of electron Landau damping and electron-ion collisions, this transport increase can be quite dramatic. Finally, the results of the simulations are compared to tokamak experiments, and encouraging agreement is found with measured density and temperature fluctuation spectra. Direct comparisons of transport fluxes reveal that electromagnetic effects are important at characteristic edge parameters, bringing predicted fluxes more closely in line with observations.

"Magnetic Reconnection Code: Applications to Sawtooth Oscillations, Error-Field Induced Islands, and the Dynamo Effect" - Final Technical Report

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

Fitzpatrick, Richard

2007-09-24

Dr. Fitzpatrick has written an MHD code in order to investigate the interaction of tearing modes with flow and external magnetic perturbations, which has been successfully benchmarked against both linear and nonlinear theory and used to investigate error-field penetration in flowing plasmas. The same code was used to investigate the so-called Taylor problem. He employed the University of Chicago's FLASH code to further investigate the Taylor problem, discovering a new aspect of the problem. Dr. Fitzpatrick has written a 2-D Hall MHD code and used it to investigate the collisionless Taylor problem. Dr. Waelbroeck has performed an investigation of themore » scaling of the error-field penetration threshold in collisionless plasmas. Paul Watson and Dr. Fitzpatrick have written a fully-implicit extended-MHD code using the PETSC framework. Five publications have resulted from this grant work.« less

The CRONOS Code for Astrophysical Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Kissmann, R.; Kleimann, J.; Krebl, B.; Wiengarten, T.

2018-06-01

We describe the magnetohydrodynamics (MHD) code CRONOS, which has been used in astrophysics and space-physics studies in recent years. CRONOS has been designed to be easily adaptable to the problem in hand, where the user can expand or exchange core modules or add new functionality to the code. This modularity comes about through its implementation using a C++ class structure. The core components of the code include solvers for both hydrodynamical (HD) and MHD problems. These problems are solved on different rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. CRONOS uses a finite-volume description with different approximate Riemann solvers that can be chosen at runtime. Here, we describe the implementation of the code with a view toward its ongoing development. We illustrate the code’s potential through several (M)HD test problems and some astrophysical applications.

Features of Discontinuous Galerkin Algorithms in Gkeyll, and Exponentially-Weighted Basis Functions

NASA Astrophysics Data System (ADS)

Hammett, G. W.; Hakim, A.; Shi, E. L.

2016-10-01

There are various versions of Discontinuous Galerkin (DG) algorithms that have interesting features that could help with challenging problems of higher-dimensional kinetic problems (such as edge turbulence in tokamaks and stellarators). We are developing the gyrokinetic code Gkeyll based on DG methods. Higher-order methods do more FLOPS to extract more information per byte, thus reducing memory and communication costs (which are a bottleneck for exascale computing). The inner product norm can be chosen to preserve energy conservation with non-polynomial basis functions (such as Maxwellian-weighted bases), which alternatively can be viewed as a Petrov-Galerkin method. This allows a full- F code to benefit from similar Gaussian quadrature employed in popular δf continuum gyrokinetic codes. We show some tests for a 1D Spitzer-Härm heat flux problem, which requires good resolution for the tail. For two velocity dimensions, this approach could lead to a factor of 10 or more speedup. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.

Gyrokinetic micro-turbulence simulations on the NERSC 16-way SMP IBM SP computer: experiences and performance results

NASA Astrophysics Data System (ADS)

Ethier, Stephane; Lin, Zhihong

2001-10-01

Earlier this year, the National Energy Research Scientific Computing center (NERSC) took delivery of the second most powerful computer in the world. With its 2,528 processors running at a peak performance of 1.5 GFlops, this IBM SP machine has a theoretical performance of almost 3.8 TFlops. To efficiently harness such computing power in one single code is not an easy task and requires a good knowledge of the computer's architecture. Here we present the steps that we followed to improve our gyrokinetic micro-turbulence code GTC in order to take advantage of the new 16-way shared memory nodes of the NERSC IBM SP. Performance results are shown as well as details about the improved mixed-mode MPI-OpenMP model that we use. The enhancements to the code allowed us to tackle much bigger problem sizes, getting closer to our goal of simulating an ITER-size tokamak with both kinetic ions and electrons.(This work is supported by DOE Contract No. DE-AC02-76CH03073 (PPPL), and in part by the DOE Fusion SciDAC Project.)

Advances in continuum kinetic and gyrokinetic simulations of turbulence on open-field line geometries

NASA Astrophysics Data System (ADS)

Hakim, Ammar; Shi, Eric; Juno, James; Bernard, Tess; Hammett, Greg

2017-10-01

For weakly collisional (or collisionless) plasmas, kinetic effects are required to capture the physics of micro-turbulence. We have implemented solvers for kinetic and gyrokinetic equations in the computational plasma physics framework, Gkeyll. We use a version of discontinuous Galerkin scheme that conserves energy exactly. Plasma sheaths are modeled with novel boundary conditions. Positivity of distribution functions is maintained via a reconstruction method, allowing robust simulations that continue to conserve energy even with positivity limiters. We have performed a large number of benchmarks, verifying the accuracy and robustness of our code. We demonstrate the application of our algorithm to two classes of problems (a) Vlasov-Maxwell simulations of turbulence in a magnetized plasma, applicable to space plasmas; (b) Gyrokinetic simulations of turbulence in open-field-line geometries, applicable to laboratory plasmas. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.

Full-f XGC1 gyrokinetic study of improved ion energy confinement from impurity stabilization of ITG turbulence

NASA Astrophysics Data System (ADS)

Kim, Kyuho; Kwon, Jae-Min; Chang, C. S.; Seo, Janghoon; Ku, S.; Choe, W.

2017-06-01

Flux-driven full-f gyrokinetic simulations are performed to study carbon impurity effects on the ion temperature gradient (ITG) turbulence and ion thermal transport in a toroidal geometry. Employing the full-f gyrokinetic code XGC1, both main ions and impurities are evolved self-consistently including turbulence and neoclassical physics. It is found that the carbon impurity profile self-organizes to form an inwardly peaked density profile, which weakens the ITG instabilities and reduces the overall fluctuations and ion thermal transport. A stronger reduction appears in the low frequency components of the fluctuations. The global structure of E × B flow also changes, resulting in the reduction of global avalanche like transport events in the impure plasma. Detailed properties of impurity transport are also studied, and it is revealed that both the inward neoclassical pinch and the outward turbulent transport are equally important in the formation of the steady state impurity profile.

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).

Gyrokinetic simulation of edge blobs and divertor heat-load footprint

NASA Astrophysics Data System (ADS)

Chang, C. S.; Ku, S.; Hager, R.; Churchill, M.; D'Azevedo, E.; Worley, P.

2015-11-01

Gyrokinetic study of divertor heat-load width Lq has been performed using the edge gyrokinetic code XGC1. Both neoclassical and electrostatic turbulence physics are self-consistently included in the simulation with fully nonlinear Fokker-Planck collision operation and neutral recycling. Gyrokinetic ions and drift kinetic electrons constitute the plasma in realistic magnetic separatrix geometry. The electron density fluctuations from nonlinear turbulence form blobs, as similarly seen in the experiments. DIII-D and NSTX geometries have been used to represent today's conventional and tight aspect ratio tokamaks. XGC1 shows that the ion neoclassical orbit dynamics dominates over the blob physics in setting Lq in the sample DIII-D and NSTX plasmas, re-discovering the experimentally observed 1/Ip type scaling. Magnitude of Lq is in the right ballpark, too, in comparison with experimental data. However, in an ITER standard plasma, XGC1 shows that the negligible neoclassical orbit excursion effect makes the blob dynamics to dominate Lq. Differently from Lq 1mm (when mapped back to outboard midplane) as was predicted by simple-minded extrapolation from the present-day data, XGC1 shows that Lq in ITER is about 1 cm that is somewhat smaller than the average blob size. Supported by US DOE and the INCITE program.

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.

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

NASA Astrophysics Data System (ADS)

González-Avilés, J. J.; Cruz-Osorio, A.; Lora-Clavijo, F. D.; Guzmán, F. S.

2015-12-01

We present a new 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 centres on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvénic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the Harten-Lax-van Leer-Einfeldt (HLLE) flux formula combined with Minmod, MC, and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.

Solving free-plasma-boundary problems with the SIESTA MHD code

NASA Astrophysics Data System (ADS)

Sanchez, R.; Peraza-Rodriguez, H.; Reynolds-Barredo, J. M.; Tribaldos, V.; Geiger, J.; Hirshman, S. P.; Cianciosa, M.

2017-10-01

SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for 3D magnetic configurations. It is an iterative code that uses the solution obtained by the VMEC code to provide a background coordinate system and an initial guess of the solution. The final solution that SIESTA finds can exhibit magnetic islands and stochastic regions. In its original implementation, SIESTA addressed only fixed-boundary problems. This fixed boundary condition somewhat restricts its possible applications. In this contribution we describe a recent extension of SIESTA that enables it to address free-plasma-boundary situations, opening up the possibility of investigating problems with SIESTA in which the plasma boundary is perturbed either externally or internally. As an illustration, the extended version of SIESTA is applied to a configuration of the W7-X stellarator.

The STD/MHD codes - Comparison of analyses with experiments at AEDC/HPDE, Reynolds Metal Co., and Hercules, Inc. [for MHD generator flows

NASA Technical Reports Server (NTRS)

Vetter, A. A.; Maxwell, C. D.; Swean, T. F., Jr.; Demetriades, S. T.; Oliver, D. A.; Bangerter, C. D.

1981-01-01

Data from sufficiently well-instrumented, short-duration experiments at AEDC/HPDE, Reynolds Metal Co., and Hercules, Inc., are compared to analyses with multidimensional and time-dependent simulations with the STD/MHD computer codes. These analyses reveal detailed features of major transient events, severe loss mechanisms, and anomalous MHD behavior. In particular, these analyses predicted higher-than-design voltage drops, Hall voltage overshoots, and asymmetric voltage drops before the experimental data were available. The predictions obtained with these analyses are in excellent agreement with the experimental data and the failure predictions are consistent with the experiments. The design of large, high-interaction or advanced MHD experiments will require application of sophisticated, detailed and comprehensive computational procedures in order to account for the critical mechanisms which led to the observed behavior in these experiments.

A correlation electron cyclotron emission diagnostic and the importance of multifield fluctuation measurements for testing nonlinear gyrokinetic turbulence simulations.

PubMed

White, A E; Schmitz, L; Peebles, W A; Carter, T A; Rhodes, T L; Doyle, E J; Gourdain, P A; Hillesheim, J C; Wang, G; Holland, C; Tynan, G R; Austin, M E; McKee, G R; Shafer, M W; Burrell, K H; Candy, J; DeBoo, J C; Prater, R; Staebler, G M; Waltz, R E; Makowski, M A

2008-10-01

A correlation electron cyclotron emission (CECE) diagnostic has been used to measure local, turbulent fluctuations of the electron temperature in the core of DIII-D plasmas. This paper describes the hardware and testing of the CECE diagnostic and highlights the importance of measurements of multifield fluctuation profiles for the testing and validation of nonlinear gyrokinetic codes. The process of testing and validating such codes is critical for extrapolation to next-step fusion devices. For the first time, the radial profiles of electron temperature and density fluctuations are compared to nonlinear gyrokinetic simulations. The CECE diagnostic at DIII-D uses correlation radiometry to measure the rms amplitude and spectrum of the electron temperature fluctuations. Gaussian optics are used to produce a poloidal spot size with w(o) approximately 1.75 cm in the plasma. The intermediate frequency filters and the natural linewidth of the EC emission determine the radial resolution of the CECE diagnostic, which can be less than 1 cm. Wavenumbers resolved by the CECE diagnostic are k(theta) < or = 1.8 cm(-1) and k(r) < or = 4 cm(-1), relevant for studies of long-wavelength turbulence associated with the trapped electron mode and the ion temperature gradient mode. In neutral beam heated L-mode plasmas, core electron temperature fluctuations in the region 0.5 < r/a < 0.9, increase with radius from approximately 0.5% to approximately 2%, similar to density fluctuations that are measured simultaneously with beam emission spectroscopy. After incorporating "synthetic diagnostics" to effectively filter the code output, the simulations reproduce the characteristics of the turbulence and transport at one radial location r/a = 0.5, but not at a second location, r/a = 0.75. These results illustrate that measurements of the profiles of multiple fluctuating fields can provide a significant constraint on the turbulence models employed by the code.

Flux tube gyrokinetic simulations of the edge pedestal

NASA Astrophysics Data System (ADS)

Parker, Scott; Wan, Weigang; Chen, Yang

2011-10-01

The linear instabilities of DIII-D H-mode pedestal are studied with gyrokinetic micro-turbulence simulations. The simulation code GEM is an electromagnetic δf code with global tokamak geometry in the form of Miller equilibrium. Local flux tube simulations are carried out for multiple positions of two DIII-D profiles: shot #98889 and shot #131997. Near the top of the pedestal, the instability is clearly ITG. The dominant instability of the pedestal appears at the steep gradient region, and it is identified as a low frequency mode mostly driven by electron temperature gradient. The mode propagates along the electron diamagnetic direction for low n and may propagate along the ion direction for high n. At some positions near the steep gradient region, an ion instability is found which shows some characteristics of kinetic ballooning mode (KBM). These results will be compared to the results of E. Wang et al. and D. Fulton et al. in the same session. We thank R. Groebner and P. Snyder for providing experimental profiles and helpful discussions.

Calculation of the Neoclassical Radial Electric Field using a Gyrokinetic δ f Code

NASA Astrophysics Data System (ADS)

Lewandowski, J. L. V.; Boozer, A.; Williams, J.; Lin, Z.; Zarnstorff, M.

2000-10-01

The calculation of the radial electric field in stellarator devices is an important issue in neoclassical transport. The radial electric field, which is also related to the formation of transport barriers, can affect the anomalous transport. In stellarator configurations which depart only weakly from axi-symmetry, a direct Monte Carlo calculations of the radial electric is difficult due to the large statistical fluctuations. We present a novel method based on the evaluation of the perpendicular ( p_⊥ ) and parallel ( p_|| ) pressures. The variation of widehatp ≡ ( p_|| + p_⊥ ) /2 on the magnetic surface provides a low-noise calculation of the radial electric field. The low-noise method has been implemented in a three-dimensional gyro-kinetic particle code [1]. The calculation of the radial electric field for the National Compact Stellarator Experiment [2] will be presented. [ 1 ] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang, and R. White Science 281, 1835 (1998). [ 2 ] A. Reiman et al, invited talk (this conference).

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.

Global magnetosphere simulations using constrained-transport Hall-MHD with CWENO reconstruction

NASA Astrophysics Data System (ADS)

Lin, L.; Germaschewski, K.; Maynard, K. M.; Abbott, S.; Bhattacharjee, A.; Raeder, J.

2013-12-01

We present a new CWENO (Centrally-Weighted Essentially Non-Oscillatory) reconstruction based MHD solver for the OpenGGCM global magnetosphere code. The solver was built using libMRC, a library for creating efficient parallel PDE solvers on structured grids. The use of libMRC gives us access to its core functionality of providing an automated code generation framework which takes a user provided PDE right hand side in symbolic form to generate an efficient, computer architecture specific, parallel code. libMRC also supports block-structured adaptive mesh refinement and implicit-time stepping through integration with the PETSc library. We validate the new CWENO Hall-MHD solver against existing solvers both in standard test problems as well as in global magnetosphere simulations.

Helioseismic Constraints on New Solar Models from the MoSEC Code

NASA Technical Reports Server (NTRS)

Elliott, J. R.

1998-01-01

Evolutionary solar models are computed using a new stellar evolution code, MOSEC (Modular Stellar Evolution Code). This code has been designed with carefully controlled truncation errors in order to achieve a precision which reflects the increasingly accurate determination of solar interior structure by helioseismology. A series of models is constructed to investigate the effects of the choice of equation of state (OPAL or MHD-E, the latter being a version of the MHD equation of state recalculated by the author), the inclusion of helium and heavy-element settling and diffusion, and the inclusion of a simple model of mixing associated with the solar tachocline. The neutrino flux predictions are discussed, while the sound speed of the computed models is compared to that of the sun via the latest inversion of SOI-NMI p-mode frequency data. The comparison between models calculated with the OPAL and MHD-E equations of state is particularly interesting because the MHD-E equation of state includes relativistic effects for the electrons, whereas neither MHD nor OPAL do. This has a significant effect on the sound speed of the computed model, worsening the agreement with the solar sound speed. Using the OPAL equation of state and including the settling and diffusion of helium and heavy elements produces agreement in sound speed with the helioseismic results to within about +.-0.2%; the inclusion of mixing slightly improves the agreement.

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

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.

Multi-Fluid Simulations of a Coupled Ionosphere-Magnetosphere System

NASA Astrophysics Data System (ADS)

Gombosi, T. I.; Glocer, A.; Toth, G.; Ridley, A. J.; Sokolov, I. V.; de Zeeuw, D. L.

2008-05-01

In the last decade we have developed the Space Weather Modeling Framework (SWMF) that efficiently couples together different models describing the interacting regions of the space environment. Many of these domain models (such as the global solar corona, the inner heliosphere or the global magnetosphere) are based on MHD and are represented by our multiphysics code, BATS-R-US. BATS-R-US can solve the equations of "standard" ideal MHD, but it can also go beyond this first approximation. It can solve resistive MHD, Hall MHD, semi-relativistic MHD (that keeps the displacement current), multispecies (different ion species have different continuity equations) and multifluid (all ion species have separate continuity, momentum and energy equations) MHD. Recently we added two-fluid Hall MHD (solving the electron and ion energy equations separately) and are working on an extended magnetohydrodynamics model with anisotropic pressures. Ionosheric outflow can be a significant contributor to the plasma population of the magnetosphere during active geomagnetic conditions. This talk will present preliminary results of our simulations when we couple a new field- aligned multi-fluid polar wind code to the Ionosphere Electrodynamics (IE), and Global Magnetosphere (GM) components of the SWMF. We use multi-species and multi-fluid MHD to track the resulting plasma composition in the magnetosphere.

Magnetohydrodynamic modelling of exploding foil initiators

NASA Astrophysics Data System (ADS)

Neal, William

2015-06-01

Magnetohydrodynamic (MHD) codes are currently being developed, and used, to predict the behaviour of electrically-driven flyer-plates. These codes are of particular interest to the design of exploding foil initiator (EFI) detonators but there is a distinct lack of comparison with high-fidelity experimental data. This study aims to compare a MHD code with a collection of temporally and spatially resolved diagnostics including PDV, dual-axis imaging and streak imaging. The results show the code's excellent representation of the flyer-plate launch and highlight features within the experiment that the model fails to capture.

Gyrokinetic modeling of impurity peaking in JET H-mode plasmas

NASA Astrophysics Data System (ADS)

Manas, P.; Camenen, Y.; Benkadda, S.; Weisen, H.; Angioni, C.; Casson, F. J.; Giroud, C.; Gelfusa, M.; Maslov, M.

2017-06-01

Quantitative comparisons are presented between gyrokinetic simulations and experimental values of the carbon impurity peaking factor in a database of JET H-modes during the carbon wall era. These plasmas feature strong NBI heating and hence high values of toroidal rotation and corresponding gradient. Furthermore, the carbon profiles present particularly interesting shapes for fusion devices, i.e., hollow in the core and peaked near the edge. Dependencies of the experimental carbon peaking factor ( R / L nC ) on plasma parameters are investigated via multilinear regressions. A marked correlation between R / L nC and the normalised toroidal rotation gradient is observed in the core, which suggests an important role of the rotation in establishing hollow carbon profiles. The carbon peaking factor is then computed with the gyrokinetic code GKW, using a quasi-linear approach, supported by a few non-linear simulations. The comparison of the quasi-linear predictions to the experimental values at mid-radius reveals two main regimes. At low normalised collisionality, ν * , and T e / T i < 1 , the gyrokinetic simulations quantitatively recover experimental carbon density profiles, provided that rotodiffusion is taken into account. In contrast, at higher ν * and T e / T i > 1 , the very hollow experimental carbon density profiles are never predicted by the simulations and the carbon density peaking is systematically over estimated. This points to a possible missing ingredient in this regime.

Microinstabilities in the pedestal region

NASA Astrophysics Data System (ADS)

Dickinson, David; Dudson, Benjamin; Wilson, Howard; Roach, Colin

2014-10-01

The regulation of transport at the pedestal top is important for the inter-ELM pedestal dynamics. Linear gyrokinetic analysis of the pedestal region during an ELM cycle on MAST has shown kinetic ballooning modes to be unstable at the knee of the pressure profile and in the steep pedestal region whilst microtearing modes (MTMs) dominate in the shallow gradient region inboard of the pedestal top. The transition between these instabilities at the pedestal knee has been observed in low and high collisionality MAST pedestals, and is likely to play an important role in the broadening of the pedestal. Nonlinear simulations are needed in this region to understand the microturbulence, the corresponding transport fluxes, and to gain further insight into the processes underlying the pedestal evolution. Such gyrokinetic simulations are numerically challenging and recent upgrades to the GS2 gyrokinetic code help improve their feasibility. We are also exploring reduced models that capture the relevant physics using the plasma simulation framework BOUT + + . An electromagnetic gyrofluid model has recently been implemented with BOUT + + that has significantly reduced computational cost compared to the gyrokinetic simulations against which it will be benchmarked. This work was funded by the RCUK Energy programme, EURATOM and a EUROFusion fellowship WP14-FRF-CCFE/Dickinson and was carried out using: HELIOS at IFERC, Japan; ARCHER (EPSRC Grant No. EP/L000237/1); HECToR (EPSRC Grant No. EP/H002081/1).

Tractable flux-driven temperature, density, and rotation profile evolution with the quasilinear gyrokinetic transport model QuaLiKiz

NASA Astrophysics Data System (ADS)

Citrin, J.; Bourdelle, C.; Casson, F. J.; Angioni, C.; Bonanomi, N.; Camenen, Y.; Garbet, X.; Garzotti, L.; Görler, T.; Gürcan, O.; Koechl, F.; Imbeaux, F.; Linder, O.; van de Plassche, K.; Strand, P.; Szepesi, G.; Contributors, JET

2017-12-01

Quasilinear turbulent transport models are a successful tool for prediction of core tokamak plasma profiles in many regimes. Their success hinges on the reproduction of local nonlinear gyrokinetic fluxes. We focus on significant progress in the quasilinear gyrokinetic transport model QuaLiKiz (Bourdelle et al 2016 Plasma Phys. Control. Fusion 58 014036), which employs an approximated solution of the mode structures to significantly speed up computation time compared to full linear gyrokinetic solvers. Optimisation of the dispersion relation solution algorithm within integrated modelling applications leads to flux calculations × {10}6-7 faster than local nonlinear simulations. This allows tractable simulation of flux-driven dynamic profile evolution including all transport channels: ion and electron heat, main particles, impurities, and momentum. Furthermore, QuaLiKiz now includes the impact of rotation and temperature anisotropy induced poloidal asymmetry on heavy impurity transport, important for W-transport applications. Application within the JETTO integrated modelling code results in 1 s of JET plasma simulation within 10 h using 10 CPUs. Simultaneous predictions of core density, temperature, and toroidal rotation profiles for both JET hybrid and baseline experiments are presented, covering both ion and electron turbulence scales. The simulations are successfully compared to measured profiles, with agreement mostly in the 5%-25% range according to standard figures of merit. QuaLiKiz is now open source and available at www.qualikiz.com.

Gyrokinetic simulation of residual turbulence in transport barriers

NASA Astrophysics Data System (ADS)

Jenko, Frank; Told, Daniel; Goerler, Tobias; Brunner, Stephan; Sautter, Olivier

2011-10-01

One of the ultimate aims for gyrokinetic simulation is to describe the formation and evolution of transport barriers. An important step in that direction is the study of the residual turbulence in established barriers - a challenging task in itself, given that a wide range of spatio-temporal scales can be involved. In the present work, we employ the physically comprehensive, nonlocal gyrokinetic turbulence code GENE to study turbulence in both core and edge transport barriers. First, we apply GENE to a set of discharges in the TCV tokamak which exhibit electron ITBs. Nonlinear gyrokinetic simulations are used to examine the influence of a varying current profile on the strength of the barrier. For each case, the transport spectra reveal how much transport (for each channel) is done in the low-k, medium-k, and high-k regimes, respectively. The role of ETG turbulence is discussed. Second, we explore the role of ETG turbulence in a typical ASDEX Upgrade H-mode discharge. Numerical convergence is carefully examined, and new insights on the characteristics of ETG turbulence in the edge will be discussed, focusing particularly on the role of streamers, which had been found to be a necessary ingredient for experimentally relevant ETG transport in core plasmas. The radial dependence of the resulting electron heat diffusivity is also examined and a simple ETG model is presented which can be used in future edge modeling efforts.

Gyrofluid Modeling of Turbulent, Kinetic Physics

NASA Astrophysics Data System (ADS)

Despain, Kate Marie

2011-12-01

Gyrofluid models to describe plasma turbulence combine the advantages of fluid models, such as lower dimensionality and well-developed intuition, with those of gyrokinetics models, such as finite Larmor radius (FLR) effects. This allows gyrofluid models to be more tractable computationally while still capturing much of the physics related to the FLR of the particles. We present a gyrofluid model derived to capture the behavior of slow solar wind turbulence and describe the computer code developed to implement the model. In addition, we describe the modifications we made to a gyrofluid model and code that simulate plasma turbulence in tokamak geometries. Specifically, we describe a nonlinear phase mixing phenomenon, part of the E x B term, that was previously missing from the model. An inherently FLR effect, it plays an important role in predicting turbulent heat flux and diffusivity levels for the plasma. We demonstrate this importance by comparing results from the updated code to studies done previously by gyrofluid and gyrokinetic codes. We further explain what would be necessary to couple the updated gyrofluid code, gryffin, to a turbulent transport code, thus allowing gryffin to play a role in predicting profiles for fusion devices such as ITER and to explore novel fusion configurations. Such a coupling would require the use of Graphical Processing Units (GPUs) to make the modeling process fast enough to be viable. Consequently, we also describe our experience with GPU computing and demonstrate that we are poised to complete a gryffin port to this innovative architecture.

Cross-separatrix Coupling in Nonlinear Global Electrostatic Turbulent Transport in C-2U

NASA Astrophysics Data System (ADS)

Lau, Calvin; Fulton, Daniel; Bao, Jian; Lin, Zhihong; Binderbauer, Michl; Tajima, Toshiki; Schmitz, Lothar; TAE Team

2017-10-01

In recent years, the progress of the C-2/C-2U advanced beam-driven field-reversed configuration (FRC) experiments at Tri Alpha Energy, Inc. has pushed FRCs to transport limited regimes. Understanding particle and energy transport is a vital step towards an FRC reactor, and two particle-in-cell microturbulence codes, the Gyrokinetic Toroidal Code (GTC) and A New Code (ANC), are being developed and applied toward this goal. Previous local electrostatic GTC simulations find the core to be robustly stable with drift-wave instability only in the scrape-off layer (SOL) region. However, experimental measurements showed fluctuations in both regions; one possibility is that fluctuations in the core originate from the SOL, suggesting the need for non-local simulations with cross-separatrix coupling. Current global ANC simulations with gyrokinetic ions and adiabatic electrons find that non-local effects (1) modify linear growth-rates and frequencies of instabilities and (2) allow instability to move from the unstable SOL to the linearly stable core. Nonlinear spreading is also seen prior to mode saturation. We also report on the progress of the first turbulence simulations in the SOL. This work is supported by the Norman Rostoker Fellowship.

Edge gyrokinetic theory and continuum simulations

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Dorr, M. R.; Hittinger, J. A.; Bodi, K.; Candy, J.; Cohen, B. I.; Cohen, R. H.; Colella, P.; Kerbel, G. D.; Krasheninnikov, S.; Nevins, W. M.; Qin, H.; Rognlien, T. D.; Snyder, P. B.; Umansky, M. V.

2007-08-01

The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five-dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential and mirror ratio, and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the plateau regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL.

A numerical code for a three-dimensional magnetospheric MHD equilibrium model

NASA Technical Reports Server (NTRS)

Voigt, G.-H.

1992-01-01

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution.

Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

NASA Astrophysics Data System (ADS)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.

Gyrokinetic Simulations of JET Carbon and ITER-Like Wall Pedestals

NASA Astrophysics Data System (ADS)

Hatch, David; Kotschenreuther, Mike; Mahajan, Swadesh; Liu, Xing; Blackmon, Austin; Giroud, Carine; Hillesheim, Jon; Maggi, Costanza; Saarelma, Samuli; JET Contributors Team

2017-10-01

Gyrokinetic simulations using the GENE code are presented, which target a fundamental understanding of JET pedestal transport and, in particular, its modification after installation of an ITER like wall (ILW). A representative pre-ILW (carbon wall) discharge is analyzed as a base case. In this discharge, magnetic diagnostics observe washboard modes, which preferentially affect the temperature pedestal and have frequencies (accounting for Doppler shift) consistent with microtearing modes and inconsistent with kinetic ballooning modes. A similar ILW discharge is examined, which recovers a similar value of H98, albeit at reduced pedestal temperature. This discharge is distinguished by a much higher value of eta, which produces strong ITG and ETG driven instabilities in gyrokinetic simulations. Experimental observations provide several targets for comparisons with simulation data, including the toroidal mode number and frequency of magnetic fluctuations, heat fluxes, and inter-ELM profile evolution. Strategies for optimizing pedestal performance will also be discussed. This work was supported by U.S. DOE Contract No. DE-FG02-04ER54742 and by EUROfusion under Grant No. 633053.

Linear gyrokinetic simulations of microinstabilities within the pedestal region of H-mode NSTX discharges in a highly shaped geometry

DOE PAGES

Coury, M.; Guttenfelder, W.; Mikkelsen, D. R.; ...

2016-06-30

Linear (local) gyrokinetic predictions of edge microinstabilities in highly shaped, lithiated and non-lithiated NSTX discharges are reported using the gyrokinetic code GS2. Microtearing modes dominate the non-lithiated pedestal top. The stabilization of these modes at the lithiated pedestal top enables the electron temperature pedestal to extend further inwards, as observed experimentally. Kinetic ballooning modes are found to be unstable mainly at the mid-pedestal of both types of discharges, with un- stable trapped electron modes nearer the separatrix region. At electron wavelengths, ETG modes are found to be unstable from mid-pedestal outwards for η e, exp ~2.2 with higher growth ratesmore » for the lithiated discharge. Near the separatrix, the critical temperature gradient for driving ETG modes is reduced in the presence of lithium, re ecting the reduction of the lithiated density gradients observed experimentally. A preliminary linear study in the edge of non-lithiated discharges shows that the equilibrium shaping alters the electrostatic modes stability, found more unstable at high plasma shaping.« less

Visualizing Gyrokinetic Turbulence in a Tokamak

NASA Astrophysics Data System (ADS)

Stantchev, George

2005-10-01

Multi-dimensional data output from gyrokinetic microturbulence codes are often difficult to visualize, in part due to the non-trivial geometry of the underlying grids, in part due to high irregularity of the relevant scalar field structures in turbulent regions. For instance, traditional isosurface extraction methods are likely to fail for the electrostatic potential field whose level sets may exhibit various geometric pathologies. To address these issues we develop an advanced interactive 3D gyrokinetic turbulence visualization framework which we apply in the study of microtearing instabilities calculated with GS2 in the MAST and NSTX geometries. In these simulations GS2 uses field-line-following coordinates such that the computational domain maps in physical space to a long, twisting flux tube with strong cross-sectional shear. Using statistical wavelet analysis we create a sparse multiple-scale volumetric representation of the relevant scalar fields, which we visualize via a variation of the so called splatting technique. To handle the problem of highly anisotropic flux tube configurations we adapt a geometry-driven surface illumination algorithm that places local light sources for effective feature-enhanced visualization.

Verification of Gyrokinetic codes: Theoretical background and applications

NASA Astrophysics Data System (ADS)

Tronko, Natalia; Bottino, Alberto; Görler, Tobias; Sonnendrücker, Eric; Told, Daniel; Villard, Laurent

2017-05-01

In fusion plasmas, the strong magnetic field allows the fast gyro-motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) codes play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the subsequent transport. Naturally, these codes require thorough verification and validation. Here, we present a new and generic theoretical framework and specific numerical applications to test the faithfulness of the implemented models to theory and to verify the domain of applicability of existing GK codes. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which has rarely been done and therefore makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK code's equations to access the limits of their applicability. The verification of the numerical scheme is proposed via the benchmark effort. In this work, specific examples of code verification are presented for two GK codes: the multi-species electromagnetic ORB5 (PIC) and the radially global version of GENE (Eulerian). The proposed methodology can be applied to any existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell equations implemented in the ORB5 and GENE codes using the Lagrangian variational formulation. At the computational level, detailed verifications of global electromagnetic test cases developed from the CYCLONE Base Case are considered, including a parametric β-scan covering the transition from ITG to KBM and the spectral properties at the nominal β value.

Verification of Gyrokinetic codes: theoretical background and applications

NASA Astrophysics Data System (ADS)

Tronko, Natalia

2016-10-01

In fusion plasmas the strong magnetic field allows the fast gyro motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) codes play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the consequent transport. We present a new and generic theoretical framework and specific numerical applications to test the validity and the domain of applicability of existing GK codes. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK code's equations to access the limits of their applicability. The indirect verification of numerical scheme is proposed via the Benchmark process. In this work, specific examples of code verification are presented for two GK codes: the multi-species electromagnetic ORB5 (PIC), and the radially global version of GENE (Eulerian). The proposed methodology can be applied to any existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell equations using the generic variational formulation. Then, we derive and include the models implemented in ORB5 and GENE inside this hierarchy. At the computational level, detailed verification of global electromagnetic test cases based on the CYCLONE are considered, including a parametric β-scan covering the transition between the ITG to KBM and the spectral properties at the nominal β value.

Combining electromagnetic gyro-kinetic particle-in-cell simulations with collisions

NASA Astrophysics Data System (ADS)

Slaby, Christoph; Kleiber, Ralf; Könies, Axel

2017-09-01

It has been an open question whether for electromagnetic gyro-kinetic particle-in-cell (PIC) simulations pitch-angle collisions and the recently introduced pullback transformation scheme (Mishchenko et al., 2014; Kleiber et al., 2016) are consistent. This question is positively answered by comparing the PIC code EUTERPE with an approach based on an expansion of the perturbed distribution function in eigenfunctions of the pitch-angle collision operator (Legendre polynomials) to solve the electromagnetic drift-kinetic equation with collisions in slab geometry. It is shown how both approaches yield the same results for the frequency and damping rate of a kinetic Alfvén wave and how the perturbed distribution function is substantially changed by the presence of pitch-angle collisions.

Computer Simulation of the VASIMR Engine

NASA Technical Reports Server (NTRS)

Garrison, David

2005-01-01

The goal of this project is to develop a magneto-hydrodynamic (MHD) computer code for simulation of the VASIMR engine. This code is designed be easy to modify and use. We achieve this using the Cactus framework, a system originally developed for research in numerical relativity. Since its release, Cactus has become an extremely powerful and flexible open source framework. The development of the code will be done in stages, starting with a basic fluid dynamic simulation and working towards a more complex MHD code. Once developed, this code can be used by students and researchers in order to further test and improve the VASIMR engine.

A Comprehensive High Performance Predictive Tool for Fusion Liquid Metal Hydromagnetics

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

Huang, Peter; Chhabra, Rupanshi; Munipalli, Ramakanth

In Phase I SBIR project, HyPerComp and Texcel initiated the development of two induction-based MHD codes as a predictive tool for fusion hydro-magnetics. The newly-developed codes overcome the deficiency of other MHD codes based on the quasi static approximation by defining a more general mathematical model that utilizes the induced magnetic field rather than the electric potential as the main electromagnetic variable. The UCLA code is a finite-difference staggered-mesh code that serves as a supplementary tool to the massively-parallel finite-volume code developed by HyPerComp. As there is no suitable experimental data under blanket-relevant conditions for code validation, code-to-code comparisons andmore » comparisons against analytical solutions were successfully performed for three selected test cases: (1) lid-driven MHD flow, (2) flow in a rectangular duct in a transverse magnetic field, and (3) unsteady finite magnetic Reynolds number flow in a rectangular enclosure. The performed tests suggest that the developed codes are accurate and robust. Further work will focus on enhancing the code capabilities towards higher flow parameters and faster computations. At the conclusion of the current Phase-II Project we have completed the preliminary validation efforts in performing unsteady mixed-convection MHD flows (against limited data that is currently available in literature), and demonstrated flow behavior in large 3D channels including important geometrical features. Code enhancements such as periodic boundary conditions, unmatched mesh structures are also ready. As proposed, we have built upon these strengths and explored a much increased range of Grashof numbers and Hartmann numbers under various flow conditions, ranging from flows in a rectangular duct to prototypic blanket modules and liquid metal PFC. Parametric studies, numerical and physical model improvements to expand the scope of simulations, code demonstration, and continued validation activities have also been completed.« less

Resolving the Kinetic Reconnection Length Scale in Global Magnetospheric Simulations with MHD-EPIC

NASA Astrophysics Data System (ADS)

Toth, G.; Chen, Y.; Cassak, P.; Jordanova, V.; Peng, B.; Markidis, S.; Gombosi, T. I.

2016-12-01

We have recently developed a new modeling capability: the Magnetohydrodynamics with Embedded Particle-in-Cell (MHD-EPIC) algorithm with support from Los Alamos SHIELDS and NSF INSPIRE grants. We have implemented MHD-EPIC into the Space Weather Modeling Framework (SWMF) using the implicit Particle-in-Cell (iPIC3D) and the BATS-R-US extended magnetohydrodynamic codes. The MHD-EPIC model allows two-way coupled simulations in two and three dimensions with multiple embedded PIC regions. Both BATS-R-US and iPIC3D are massively parallel codes. The MHD-EPIC approach allows global magnetosphere simulations with embedded kinetic simulations. For small magnetospheres, like Ganymede or Mercury, we can easily resolve the ion scales around the reconnection sites. Modeling the Earth magnetosphere is very challenging even with our efficient MHD-EPIC model due to the large separation between the global and ion scales. On the other hand the large separation of scales may be exploited: the solution may not be sensitive to the ion inertial length as long as it is small relative to the global scales. The ion inertial length can be varied by changing the ion mass while keeping the MHD mass density, the velocity, and pressure the same for the initial and boundary conditions. Our two-dimensional MHD-EPIC simulations for the dayside reconnection region show in fact, that the overall solution is not sensitive to ion inertial length. The shape, size and frequency of flux transfer events are very similar for a wide range of ion masses. Our results mean that 3D MHD-EPIC simulations for the Earth and other large magnetospheres can be made computationally affordable by artificially increasing the ion mass: the required grid resolution and time step in the PIC model are proportional to the ion inertial length. Changing the ion mass by a factor of 4, for example, speeds up the PIC code by a factor of 256. In fact, this approach allowed us to perform an hour-long 3D MHD-EPIC simulations for the Earth magnetosphere.

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

Fu, Guoyong; Budny, Robert; Gorelenkov, Nikolai

We report here the work done for the FY14 OFES Theory Performance Target as given below: "Understanding alpha particle confinement in ITER, the world's first burning plasma experiment, is a key priority for the fusion program. In FY 2014, determine linear instability trends and thresholds of energetic particle-driven shear Alfven eigenmodes in ITER for a range of parameters and profiles using a set of complementary simulation models (gyrokinetic, hybrid, and gyrofluid). Carry out initial nonlinear simulations to assess the effects of the unstable modes on energetic particle transport". In the past year (FY14), a systematic study of the alpha-driven Alfvenmore » modes in ITER has been carried out jointly by researchers from six institutions involving seven codes including the transport simulation code TRANSP (R. Budny and F. Poli, PPPL), three gyrokinetic codes: GEM (Y. Chen, Univ. of Colorado), GTC (J. McClenaghan, Z. Lin, UCI), and GYRO (E. Bass, R. Waltz, UCSD/GA), the hybrid code M3D-K (G.Y. Fu, PPPL), the gyro-fluid code TAEFL (D. Spong, ORNL), and the linear kinetic stability code NOVA-K (N. Gorelenkov, PPPL). A range of ITER parameters and profiles are specified by TRANSP simulation of a hybrid scenario case and a steady-state scenario case. Based on the specified ITER equilibria linear stability calculations are done to determine the stability boundary of alpha-driven high-n TAEs using the five initial value codes (GEM, GTC, GYRO, M3D-K, and TAEFL) and the kinetic stability code (NOVA-K). Both the effects of alpha particles and beam ions have been considered. Finally, the effects of the unstable modes on energetic particle transport have been explored using GEM and M3D-K.« less

Benchmarking gyrokinetic simulations in a toroidal flux-tube

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

Chen, Y.; Parker, S. E.; Wan, W.

2013-09-15

A flux-tube model is implemented in the global turbulence code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] in order to facilitate benchmarking with Eulerian codes. The global GEM assumes the magnetic equilibrium to be completely given. The initial flux-tube implementation simply selects a radial location as the center of the flux-tube and a radial size of the flux-tube, sets all equilibrium quantities (B, ∇B, etc.) to be equal to the values at the center of the flux-tube, and retains only a linear radial profile of the safety factor needed for boundary conditions. This implementationmore » shows disagreement with Eulerian codes in linear simulations. An alternative flux-tube model based on a complete local equilibrium solution of the Grad-Shafranov equation [J. Candy, Plasma Phys. Controlled Fusion 51, 105009 (2009)] is then implemented. This results in better agreement between Eulerian codes and the particle-in-cell (PIC) method. The PIC algorithm based on the v{sub ||}-formalism [J. Reynders, Ph.D. dissertation, Princeton University, 1992] and the gyrokinetic ion/fluid electron hybrid model with kinetic electron closure [Y. Chan and S. E. Parker, Phys. Plasmas 18, 055703 (2011)] are also implemented in the flux-tube geometry and compared with the direct method for both the ion temperature gradient driven modes and the kinetic ballooning modes.« less

Gyrokinetic particle-in-cell optimization on emerging multi- and manycore platforms

DOE PAGES

Madduri, Kamesh; Im, Eun-Jin; Ibrahim, Khaled Z.; ...

2011-03-02

The next decade of high-performance computing (HPC) systems will see a rapid evolution and divergence of multi- and manycore architectures as power and cooling constraints limit increases in microprocessor clock speeds. Understanding efficient optimization methodologies on diverse multicore designs in the context of demanding numerical methods is one of the greatest challenges faced today by the HPC community. In this paper, we examine the efficient multicore optimization of GTC, a petascale gyrokinetic toroidal fusion code for studying plasma microturbulence in tokamak devices. For GTC’s key computational components (charge deposition and particle push), we explore efficient parallelization strategies across a broadmore » range of emerging multicore designs, including the recently-released Intel Nehalem-EX, the AMD Opteron Istanbul, and the highly multithreaded Sun UltraSparc T2+. We also present the first study on tuning gyrokinetic particle-in-cell (PIC) algorithms for graphics processors, using the NVIDIA C2050 (Fermi). Our work discusses several novel optimization approaches for gyrokinetic PIC, including mixed-precision computation, particle binning and decomposition strategies, grid replication, SIMDized atomic floating-point operations, and effective GPU texture memory utilization. Overall, we achieve significant performance improvements of 1.3–4.7× on these complex PIC kernels, despite the inherent challenges of data dependency and locality. Finally, our work also points to several architectural and programming features that could significantly enhance PIC performance and productivity on next-generation architectures.« less

Creating Synthetic Coronal Observational Data From MHD Models: The Forward Technique

NASA Technical Reports Server (NTRS)

Rachmeler, Laurel A.; Gibson, Sarah E.; Dove, James; Kucera, Therese Ann

2010-01-01

We present a generalized forward code for creating simulated corona) observables off the limb from numerical and analytical MHD models. This generalized forward model is capable of creating emission maps in various wavelengths for instruments such as SXT, EIT, EIS, and coronagraphs, as well as spectropolari metric images and line profiles. The inputs to our code can be analytic models (of which four come with the code) or 2.5D and 3D numerical datacubes. We present some examples of the observable data created with our code as well as its functional capabilities. This code is currently available for beta-testing (contact authors), with the ultimate goal of release as a SolarSoft package

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.

A Fast MHD Code for Gravitationally Stratified Media using Graphical Processing Units: SMAUG

NASA Astrophysics Data System (ADS)

Griffiths, M. K.; Fedun, V.; Erdélyi, R.

2015-03-01

Parallelization techniques have been exploited most successfully by the gaming/graphics industry with the adoption of graphical processing units (GPUs), possessing hundreds of processor cores. The opportunity has been recognized by the computational sciences and engineering communities, who have recently harnessed successfully the numerical performance of GPUs. For example, parallel magnetohydrodynamic (MHD) algorithms are important for numerical modelling of highly inhomogeneous solar, astrophysical and geophysical plasmas. Here, we describe the implementation of SMAUG, the Sheffield Magnetohydrodynamics Algorithm Using GPUs. SMAUG is a 1-3D MHD code capable of modelling magnetized and gravitationally stratified plasma. The objective of this paper is to present the numerical methods and techniques used for porting the code to this novel and highly parallel compute architecture. The methods employed are justified by the performance benchmarks and validation results demonstrating that the code successfully simulates the physics for a range of test scenarios including a full 3D realistic model of wave propagation in the solar atmosphere.

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

NASA Astrophysics Data System (ADS)

Akcay, Cihan; Kim, Charlson C.; Victor, Brian S.; Jarboe, Thomas R.

2013-08-01

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth di to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification Itor/Iinj and formation time τf demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates Itor/Iinj and exhibits much a longer τf. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.

Study of the L-mode tokamak plasma “shortfall” with local and global nonlinear gyrokinetic δf particle-in-cell simulation

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

Chowdhury, J.; Wan, Weigang; Chen, Yang

2014-11-15

The δ f particle-in-cell code GEM is used to study the transport “shortfall” problem of gyrokinetic simulations. In local simulations, the GEM results confirm the previously reported simulation results of DIII-D [Holland et al., Phys. Plasmas 16, 052301 (2009)] and Alcator C-Mod [Howard et al., Nucl. Fusion 53, 123011 (2013)] tokamaks with the continuum code GYRO. Namely, for DIII-D the simulations closely predict the ion heat flux at the core, while substantially underpredict transport towards the edge; while for Alcator C-Mod, the simulations show agreement with the experimental values of ion heat flux, at least within the range of experimental error.more » Global simulations are carried out for DIII-D L-mode plasmas to study the effect of edge turbulence on the outer core ion heat transport. The edge turbulence enhances the outer core ion heat transport through turbulence spreading. However, this edge turbulence spreading effect is not enough to explain the transport underprediction.« less

Gyrokinetic continuum simulations of turbulence in the Texas Helimak

NASA Astrophysics Data System (ADS)

Bernard, T. N.; Shi, E. L.; Hammett, G. W.; Hakim, A.; Taylor, E. I.

2017-10-01

We have used the Gkeyll code to perform 3x-2v full-f gyrokinetic continuum simulations of electrostatic plasma turbulence in the Texas Helimak. The Helimak is an open field-line experiment with magnetic curvature and shear. It is useful for validating numerical codes due to its extensive diagnostics and simple, helical geometry, which is similar to the scrape-off layer region of tokamaks. Interchange and drift-wave modes are the main turbulence mechanisms in the device, and potential biasing is applied to study the effect of velocity shear on turbulence reduction. With Gkeyll, we varied field-line pitch angle and simulated biased and unbiased cases to study different turbulent regimes and turbulence reduction. These are the first kinetic simulations of the Helimak and resulting plasma profiles agree fairly well with experimental data. This research demonstrates Gkeyll's progress towards 5D simulations of the SOL region of fusion devices. Supported by the U.S. DOE SCGSR program under contract DE-SC0014664, the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE contract DE-AC02-09CH11466.

Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence

NASA Astrophysics Data System (ADS)

Plunk, G. G.; Tatsuno, T.

2011-04-01

The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code AstroGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.

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.

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

Off-design performance analysis of MHD generator channels

NASA Technical Reports Server (NTRS)

Wilson, D. R.; Williams, T. S.

1980-01-01

A computer code for performing parametric design point calculations, and evaluating the off-design performance of MHD generators has been developed. The program is capable of analyzing Faraday, Hall, and DCW channels, including the effect of electrical shorting in the gas boundary layers and coal slag layers. Direct integration of the electrode voltage drops is included. The program can be run in either the design or off-design mode. Details of the computer code, together with results of a study of the design and off-design performance of the proposed ETF MHD generator are presented. Design point variations of pre-heat and stoichiometry were analyzed. The off-design study included variations in mass flow rate and oxygen enrichment.

Comparing simulation of plasma turbulence with experiment. II. Gyrokinetic simulations

NASA Astrophysics Data System (ADS)

Ross, David W.; Dorland, William

2002-12-01

The direct quantitative correspondence between theoretical predictions and the measured plasma fluctuations and transport is tested by performing nonlinear gyrokinetic simulations with the GS2 code. This is a continuation of previous work with gyrofluid simulations [D. W. Ross et al., Phys. Plasmas 9, 177 (2002)], and the same L-mode reference discharge in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] is studied. The simulated turbulence is dominated by ion temperature gradient (ITG) modes, corrected by trapped-electron, passing-electron and impurity effects. The energy fluxes obtained in the gyrokinetic simulations are comparable to, even somewhat higher than, those of the earlier work, and the simulated ion thermal transport, corrected for E×B flow shear, exceeds the experimental value by more than a factor of 2. The simulation also overestimates the density fluctuation level. Varying the local temperature gradient shows a stiff response in the flux and an apparent up-shift from the linear mode threshold [A. M. Dimits et al., Phys. Plasmas 7, 969 (2000)]. This effect is insufficient, within the estimated error, to bring the results into conformity with the experiment.

Gyrokinetic simulations of particle transport in pellet fuelled JET discharges

NASA Astrophysics Data System (ADS)

Tegnered, D.; Oberparleiter, M.; Nordman, H.; Strand, P.; Garzotti, L.; Lupelli, I.; Roach, C. M.; Romanelli, M.; Valovič, M.; Contributors, JET

2017-10-01

Pellet injection is a likely fuelling method of reactor grade plasmas. When the pellet ablates, it will transiently perturb the density and temperature profiles of the plasma. This will in turn change dimensionless parameters such as a/{L}n,a/{L}T and plasma β. The microstability properties of the plasma then changes which influences the transport of heat and particles. In this paper, gyrokinetic simulations of a JET L-mode pellet fuelled discharge are performed. The ion temperature gradient/trapped electron mode turbulence is compared at the time point when the effect from the pellet is the most pronounced with a hollow density profile and when the profiles have relaxed again. Linear and nonlinear simulations are performed using the gyrokinetic code GENE including electromagnetic effects and collisions in a realistic geometry in local mode. Furthermore, global nonlinear simulations are performed in order to assess any nonlocal effects. It is found that the positive density gradient has a stabilizing effect that is partly counteracted by the increased temperature gradient in the this region. The effective diffusion coefficients are reduced in the positive density region region compared to the intra pellet time point. No major effect on the turbulent transport due to nonlocal effects are observed.

Graphics Processing Unit Acceleration of Gyrokinetic Turbulence Simulations

NASA Astrophysics Data System (ADS)

Hause, Benjamin; Parker, Scott; Chen, Yang

2013-10-01

We find a substantial increase in on-node performance using Graphics Processing Unit (GPU) acceleration in gyrokinetic delta-f particle-in-cell simulation. Optimization is performed on a two-dimensional slab gyrokinetic particle simulation using the Portland Group Fortran compiler with the OpenACC compiler directives and Fortran CUDA. Mixed implementation of both Open-ACC and CUDA is demonstrated. CUDA is required for optimizing the particle deposition algorithm. We have implemented the GPU acceleration on a third generation Core I7 gaming PC with two NVIDIA GTX 680 GPUs. We find comparable, or better, acceleration relative to the NERSC DIRAC cluster with the NVIDIA Tesla C2050 computing processor. The Tesla C 2050 is about 2.6 times more expensive than the GTX 580 gaming GPU. We also see enormous speedups (10 or more) on the Titan supercomputer at Oak Ridge with Kepler K20 GPUs. Results show speed-ups comparable or better than that of OpenMP models utilizing multiple cores. The use of hybrid OpenACC, CUDA Fortran, and MPI models across many nodes will also be discussed. Optimization strategies will be presented. We will discuss progress on optimizing the comprehensive three dimensional general geometry GEM code.

A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Du, Jian; Glimm, James; Xu, Zhiliang

2007-10-01

We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic-elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic solvers, and the embedded boundary method for the elliptic problem in complex domains. The numerical algorithm has been implemented as an MHD extension of FronTier, a hydrodynamic code with free interface support. The code is applicable for numerical simulations of free surface flows of conductive liquids or weakly ionized plasmas. The code has been validated through the comparison of numerical simulations of a liquid metal jet in a non-uniform magnetic field with experiments and theory. Simulations of the Muon Collider/Neutrino Factory target have also been discussed.

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.

The impact of collisionality, FLR, and parallel closure effects on instabilities in the tokamak pedestal: Numerical studies with the NIMROD code

DOE PAGES

King, J. R.; Pankin, A. Y.; Kruger, S. E.; ...

2016-06-24

The extended-MHD NIMROD code [C. R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD model complexity is increased incrementally, resistive and first-order finite-Larmour radius effects are destabilizing and stabilizing, respectively. Lastly, the full result is compared to local analytic calculations which are found to overpredict both the resistive destabilization and drift stabilization in comparison to the NIMROD computations.

The impact of collisionality, FLR, and parallel closure effects on instabilities in the tokamak pedestal: Numerical studies with the NIMROD code

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

King, J. R.; Pankin, A. Y.; Kruger, S. E.

The extended-MHD NIMROD code [C. R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD model complexity is increased incrementally, resistive and first-order finite-Larmour radius effects are destabilizing and stabilizing, respectively. The full result is compared to local analytic calculations which are found to overpredict both the resistive destabilization and drift stabilization in comparison to the NIMROD computations.

The impact of collisionality, FLR, and parallel closure effects on instabilities in the tokamak pedestal: Numerical studies with the NIMROD code

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

King, J. R.; Pankin, A. Y.; Kruger, S. E.

The extended-MHD NIMROD code [C. R. Sovinec and J. R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD model complexity is increased incrementally, resistive and first-order finite-Larmour radius effects are destabilizing and stabilizing, respectively. Lastly, the full result is compared to local analytic calculations which are found to overpredict both the resistive destabilization and drift stabilization in comparison to the NIMROD computations.

Research and development studies for MHD/coal power flow train components. Part II. Diagnostics and instrumentation MHD channel combutor. Progres report. [Flow calculations for combustors

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

Bloom, M.H.; Lederman, S.; Sforza, P.

1980-01-01

This is Part II of the Technical Progress Report on Tasks II-IV of the subject contract. It deals sequentially with Diagnostics and Instrumentation, the MHD Channel and the Combustor. During this period, a significant effort has gone into establishing a schematic design of a laser diagnostic system which can be applied to the flow-train of the MHD system, and to acquiring, assembling and shaking down a laboratory set-up upon which a prototype can be based. With further reference to the MHD Channel, a model analysis has been initiated of the two-dimensional MHD boundary layer between two electrodes in the limitmore » of small magnetic Reynolds numbers with negligible effect of the flow on the applied magnetic field. An objective of this model study is the assessment of variations in initial conditions on the boundary layer behavior. Finally, the problem of combustion modeling has been studied on an initial basis. The open reports on this subject depict a high degree of empiricism, centering attention on global behavior mainly. A quasi-one-dimensional model code has been set-up to check some of the existing estimates. Also a code for equilibrium combustion has been activated.« less

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

NASA Technical Reports Server (NTRS)

Deane, Anil E.

1996-01-01

Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

The PLUTO code for astrophysical gasdynamics .

NASA Astrophysics Data System (ADS)

Mignone, A.

Present numerical codes appeal to a consolidated theory based on finite difference and Godunov-type schemes. In this context we have developed a versatile numerical code, PLUTO, suitable for the solution of high-mach number flow in 1, 2 and 3 spatial dimensions and different systems of coordinates. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. The code is freely distributed under the GNU public license and it is available for download to the astrophysical community at the URL http://plutocode.to.astro.it.

Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Held, Eric D.

2015-09-01

Neoclassical tearing modes are macroscopic (L ∼ 1 m) instabilities in magnetic fusion experiments; if unchecked, these modes degrade plasma performance and may catastrophically destroy plasma confinement by inducing a disruption. Fortunately, the use of properly tuned and directed radiofrequency waves (λ ∼ 1 mm) can eliminate these modes. Numerical modeling of this difficult multiscale problem requires the integration of separate mathematical models for each length and time scale (Jenkins and Kruger, 2012 [21]); the extended MHD model captures macroscopic plasma evolution while the RF model tracks the flow and deposition of injected RF power through the evolving plasma profiles. The scale separation enables use of the eikonal (ray-tracing) approximation to model the RF wave propagation. In this work we demonstrate a technique, based on methods of computational geometry, for mapping the ensuing RF data (associated with discrete ray trajectories) onto the finite-element/pseudospectral grid that is used to model the extended MHD physics. In the new representation, the RF data can then be used to construct source terms in the equations of the extended MHD model, enabling quantitative modeling of RF-induced tearing mode stabilization. Though our specific implementation uses the NIMROD extended MHD (Sovinec et al., 2004 [22]) and GENRAY RF (Smirnov et al., 1994 [23]) codes, the approach presented can be applied more generally to any code coupling requiring the mapping of ray tracing data onto Eulerian grids.

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

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

White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.

2015-05-15

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and comparemore » with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.« less

Recent gyrokinetic turbulence insights with GENE and direct comparison with experimental measurements

NASA Astrophysics Data System (ADS)

Goerler, Tobias

2017-10-01

Throughout the last years direct comparisons between gyrokinetic turbulence simulations and experimental measurements have been intensified substantially. Such studies are largely motivated by the urgent need for reliable transport predictions for future burning plasma devices and the associated necessity for validating the numerical tools. On the other hand, they can be helpful to assess the way a particular diagnostic experiences turbulence and provide ideas for further optimization and the physics that may not yet be accessible. Here, synthetic diagnostics, i.e. models that mimic the spatial and sometimes temporal response of the experimental diagnostic, play an important role. In the contribution at hand, we focus on recent gyrokinetic GENE simulations dedicated to ASDEX Upgrade L-mode plasmas and comparison with various turbulence measurements. Particular emphasis will be given to density fluctuation spectra which are experimentally accessible via Doppler reflectometry. A sophisticated synthetic diagnostic involving a fullwave code has recently been established and solves the long-lasting question on different spectral roll-overs in gyrokinetic and measured spectra as well as the potentially different power laws in the O- and X-mode signals. The demonstrated agreement furthermore extends the validation data base deep into spectral space and confirms a proper coverage of the turbulence cascade physics. The flux-matched GENE simulations are then used to study the sensitivity of the latter to the main microinstability drive and investigate the energetics at the various scales. Additionally, electron scale turbulence based modifications of the high-k power law spectra in such plasmas will be presented and their visibility in measurable signals be discussed.

Edge Simulation Laboratory Progress and Plans

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

Cohen, R

The Edge Simulation Laboratory (ESL) is a project to develop a gyrokinetic code for MFE edge plasmas based on continuum (Eulerian) techniques. ESL is a base-program activity of OFES, with an allied algorithm research activity funded by the OASCR base math program. ESL OFES funds directly support about 0.8 FTE of career staff at LLNL, a postdoc and a small fraction of an FTE at GA, and a graduate student at UCSD. In addition the allied OASCR program funds about 1/2 FTE each in the computations directorates at LBNL and LLNL. OFES ESL funding for LLNL and UCSD began inmore » fall 2005, while funding for GA and the math team began about a year ago. ESL's continuum approach is a complement to the PIC-based methods of the CPES Project, and was selected (1) because of concerns about noise issues associated with PIC in the high-density-contrast environment of the edge pedestal, (2) to be able to exploit advanced numerical methods developed for fluid codes, and (3) to build upon the successes of core continuum gyrokinetic codes such as GYRO, GS2 and GENE. The ESL project presently has three components: TEMPEST, a full-f, full-geometry (single-null divertor, or arbitrary-shape closed flux surfaces) code in E, {mu} (energy, magnetic-moment) coordinates; EGK, a simple-geometry rapid-prototype code, presently of; and the math component, which is developing and implementing algorithms for a next-generation code. Progress would be accelerated if we could find funding for a fourth, computer science, component, which would develop software infrastructure, provide user support, and address needs for data handing and analysis. We summarize the status and plans for the three funded activities.« less

Energetically consistent collisional gyrokinetics

DOE PAGES

Burby, J. W.; Brizard, A. J.; Qin, H.

2015-10-30

Here, we present a formulation of collisional gyrokinetic theory with exact conservation laws for energy and canonical toroidal momentum. Collisions are accounted for by a nonlinear gyrokinetic Landau operator. Gyroaveraging and linearization do not destroy the operator's conservation properties. Just as in ordinary kinetic theory, the conservation laws for collisional gyrokinetic theory are selected by the limiting collisionless gyrokinetic theory. (C) 2015 AIP Publishing LLC.

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

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.; Canik, J. M.

2016-04-01

> The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces) of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.

Three-dimensional computer simulation of non-reacting jet-gas flow mixing in an MHD second stage combustor

NASA Astrophysics Data System (ADS)

Chang, S. L.; Lottes, S. A.; Berry, G. F.

Argonne National Laboratory is investigating the non-reacting jet-gas mixing patterns in a magnetohydrodynamics (MHD) second stage combustor by using a three-dimensional single-phase hydrodynamics computer program. The computer simulation is intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may improve downstream MHD channel performance. The code is used to examine the three-dimensional effects of the side walls and the distributed jet flows on the non-reacting jet-gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

Benchmark studies of the gyro-Landau-fluid code and gyro-kinetic codes on kinetic ballooning modes

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

Tang, T. F.; Lawrence Livermore National Laboratory, Livermore, California 94550; Xu, X. Q.

2016-03-15

A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 + 1 code on KBMs. To verify our code on the KBM case, we first perform the beta scan basedmore » on “Cyclone base case parameter set.” We find that the growth rate is almost the same for two codes, and the KBM mode is further destabilized as beta increases. For JET-like global circular equilibria, as the modes localize in peak pressure gradient region, a linear local beta scan using the same set of equilibria has been performed at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-electron collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular set of cbm18 equilibria, using GYRO code, shows different trends for the low-n and high-n modes. The low-n modes show that the linear growth rate peaks at peak pressure gradient position as GLF results. However, for high-n modes, the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs in ion diamagnetic drift direction steadily approaches and crosses over to the electron diamagnetic drift direction.« less

Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths

NASA Astrophysics Data System (ADS)

Monreal, Pedro; Calvo, Iván; Sánchez, Edilberto; Parra, Félix I.; Bustos, Andrés; Könies, Axel; Kleiber, Ralf; Görler, Tobias

2016-04-01

In the linear collisionless limit, a zonal potential perturbation in a toroidal plasma relaxes, in general, to a non-zero residual value. Expressions for the residual value in tokamak and stellarator geometries, and for arbitrary wavelengths, are derived. These expressions involve averages over the lowest order particle trajectories, that typically cannot be evaluated analytically. In this work, an efficient numerical method for the evaluation of such expressions is reported. It is shown that this method is faster than direct gyrokinetic simulations performed with the Gene and EUTERPE codes. Calculations of the residual value in stellarators are provided for much shorter wavelengths than previously available in the literature. Electrons must be treated kinetically in stellarators because, unlike in tokamaks, kinetic electrons modify the residual value even at long wavelengths. This effect, that had already been predicted theoretically, is confirmed by gyrokinetic simulations.

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

Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T.

Here, five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currentsmore » to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.« less

SciDAC GSEP: Gyrokinetic Simulation of Energetic Particle Turbulence and Transport

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

Lin, Zhihong

Energetic particle (EP) confinement is a key physics issue for burning plasma experiment ITER, the crucial next step in the quest for clean and abundant energy, since ignition relies on self-heating by energetic fusion products (α-particles). Due to the strong coupling of EP with burning thermal plasmas, plasma confinement property in the ignition regime is one of the most uncertain factors when extrapolating from existing fusion devices to the ITER tokamak. EP population in current tokamaks are mostly produced by auxiliary heating such as neutral beam injection (NBI) and radio frequency (RF) heating. Remarkable progress in developing comprehensive EP simulationmore » codes and understanding basic EP physics has been made by two concurrent SciDAC EP projects GSEP funded by the Department of Energy (DOE) Office of Fusion Energy Science (OFES), which have successfully established gyrokinetic turbulence simulation as a necessary paradigm shift for studying the EP confinement in burning plasmas. Verification and validation have rapidly advanced through close collaborations between simulation, theory, and experiment. Furthermore, productive collaborations with computational scientists have enabled EP simulation codes to effectively utilize current petascale computers and emerging exascale computers. We review here key physics progress in the GSEP projects regarding verification and validation of gyrokinetic simulations, nonlinear EP physics, EP coupling with thermal plasmas, and reduced EP transport models. Advances in high performance computing through collaborations with computational scientists that enable these large scale electromagnetic simulations are also highlighted. These results have been widely disseminated in numerous peer-reviewed publications including many Phys. Rev. Lett. papers and many invited presentations at prominent fusion conferences such as the biennial International Atomic Energy Agency (IAEA) Fusion Energy Conference and the annual meeting of the American Physics Society, Division of Plasma Physics (APS-DPP).« 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.

MHD thrust vectoring of a rocket engine

NASA Astrophysics Data System (ADS)

Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic

2016-09-01

In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.

MHD and resonant instabilities in JT-60SA during current ramp-up with off-axis N-NB injection

NASA Astrophysics Data System (ADS)

Bierwage, A.; Toma, M.; Shinohara, K.

2017-12-01

The excitation of magnetohydrodynamic (MHD) and resonant instabilities and their effect on the plasma profiles during the current ramp-up phase of a beam-driven JT-60SA tokamak plasma is studied using the MHD-PIC hybrid code MEGA. In the simple scenario considered, the plasma is only driven by one negative-ion-based neutral beam, depositing 500 keV deuterons at 5 MW power off-axis at about mid-radius. The beam injection starts half-way in the ramp-up phase. Within 1 s, the beam-driven plasma current and fast ion pressure produce a configuration that is strongly unstable to rapidly growing MHD and resonant modes. Using MEGA, modes with low toroidal mode numbers in the range n = 1-4 are examined in detail and shown to cause substantial changes in the plasma profiles. The necessity to develop reduced models and incorporate the effects of such instabilities in integrated codes used to simulate the evolution of entire plasma discharges is discussed.

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

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

Akcay, Cihan; Victor, Brian S.; Jarboe, Thomas R.

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth d{sub i} to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeledmore » as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification (I{sub tor}/I{sub inj}) and formation time τ{sub f} demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates (I{sub tor}/I{sub inj}) and exhibits much a longer τ{sub f}. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.« less

Mixing of the Interstellar and Solar Plasmas at the Heliospheric Interface

DOE PAGES

Pogorelov, N. V.; Borovikov, S. N.

2015-10-12

From the ideal MHD perspective, the heliopause is a tangential discontinuity that separates the solar wind plasma from the local interstellar medium plasma. There are physical processes, however, that make the heliopause permeable. They can be subdivided into kinetic and MHD categories. Kinetic processes occur on small length and time scales, and cannot be resolved with MHD equations. On the other hand, MHD instabilities of the heliopause have much larger scales and can be easily observed by spacecraft. The heliopause may also be a subject of magnetic reconnection. In this paper, we discuss mechanisms of plasma mixing at the heliopausemore » in the context of Voyager 1 observations. Numerical results are obtained with a Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), which is a package of numerical codes capable of performing adaptive mesh refinement simulations of complex plasma flows in the presence of discontinuities and charge exchange between ions and neutral atoms. The flow of the ionized component is described with the ideal MHD equations, while the transport of atoms is governed either by the Boltzmann equation or multiple Euler gas dynamics equations. The code can also treat nonthermal ions and turbulence produced by them.« less

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.

Modeling of ion orbit loss and intrinsic toroidal rotation with the COGENT code

NASA Astrophysics Data System (ADS)

Dorf, M.; Dorr, M.; Cohen, R.; Rognlien, T.; Hittinger, J.

2014-10-01

We discuss recent advances in cross-separatrix neoclassical transport simulations with COGENT, a continuum gyro-kinetic code being developed by the Edge Simulation Laboratory (ESL) collaboration. The COGENT code models the axisymmetric transport properties of edge plasmas including the effects of nonlinear (Fokker-Planck) collisions and a self-consistent electrostatic potential. Our recent work has focused on studies of ion orbit loss and the associated toroidal rotation driven by this mechanism. The results of the COGENT simulations are discussed and analyzed for the parameters of the DIII-D experiment. Work performed for USDOE at LLNL under Contract DE-AC52-07NA27344.

Assessment of the MHD capability in the ATHENA code using data from the ALEX facility

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

Roth, P.A.

1989-03-01

The ATHENA (Advanced Thermal Hydraulic Energy Network Analyzer) code is a system transient analysis code with multi-loop, multi-fluid capabilities, which is available to the fusion community at the National Magnetic Fusion Energy Computing Center (NMFECC). The work reported here assesses the ATHENA magnetohydrodynamic (MHD) pressure drop model for liquid metals flowing through a strong magnetic field. An ATHENA model was developed for two simple geometry, adiabatic test sections used in the Argonne Liquid Metal Experiment (ALEX) at Argonne National Laboratory (ANL). The pressure drops calculated by ATHENA agreed well with the experimental results from the ALEX facility.

Porting a Hall MHD Code to a Graphic Processing Unit

NASA Technical Reports Server (NTRS)

Dorelli, John C.

2011-01-01

We present our experience porting a Hall MHD code to a Graphics Processing Unit (GPU). The code is a 2nd order accurate MUSCL-Hancock scheme which makes use of an HLL Riemann solver to compute numerical fluxes and second-order finite differences to compute the Hall contribution to the electric field. The divergence of the magnetic field is controlled with Dedner?s hyperbolic divergence cleaning method. Preliminary benchmark tests indicate a speedup (relative to a single Nehalem core) of 58x for a double precision calculation. We discuss scaling issues which arise when distributing work across multiple GPUs in a CPU-GPU cluster.

Advanced Discontinuous Galerkin Algorithms and First Open-Field Line Turbulence Simulations

NASA Astrophysics Data System (ADS)

Hammett, G. W.; Hakim, A.; Shi, E. L.

2016-10-01

New versions of Discontinuous Galerkin (DG) algorithms have interesting features that may help with challenging problems of higher-dimensional kinetic problems. We are developing the gyrokinetic code Gkeyll based on DG. DG also has features that may help with the next generation of Exascale computers. Higher-order methods do more FLOPS to extract more information per byte, thus reducing memory and communications costs (which are a bottleneck at exascale). DG uses efficient Gaussian quadrature like finite elements, but keeps the calculation local for the kinetic solver, also reducing communication. Sparse grid methods might further reduce the cost significantly in higher dimensions. The inner product norm can be chosen to preserve energy conservation with non-polynomial basis functions (such as Maxwellian-weighted bases), which can be viewed as a Petrov-Galerkin method. This allows a full- F code to benefit from similar Gaussian quadrature as used in popular δf gyrokinetic codes. Consistent basis functions avoid high-frequency numerical modes from electromagnetic terms. We will show our first results of 3 x + 2 v simulations of open-field line/SOL turbulence in a simple helical geometry (like Helimak/TORPEX), with parameters from LAPD, TORPEX, and NSTX. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.

Self-generated zonal flows in the plasma turbulence driven by trapped-ion and trapped-electron instabilities

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

Drouot, T.; Gravier, E.; Reveille, T.

This paper presents a study of zonal flows generated by trapped-electron mode and trapped-ion mode micro turbulence as a function of two plasma parameters—banana width and electron temperature. For this purpose, a gyrokinetic code considering only trapped particles is used. First, an analytical equation giving the predicted level of zonal flows is derived from the quasi-neutrality equation of our model, as a function of the density fluctuation levels and the banana widths. Then, the influence of the banana width on the number of zonal flows occurring in the system is studied using the gyrokinetic code. Finally, the impact of themore » temperature ratio T{sub e}/T{sub i} on the reduction of zonal flows is shown and a close link is highlighted between reduction and different gyro-and-bounce-average ion and electron density fluctuation levels. This reduction is found to be due to the amplitudes of gyro-and-bounce-average density perturbations n{sub e} and n{sub i} gradually becoming closer, which is in agreement with the analytical results given by the quasi-neutrality equation.« less

Study of neoclassical effects on the pedestal structure in ELMy H-mode plasmas

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Bateman, G.; Kritz, A. H.; Rafiq, T.; Park, G. Y.; Ku, S.; Chang, C. S.; Snyder, P. B.

2009-11-01

The neoclassical effects on the H-mode pedestal structure are investigated in this study. First principles' kinetic simulations of the neoclassical pedestal dynamics are combined with the MHD stability conditions for triggering ELM crashes that limit the pedestal width and height in H-mode plasmas. The neoclassical kinetic XGC0 code [1] is used to produce systematic scans over plasma parameters including plasma current, elongation, and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD stability ELITE code [2]. The scalings of the pedestal width and height are presented as a function of the scanned plasma parameters. Simulations with the XGC0 code, which include coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. Differences in the electron and ion pedestal scalings are investigated. [1] C.S. Chang et al, Phys. Plasmas 11 (2004) 2649. [2] P.B. Snyder et al, Phys. Plasmas, 9 (2002) 2037.

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

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

Anninos, Peter; Lau, Cheuk; Bryant, Colton

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performedmore » separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.« less

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

NASA Astrophysics Data System (ADS)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

Optimized up-down asymmetry to drive fast intrinsic rotation in tokamaks

NASA Astrophysics Data System (ADS)

Ball, Justin; Parra, Felix I.; Landreman, Matt; Barnes, Michael

2018-02-01

Breaking the up-down symmetry of the tokamak poloidal cross-section can significantly increase the spontaneous rotation due to turbulent momentum transport. In this work, we optimize the shape of flux surfaces with both tilted elongation and tilted triangularity in order to maximize this drive of intrinsic rotation. Nonlinear gyrokinetic simulations demonstrate that adding optimally-tilted triangularity can double the momentum transport of a tilted elliptical shape. This work indicates that tilting the elongation and triangularity in an ITER-like device can reduce the energy transport and drive intrinsic rotation with an Alfvén Mach number of roughly 1% . This rotation is four times larger than the rotation expected in ITER and is approximately what is needed to stabilize MHD instabilities. It is shown that this optimal shape can be created using the shaping coils of several present-day experiments.

TRANSITION FROM KINETIC TO MHD BEHAVIOR IN A COLLISIONLESS PLASMA

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

Parashar, Tulasi N.; Matthaeus, William H.; Shay, Michael A.

The study of kinetic effects in heliospheric plasmas requires representation of dynamics at sub-proton scales, but in most cases the system is driven by magnetohydrodynamic (MHD) activity at larger scales. The latter requirement challenges available computational resources, which raises the question of how large such a system must be to exhibit MHD traits at large scales while kinetic behavior is accurately represented at small scales. Here we study this implied transition from kinetic to MHD-like behavior using particle-in-cell (PIC) simulations, initialized using an Orszag–Tang Vortex. The PIC code treats protons, as well as electrons, kinetically, and we address the questionmore » of interest by examining several different indicators of MHD-like behavior.« less

Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows

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

Xu, X Q; Belli, E; Bodi, K

We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependencemore » of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.« less

Gyrokinetic Simulations with External Resonant Magnetic Perturbations: Island Torque and Nonambipolar Transport with Rotation

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Waelbroeck, F. L.

2012-03-01

Static external resonant magnetic perturbations (RMPs) have been added to the δf gyrokinetic code GYRO. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr and the corresponding plasma torque (density) R[jrBθ/c], induced by islands that break the toroidal symmetry of a tokamak. This extends previous GYRO simulations for the transport of toroidal angular momentum (TAM) [1,2]. The focus is on full torus radial slice electrostatic simulations of induced q=m/n=6/3 islands with widths 5% of the minor radius. The island torque scales with the radial electric field Er the island width w, and the intensity I of the high-n micro-turbulence, as wErI^1/2. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that there is a small co-directed magnetic acceleration to the small diamagnetic co-rotation corresponding to the zero Er which can be called the residual stress [2] from an externally induced island. Finite-beta GYRO simulations of a core radial slice demonstrate island unlocking and the RMP screening. 6pt[1] R.E. Waltz, et al., Phys. Plasmas 14, 122507 (2007). [2] R.E. Waltz, et al., Phys. Plasmas 18, 042504 (2011).

New Developments in Modeling MHD Systems on High Performance Computing Architectures

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Raeder, J.; Larson, D. J.; Bhattacharjee, A.

2009-04-01

Modeling the wide range of time and length scales present even in fluid models of plasmas like MHD and X-MHD (Extended MHD including two fluid effects like Hall term, electron inertia, electron pressure gradient) is challenging even on state-of-the-art supercomputers. In the last years, HPC capacity has continued to grow exponentially, but at the expense of making the computer systems more and more difficult to program in order to get maximum performance. In this paper, we will present a new approach to managing the complexity caused by the need to write efficient codes: Separating the numerical description of the problem, in our case a discretized right hand side (r.h.s.), from the actual implementation of efficiently evaluating it. An automatic code generator is used to describe the r.h.s. in a quasi-symbolic form while leaving the translation into efficient and parallelized code to a computer program itself. We implemented this approach for OpenGGCM (Open General Geospace Circulation Model), a model of the Earth's magnetosphere, which was accelerated by a factor of three on regular x86 architecture and a factor of 25 on the Cell BE architecture (commonly known for its deployment in Sony's PlayStation 3).

Magnus: A New Resistive MHD Code with Heat Flow Terms

NASA Astrophysics Data System (ADS)

Navarro, Anamaría; Lora-Clavijo, F. D.; González, Guillermo A.

2017-07-01

We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity—but not dominant—and heat transference in a uniform 3D grid. The code is based on the finite-volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error (˜ 1× {10}-12). For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere-transition-corona region, while the second one consists of a 2D simulation of a transverse velocity pulse in a coronal loop.

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.

Hybrid-view programming of nuclear fusion simulation code in the PGAS parallel programming language XcalableMP

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

Tsugane, Keisuke; Boku, Taisuke; Murai, Hitoshi

Recently, the Partitioned Global Address Space (PGAS) parallel programming model has emerged as a usable distributed memory programming model. XcalableMP (XMP) is a PGAS parallel programming language that extends base languages such as C and Fortran with directives in OpenMP-like style. XMP supports a global-view model that allows programmers to define global data and to map them to a set of processors, which execute the distributed global data as a single thread. In XMP, the concept of a coarray is also employed for local-view programming. In this study, we port Gyrokinetic Toroidal Code - Princeton (GTC-P), which is a three-dimensionalmore » gyrokinetic PIC code developed at Princeton University to study the microturbulence phenomenon in magnetically confined fusion plasmas, to XMP as an example of hybrid memory model coding with the global-view and local-view programming models. In local-view programming, the coarray notation is simple and intuitive compared with Message Passing Interface (MPI) programming while the performance is comparable to that of the MPI version. Thus, because the global-view programming model is suitable for expressing the data parallelism for a field of grid space data, we implement a hybrid-view version using a global-view programming model to compute the field and a local-view programming model to compute the movement of particles. Finally, the performance is degraded by 20% compared with the original MPI version, but the hybrid-view version facilitates more natural data expression for static grid space data (in the global-view model) and dynamic particle data (in the local-view model), and it also increases the readability of the code for higher productivity.« less

Hybrid-view programming of nuclear fusion simulation code in the PGAS parallel programming language XcalableMP

DOE PAGES

Tsugane, Keisuke; Boku, Taisuke; Murai, Hitoshi; ...

2016-06-01

Recently, the Partitioned Global Address Space (PGAS) parallel programming model has emerged as a usable distributed memory programming model. XcalableMP (XMP) is a PGAS parallel programming language that extends base languages such as C and Fortran with directives in OpenMP-like style. XMP supports a global-view model that allows programmers to define global data and to map them to a set of processors, which execute the distributed global data as a single thread. In XMP, the concept of a coarray is also employed for local-view programming. In this study, we port Gyrokinetic Toroidal Code - Princeton (GTC-P), which is a three-dimensionalmore » gyrokinetic PIC code developed at Princeton University to study the microturbulence phenomenon in magnetically confined fusion plasmas, to XMP as an example of hybrid memory model coding with the global-view and local-view programming models. In local-view programming, the coarray notation is simple and intuitive compared with Message Passing Interface (MPI) programming while the performance is comparable to that of the MPI version. Thus, because the global-view programming model is suitable for expressing the data parallelism for a field of grid space data, we implement a hybrid-view version using a global-view programming model to compute the field and a local-view programming model to compute the movement of particles. Finally, the performance is degraded by 20% compared with the original MPI version, but the hybrid-view version facilitates more natural data expression for static grid space data (in the global-view model) and dynamic particle data (in the local-view model), and it also increases the readability of the code for higher productivity.« less

Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers

DOE PAGES

Wang, Bei; Ethier, Stephane; Tang, William; ...

2017-06-29

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability ofmore » the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. These performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.« less

Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers

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

Wang, Bei; Ethier, Stephane; Tang, William

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability ofmore » the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. These performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.« less

Validation of gyrokinetic simulations with measurements of electron temperature fluctuations and density-temperature phase angles on ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Freethy, S. J.; Görler, T.; Creely, A. J.; Conway, G. D.; Denk, S. S.; Happel, T.; Koenen, C.; Hennequin, P.; White, A. E.; ASDEX Upgrade Team

2018-05-01

Measurements of turbulent electron temperature fluctuation amplitudes, δTe ⊥/Te , frequency spectra, and radial correlation lengths, Lr(Te ⊥) , have been performed at ASDEX Upgrade using a newly upgraded Correlation ECE diagnostic in the range of scales k⊥<1.4 cm-1, kr<3.5 cm-1 ( k⊥ρs<0.28 and krρs<0.7 ). The phase angle between turbulent temperature and density fluctuations, αnT, has also been measured by using an ECE radiometer coupled to a reflectometer along the same line of sight. These quantities are used simultaneously to constrain a set of ion-scale non-linear gyrokinetic turbulence simulations of the outer core (ρtor = 0.75) of a low density, electron heated L-mode plasma, performed using the gyrokinetic simulation code, GENE. The ion and electron temperature gradients were scanned within uncertainties. It is found that gyrokinetic simulations are able to match simultaneously the electron and ion heat flux at this radius within the experimental uncertainties. The simulations were performed based on a reference discharge for which δTe ⊥/Te measurements were available, and Lr(Te ⊥) and αnT were then predicted using synthetic diagnostics prior to measurements in a repeat discharge. While temperature fluctuation amplitudes are overestimated by >50% for all simulations within the sensitivity scans performed, good quantitative agreement is found for Lr(Te ⊥) and αnT. A validation metric is used to quantify the level of agreement of individual simulations with experimental measurements, and the best agreement is found close to the experimental gradient values.

Comprehensive comparisons of geodesic acoustic mode characteristics and dynamics between Tore Supra experiments and gyrokinetic simulations

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

Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.

2015-06-15

In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation timemore » are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.« less

Nonlinear Full-f Edge Gyrokinetic Turbulence Simulations

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Dimits, A. M.; Umansky, M. V.

2008-11-01

TEMPEST is a nonlinear full-f 5D electrostatic gyrokinetic code for simulations of neoclassical and turbulent transport for tokamak plasmas. Given an initial density perturbation, 4D TEMPEST simulations show that the kinetic GAM exists in the edge in the form of outgoing waves [1], its radial scale is set by plasma profiles, and the ion temperature inhomogeneity is necessary for GAM radial propagation. From an initial Maxwellian distribution with uniform poloidal profiles on flux surfaces, the 5D TEMPEST simulations in a flux coordinates with Boltzmann electron model in a circular geometry show the development of neoclassical equilibrium, the generation of the neoclassical electric field due to neoclassical polarization, and followed by a growth of instability due to the spatial gradients. 5D TEMPEST simulations of kinetic GAM turbulent generation, radial propagation, and its impact on transport will be reported. [1] X. Q. Xu, Phys. Rev. E., 78 (2008).

Improvements of the particle-in-cell code EUTERPE for petascaling machines

NASA Astrophysics Data System (ADS)

Sáez, Xavier; Soba, Alejandro; Sánchez, Edilberto; Kleiber, Ralf; Castejón, Francisco; Cela, José M.

2011-09-01

In the present work we report some performance measures and computational improvements recently carried out using the gyrokinetic code EUTERPE (Jost, 2000 [1] and Jost et al., 1999 [2]), which is based on the general particle-in-cell (PIC) method. The scalability of the code has been studied for up to sixty thousand processing elements and some steps towards a complete hybridization of the code were made. As a numerical example, non-linear simulations of Ion Temperature Gradient (ITG) instabilities have been carried out in screw-pinch geometry and the results are compared with earlier works. A parametric study of the influence of variables (step size of the time integrator, number of markers, grid size) on the quality of the simulation is presented.

Test Particle Simulations of Electron Injection by the Bursty Bulk Flows (BBFs) using High Resolution Lyon-Feddor-Mobarry (LFM) Code

NASA Astrophysics Data System (ADS)

Eshetu, W. W.; Lyon, J.; Wiltberger, M. J.; Hudson, M. K.

2017-12-01

Test particle simulations of electron injection by the bursty bulk flows (BBFs) have been done using a test particle tracer code [1], and the output fields of the Lyon-Feddor-Mobarry global magnetohydro- dynamics (MHD) code[2]. The MHD code was run with high resolu- tion (oct resolution), and with specified solar wind conditions so as to reproduce the observed qualitative picture of the BBFs [3]. Test par- ticles were injected so that they interact with earthward propagating BBFs. The result of the simulation shows that electrons are pushed ahead of the BBFs and accelerated into the inner magnetosphere. Once electrons are in the inner magnetosphere they are further energized by drift resonance with the azimuthal electric field. In addition pitch angle scattering of electrons resulting in the violation conservation of the first adiabatic invariant has been observed. The violation of the first adiabatic invariant occurs as electrons cross a weak magnetic field region with a strong gradient of the field perturbed by the BBFs. References 1. Kress, B. T., Hudson,M. K., Looper, M. D. , Albert, J., Lyon, J. G., and Goodrich, C. C. (2007), Global MHD test particle simulations of ¿ 10 MeV radiation belt electrons during storm sudden commencement, J. Geophys. Res., 112, A09215, doi:10.1029/2006JA012218. Lyon,J. G., Fedder, J. A., and Mobarry, C.M., The Lyon- Fedder-Mobarry (LFM) Global MHD Magnetospheric Simulation Code (2004), J. Atm. And Solar-Terrestrial Phys., 66, Issue 15-16, 1333- 1350,doi:10.1016/j.jastp. Wiltberger, Merkin, M., Lyon, J. G., and Ohtani, S. (2015), High-resolution global magnetohydrodynamic simulation of bursty bulk flows, J. Geophys. Res. Space Physics, 120, 45554566, doi:10.1002/2015JA021080.

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

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

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant m=2, n=-1 , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the m=2 (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces)more » of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.« less

Numerical Simulations of Free Surface Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Glimm, James; Oh, Wonho; Prykarpatskyy, Yarema

2003-11-01

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations are based on a finite element discretization on moving grids dynamically conforming to fluid interfaces. The method has been implemented as an MHD extension of the FronTier code. The code has been applied for modeling the behavior of lithium and mercury jets in magnetic fields, laser ablation plumes, and the Richtmyer-Meshkov instability of a liquid mercury jet interacting with a high energy proton pulse in a strong magnetic field. Such an instability occurs in the target for the Muon Collider.

Investigation of island formation due to RMPs in DIII-D plasmas with the SIESTA resistive MHD equilibrium code

DOE PAGES

Hirshman, S. P.; Shafer, M. W.; Seal, S. K.; ...

2016-03-03

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant m=2, n=-1 , resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the m=2 (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces)more » of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.« less

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.

Theory-based model for the pedestal, edge stability and ELMs in tokamaks

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Bateman, G.; Brennan, D. P.; Schnack, D. D.; Snyder, P. B.; Voitsekhovitch, I.; Kritz, A. H.; Janeschitz, G.; Kruger, S.; Onjun, T.; Pacher, G. W.; Pacher, H. D.

2006-04-01

An improved model for triggering edge localized mode (ELM) crashes is developed for use within integrated modelling simulations of the pedestal and ELM cycles at the edge of H-mode tokamak plasmas. The new model is developed by using the BALOO, DCON and ELITE ideal MHD stability codes to derive parametric expressions for the ELM triggering threshold. The whole toroidal mode number spectrum is studied with these codes. The DCON code applies to low mode numbers, while the BALOO code applies to only high mode numbers and the ELITE code applies to intermediate and high mode numbers. The variables used in the parametric stability expressions are the normalized pressure gradient and the parallel current density, which drive ballooning and peeling modes. Two equilibria motivated by DIII-D geometry with different plasma triangularities are studied. It is found that the stable region in the high triangularity discharge covers a much larger region of parameter space than the corresponding stability region in the low triangularity discharge. The new ELM trigger model is used together with a previously developed model for pedestal formation and ELM crashes in the ASTRA integrated modelling code to follow the time evolution of the temperature profiles during ELM cycles. The ELM frequencies obtained in the simulations of low and high triangularity discharges are observed to increase with increasing heating power. There is a transition from second stability to first ballooning mode stability as the heating power is increased in the high triangularity simulations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.

Modeling of Feedback Stabilization of External MHD Modes in Toroidal Geometry

NASA Astrophysics Data System (ADS)

Chu, M. S.; Chance, M. S.; Okabayashi, M.

2000-10-01

The intelligent shell feedback scheme(C.M. Bishop, Plasma Phys. Contr. Nucl. Fusion 31), 1179 (1989). seeks to utilize external coils to suppress the unstable MHD modes slowed down by the resistive shell. We present a new formulation and numerical results of the interaction between the plasma and its outside vacuum region, with complete plasma response and the inclusion of a resistive vessel in general toroidal geometry. This is achieved by using the Green's function technique, which is a generalization of that previously used for the VACUUM(M.S. Chance, Phys. Plasmas 4), 2161 (1997). code and coupled with the ideal MHD code GATO. The effectiveness of different realizations of the intelligent shell concept is gauged by their ability to minimize the available free energy to drive the MHD mode. Computations indicate poloidal coverage of 30% of the total resistive wall surface area and 6 or 7 segments of ``intelligent coil'' arrays superimposed on the resistive wall will allow recovery of up to 90% the effectiveness of the ideal shell in stabilizing the ideal external kink.

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

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

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

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

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

Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo

2017-06-01

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, ofmore » the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.« less

NIMROD modeling of quiescent H-mode: reconstruction considerations and saturation mechanism

NASA Astrophysics Data System (ADS)

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

2017-02-01

The extended-MHD NIMROD code (Sovinec and King 2010 J. Comput. Phys. 229 5803) models broadband-MHD activity from a reconstruction of a quiescent H-mode shot on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614). Computations with the reconstructed toroidal and poloidal ion flows exhibit low-{{n}φ} perturbations ({{n}φ}≃ 1 -5) that grow and saturate into a turbulent-like MHD state. The workflow used to project the reconstructed state onto the NIMROD basis functions re-solves the Grad-Shafranov equation and extrapolates profiles to include scrape-off-layer currents. Evaluation of the transport from the turbulent-like MHD state leads to a relaxation of the density and temperature profiles.

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.

Optimizing fusion PIC code performance at scale on Cori Phase 2

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

Koskela, T. S.; Deslippe, J.

In this paper we present the results of optimizing the performance of the gyrokinetic full-f fusion PIC code XGC1 on the Cori Phase Two Knights Landing system. The code has undergone substantial development to enable the use of vector instructions in its most expensive kernels within the NERSC Exascale Science Applications Program. We study the single-node performance of the code on an absolute scale using the roofline methodology to guide optimization efforts. We have obtained 2x speedups in single node performance due to enabling vectorization and performing memory layout optimizations. On multiple nodes, the code is shown to scale wellmore » up to 4000 nodes, near half the size of the machine. We discuss some communication bottlenecks that were identified and resolved during the work.« less

Simulating the interaction of the heliosphere with the local interstellar medium: MHD results from a finite volume approach, first bidimensional results

NASA Technical Reports Server (NTRS)

Chanteur, G.; Khanfir, R.

1995-01-01

We have designed a full compressible MHD code working on unstructured meshes in order to be able to compute accurately sharp structures embedded in large scale simulations. The code is based on a finite volume method making use of a kinetic flux splitting. A bidimensional version of the code has been used to simulate the interaction of a moving interstellar medium, magnetized or unmagnetized with a rotating and magnetized heliopspheric plasma source. Being aware that these computations are not realistic due to the restriction to two dimensions, we present it to demonstrate the ability of this new code to handle this problem. An axisymetric version, now under development, will be operational in a few months. Ultimately we plan to run a full 3d version.

The Athena Astrophysical MHD Code in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Skinner, M. A.; Ostriker, E. C.

2011-10-01

We have developed a method for implementing cylindrical coordinates in the Athena MHD code (Skinner & Ostriker 2010). The extension has been designed to alter the existing Cartesian-coordinates code (Stone et al. 2008) as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport, a central feature of the Athena algorithm, while making use of previously implemented code modules such as the eigensystems and Riemann solvers. Angular-momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and constrained transport updates. Finally, we have developed a test suite of standard and novel problems in one-, two-, and three-dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the web.

What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?

DOE PAGES

Kim, Kyuho; Chang, C. S.; Seo, Janghoon; ...

2017-01-24

Here, in order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction. The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence. The global full-f gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the fullmore » torus simulation in an ITG unstable plasma in a model toroidal geometry. It is found that (1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence, (2) a reasonably accurate simulation can be performed if the correct wedge number N can be identified, (3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude |δΦ| and assuring that the variation of δΦ between the discrete kθ values is less than 25% compared to the peak |δΦ|, and (4) a frequency spectrum may not be used for the validity check of a wedge simulation.« less

What happens to full-f gyrokinetic transport and turbulence in a toroidal wedge simulation?

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

Kim, Kyuho; Chang, C. S.; Seo, Janghoon

Here, in order to save the computing time or to fit the simulation size into a limited computing hardware in a gyrokinetic turbulence simulation of a tokamak plasma, a toroidal wedge simulation may be utilized in which only a partial toroidal section is modeled with a periodic boundary condition in the toroidal direction. The most severe restriction in the wedge simulation is expected to be in the longest wavelength turbulence, i.e., ion temperature gradient (ITG) driven turbulence. The global full-f gyrokinetic code XGC1 is used to compare the transport and turbulence properties from a toroidal wedge simulation against the fullmore » torus simulation in an ITG unstable plasma in a model toroidal geometry. It is found that (1) the convergence study in the wedge number needs to be conducted all the way down to the full torus in order to avoid a false convergence, (2) a reasonably accurate simulation can be performed if the correct wedge number N can be identified, (3) the validity of a wedge simulation may be checked by performing a wave-number spectral analysis of the turbulence amplitude |δΦ| and assuring that the variation of δΦ between the discrete kθ values is less than 25% compared to the peak |δΦ|, and (4) a frequency spectrum may not be used for the validity check of a wedge simulation.« less

Suppressing Electron Turbulence and Triggering Internal Transport Barriers with Reversed Magnetic Shear in the National Spherical Torus Experiment

NASA Astrophysics Data System (ADS)

Peterson, Jayson Luc

2011-10-01

Observations in the National Spherical Torus Experiment (NSTX) have found electron temperature gradients that greatly exceed the linear threshold for the onset for electron temperature gradient-driven (ETG) turbulence. These discharges, deemed electron internal transport barriers (e-ITBs), coincide with a reversal in the shear of the magnetic field and with a reduction in electron-scale density fluctuations, qualitatively consistent with earlier gyrokinetic predictions. To investigate this phenomenon further, we numerically model electron turbulence in NSTX reversed-shear plasmas using the gyrokinetic turbulence code GYRO. These first-of-a-kind nonlinear gyrokinetic simulations of NSTX e-ITBs confirm that reversing the magnetic shear can allow the plasma to reach electron temperature gradients well beyond the critical gradient for the linear onset of instability. This effect is very strong, with the nonlinear threshold for significant transport approaching three times the linear critical gradient in some cases, in contrast with moderate shear cases, which can drive significant ETG turbulence at much lower gradients. In addition to the experimental implications of this upshifted nonlinear critical gradient, we explore the behavior of ETG turbulence during reversed shear discharges. This work is supported by the SciDAC Center for the Study of Plasma Microturbulence, DOE Contract DE-AC02-09CH11466, and used the resources of NCCS at ORNL and NERSC at LBNL. M. Ono et al., Nucl. Fusion 40, 557 (2000).

Self-consistent gyrokinetic modeling of neoclassical and turbulent impurity transport

NASA Astrophysics Data System (ADS)

Estève, D.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Breton, S.; Donnel, P.; Asahi, Y.; Bourdelle, C.; Dif-Pradalier, G.; Ehrlacher, C.; Emeriau, C.; Ghendrih, Ph.; Gillot, C.; Latu, G.; Passeron, C.

2018-03-01

Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code (Grandgirard et al 2016 Comput. Phys. Commun. 207 35). A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch-Schlüter regime that is probably relevant for tungsten, the standard expression for the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations (Belli et al 2012 Plasma Phys. Control. Fusion 54 015015). The thermal screening factor appears to be less than predicted analytically in the Pfirsch-Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as is usually assumed. The synergy partly results from the turbulence-driven in-out poloidal asymmetry of tungsten density. This result suggests the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

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

Madduri, Kamesh; Im, Eun-Jin; Ibrahim, Khaled Z.

The next decade of high-performance computing (HPC) systems will see a rapid evolution and divergence of multi- and manycore architectures as power and cooling constraints limit increases in microprocessor clock speeds. Understanding efficient optimization methodologies on diverse multicore designs in the context of demanding numerical methods is one of the greatest challenges faced today by the HPC community. In this paper, we examine the efficient multicore optimization of GTC, a petascale gyrokinetic toroidal fusion code for studying plasma microturbulence in tokamak devices. For GTC’s key computational components (charge deposition and particle push), we explore efficient parallelization strategies across a broadmore » range of emerging multicore designs, including the recently-released Intel Nehalem-EX, the AMD Opteron Istanbul, and the highly multithreaded Sun UltraSparc T2+. We also present the first study on tuning gyrokinetic particle-in-cell (PIC) algorithms for graphics processors, using the NVIDIA C2050 (Fermi). Our work discusses several novel optimization approaches for gyrokinetic PIC, including mixed-precision computation, particle binning and decomposition strategies, grid replication, SIMDized atomic floating-point operations, and effective GPU texture memory utilization. Overall, we achieve significant performance improvements of 1.3–4.7× on these complex PIC kernels, despite the inherent challenges of data dependency and locality. Finally, our work also points to several architectural and programming features that could significantly enhance PIC performance and productivity on next-generation architectures.« less

Simulation of ITG instabilities with fully kinetic ions and drift-kinetic electrons in tokamaks

NASA Astrophysics Data System (ADS)

Hu, Youjun; Chen, Yang; Parker, Scott

2017-10-01

A turbulence simulation model with fully kinetic ions and drift-kinetic electrons is being developed in the toroidal electromagnetic turbulence code GEM. This is motivated by the observation that gyrokinetic ions are not well justified in simulating turbulence in tokamak edges with steep density profile, where ρi / L is not small enough to be used a small parameter needed by the gyrokinetic ordering (here ρi is the gyro-radius of ions and L is the scale length of density profile). In this case, the fully kinetic ion model may be useful. Our model uses an implicit scheme to suppress high-frequency compressional Alfven waves and waves associated with the gyro-motion of ions. The ion orbits are advanced by using the well-known Boris scheme, which reproduces correct drift-motion even with large time-step comparable to the ion gyro-period. The field equation in this model is Ampere's law with the magnetic field eliminated by using an implicit scheme of Faraday's law. The current contributed by ions are computed by using an implicit δf method. A flux tube approximation is adopted, which makes the field equation much easier to solve. Numerical results of electromagnetic ITG obtained from this model will be presented and compared with the gyrokinetic results. This work is supported by U.S. Department of Energy, Office of Fusion Energy Sciences under Award No. DE-SC0008801.

Assessment of the MHD capability in the ATHENA code using data from the ALEX (Argonne Liquid Metal Experiment) facility

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

Roth, P.A.

1988-10-28

The ATHENA (Advanced Thermal Hydraulic Energy Network Analyzer) code is a system transient analysis code with multi-loop, multi-fluid capabilities, which is available to the fusion community at the National Magnetic Fusion Energy Computing Center (NMFECC). The work reported here assesses the ATHENA magnetohydrodynamic (MHD) pressure drop model for liquid metals flowing through a strong magnetic field. An ATHENA model was developed for two simple geometry, adiabatic test sections used in the Argonne Liquid Metal Experiment (ALEX) at Argonne National Laboratory (ANL). The pressure drops calculated by ATHENA agreed well with the experimental results from the ALEX facility. 13 refs., 4more » figs., 2 tabs.« less

MHD Code Optimizations and Jets in Dense Gaseous Halos

NASA Astrophysics Data System (ADS)

Gaibler, Volker; Vigelius, Matthias; Krause, Martin; Camenzind, Max

We have further optimized and extended the 3D-MHD-code NIRVANA. The magnetized part runs in parallel, reaching 19 Gflops per SX-6 node, and has a passively advected particle population. In addition, the code is MPI-parallel now - on top of the shared memory parallelization. On a 512^3 grid, we reach 561 Gflops with 32 nodes on the SX-8. Also, we have successfully used FLASH on the Opteron cluster. Scientific results are preliminary so far. We report one computation of highly resolved cocoon turbulence. While we find some similarities to earlier 2D work by us and others, we note a strange reluctancy of cold material to enter the low density cocoon, which has to be investigated further.

Alfvén ionization in an MHD-gas interactions code

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

Wilson, A. D.; Diver, D. A.

A numerical model of partially ionized plasmas is developed in order to capture their evolving ionization fractions as a result of Alfvén ionization (AI). The mechanism of, and the parameter regime necessary for, AI is discussed and an expression for the AI rate based on fluid parameters, from a gas-MHD model, is derived. This AI term is added to an existing MHD-gas interactions' code, and the result is a linear, 2D, two-fluid model that includes momentum transfer between charged and neutral species as well as an ionization rate that depends on the velocity fields of both fluids. The dynamics ofmore » waves propagating through such a partially ionized plasma are investigated, and it is found that AI has a significant influence on the fluid dynamics as well as both the local and global ionization fraction.« less

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

DOE PAGES

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul; ...

2017-08-28

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems

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

Peraza-Rodriguez, Hugo; Reynolds-Barredo, J. M.; Sanchez, Raul

Here, SIESTA is a recently developed MHD equilibrium code designed to perform fast and accurate calculations of ideal MHD equilibria for three-dimensional magnetic configurations. Since SIESTA does not assume closed magnetic surfaces, the solution can exhibit magnetic islands and stochastic regions. In its original implementation SIESTA addressed only fixed-boundary problems. That is, the shape of the plasma edge, assumed to be a magnetic surface, was kept fixed as the solution iteratively converges to equilibrium. This condition somewhat restricts the possible applications of SIESTA. In this paper we discuss an extension that will enable SIESTA to address free-plasma-boundary problems, opening upmore » the possibility of investigating problems in which the plasma boundary is perturbed either externally or internally. As an illustration, SIESTA is applied to a configuration of the W7-X stellarator.« less

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.

Database-driven web interface automating gyrokinetic simulations for validation

NASA Astrophysics Data System (ADS)

Ernst, D. R.

2010-11-01

We are developing a web interface to connect plasma microturbulence simulation codes with experimental data. The website automates the preparation of gyrokinetic simulations utilizing plasma profile and magnetic equilibrium data from TRANSP analysis of experiments, read from MDSPLUS over the internet. This database-driven tool saves user sessions, allowing searches of previous simulations, which can be restored to repeat the same analysis for a new discharge. The website includes a multi-tab, multi-frame, publication quality java plotter Webgraph, developed as part of this project. Input files can be uploaded as templates and edited with context-sensitive help. The website creates inputs for GS2 and GYRO using a well-tested and verified back-end, in use for several years for the GS2 code [D. R. Ernst et al., Phys. Plasmas 11(5) 2637 (2004)]. A centralized web site has the advantage that users receive bug fixes instantaneously, while avoiding the duplicated effort of local compilations. Possible extensions to the database to manage run outputs, toward prototyping for the Fusion Simulation Project, are envisioned. Much of the web development utilized support from the DoE National Undergraduate Fellowship program [e.g., A. Suarez and D. R. Ernst, http://meetings.aps.org/link/BAPS.2005.DPP.GP1.57.

Numerical simulation of the kinetic effects in the solar wind

NASA Astrophysics Data System (ADS)

Sokolov, I.; Toth, G.; Gombosi, T. I.

2017-12-01

Global numerical simulations of the solar wind are usually based on the ideal or resistive MagnetoHydroDynamics (MHD) equations. Within a framework of MHD the electric field is assumed to vanish in the co-moving frame of reference (ideal MHD) or to obey a simple and non-physical scalar Ohm's law (resistive MHD). The Maxwellian distribution functions are assumed, the electron and ion temperatures may be different. Non-disversive MHD waves can be present in this numerical model. The averaged equations for MHD turbulence may be included as well as the energy and momentum exchange between the turbulent and regular motion. With the use of explicit numerical scheme, the time step is controlled by the MHD wave propagtion time across the numerical cell (the CFL condition) More refined approach includes the Hall effect vie the generalized Ohm's law. The Lorentz force acting on light electrons is assumed to vanish, which gives the expression for local electric field in terms of the total electric current, the ion current as well as the electron pressure gradient and magnetic field. The waves (whistlers, ion-cyclotron waves etc) aquire dispersion and the short-wavelength perturbations propagate with elevated speed thus strengthening the CFL condition. If the grid size is sufficiently small to resolve ion skindepth scale, then the timestep is much shorter than the ion gyration period. The next natural step is to use hybrid code to resolve the ion kinetic effects. The hybrid numerical scheme employs the same generalized Ohm's law as Hall MHD and suffers from the same constraint on the time step while solving evolution of the electromagnetic field. The important distiction, however, is that by sloving particle motion for ions we can achieve more detailed description of the kinetic effect without significant degrade in the computational efficiency, because the time-step is sufficient to resolve the particle gyration. We present the fisrt numerical results from coupled BATS-R-US+ALTOR code as applied to kinetic simulations of the solar wind.

Multi-physics simulations of space weather

NASA Astrophysics Data System (ADS)

Gombosi, Tamas; Toth, Gabor; Sokolov, Igor; de Zeeuw, Darren; van der Holst, Bart; Cohen, Ofer; Glocer, Alex; Manchester, Ward, IV; Ridley, Aaron

Presently magnetohydrodynamic (MHD) models represent the "workhorse" technology for simulating the space environment from the solar corona to the ionosphere. While these models are very successful in describing many important phenomena, they are based on a low-order moment approximation of the phase-space distribution function. In the last decade our group at the Center for Space Environment Modeling (CSEM) has developed the Space Weather Modeling Framework (SWMF) that efficiently couples together different models describing the interacting regions of the space environment. Many of these domain models (such as the global solar corona, the inner heliosphere or the global magnetosphere) are based on MHD and are represented by our multiphysics code, BATS-R-US. BATS-R-US can solve the equations of "standard" ideal MHD, but it can also go beyond this first approximation. It can solve resistive MHD, Hall MHD, semi-relativistic MHD (that keeps the displacement current), multispecies (different ion species have different continuity equations) and multifluid (all ion species have separate continuity, momentum and energy equations) MHD. Recently we added two-fluid Hall MHD (solving the electron and ion energy equations separately) and are working on extended magnetohydrodynamics with anisotropic pressures. This talk will show the effects of added physics and compare space weather simulation results to "standard" ideal MHD.

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.

Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

NASA Astrophysics Data System (ADS)

Mikkelsen, D. R.; Howard, N. T.; White, A. E.; Creely, A. J.

2018-04-01

Verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for kyρs ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers. The ratio of ion to electron heat flux is similar in the two codes' simulations, but the heat fluxes themselves do not agree in almost all cases. In the I-mode regime, GENE's heat fluxes are ˜3 times those from GYRO, and they are ˜60%-100% higher than GYRO in the L-mode conditions. The GYRO under-prediction of Qe is much reduced in GENE's L-mode simulations, and it is eliminated in the I-mode simulations. This largely improved agreement with the experimental electron heat flux is offset, however, by the large overshoot of GENE's ion heat fluxes, which are 2-3 times the experimental level, and its electron heat flux overshoot at r/a = 0.80 in the I-mode. Rotation effects can explain part of the difference between the two codes' predictions, but very significant differences remain in simulations without any rotation effects.

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

NASA Astrophysics Data System (ADS)

Chacon, Luis

2006-10-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended 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 to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation. PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 (2^nd order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas, has been developed for resistive MHD, and is currently being extended to Hall MHD. In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries. L. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004) L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002); J. Comput. Phys., 188 (2), 573-592 (2003) L. Chac'on, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005 L. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006

Quasi-static MHD processes in earth's magnetosphere

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1988-01-01

An attempt is made to use the MHD equilibrium theory to describe the global magnetic field configuration of earth's magnetosphere and its time evolution under the influence of magnetospheric convection. To circumvent the difficulties inherent in today's MHD codes, use is made of a restriction to slowly time-dependent convection processes with convective velocities well below the typical Alfven speed. This restriction leads to a quasi-static MHD theory. The two-dimensional theory is outlined, and it is shown how sequences of two-dimensional equilibria evolve into a steady state configuration that is likely to become tearing mode unstable. It is then concluded that magnetospheric substorms occur periodically in earth's magnetosphere, thus being an integral part of the entire convection cycle.

NIMROD modeling of quiescent H-mode: Reconstruction considerations and saturation mechanism

DOE PAGES

King, Jacob R.; Burrell, Keith H.; Garofalo, Andrea M.; ...

2016-09-30

The extended-MHD NIMROD code (Sovinec and King 2010 J. Comput. Phys. 229 5803) models broadband-MHD activity from a reconstruction of a quiescent H-mode shot on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614). Computations with the reconstructed toroidal and poloidal ion flows exhibit low-n Φ perturbations (n Φ ≃1–5) that grow and saturate into a turbulent-like MHD state. The workflow used to project the reconstructed state onto the NIMROD basis functions re-solves the Grad–Shafranov equation and extrapolates profiles to include scrape-off-layer currents. In conclusion, evaluation of the transport from the turbulent-like MHD state leads to a relaxation of themore » density and temperature profiles.« less

NIMROD modeling of quiescent H-mode: Reconstruction considerations and saturation mechanism

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

King, Jacob R.; Burrell, Keith H.; Garofalo, Andrea M.

The extended-MHD NIMROD code (Sovinec and King 2010 J. Comput. Phys. 229 5803) models broadband-MHD activity from a reconstruction of a quiescent H-mode shot on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614). Computations with the reconstructed toroidal and poloidal ion flows exhibit low-n Φ perturbations (n Φ ≃1–5) that grow and saturate into a turbulent-like MHD state. The workflow used to project the reconstructed state onto the NIMROD basis functions re-solves the Grad–Shafranov equation and extrapolates profiles to include scrape-off-layer currents. In conclusion, evaluation of the transport from the turbulent-like MHD state leads to a relaxation of themore » density and temperature profiles.« less

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

Schnack, D.D.; Lottati, I.; Mikic, Z.

The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

Large Scale Earth's Bow Shock with Northern IMF as Simulated by PIC Code in Parallel with MHD Model

NASA Astrophysics Data System (ADS)

Baraka, Suleiman

2016-06-01

In this paper, we propose a 3D kinetic model (particle-in-cell, PIC) for the description of the large scale Earth's bow shock. The proposed version is stable and does not require huge or extensive computer resources. Because PIC simulations work with scaled plasma and field parameters, we also propose to validate our code by comparing its results with the available MHD simulations under same scaled solar wind (SW) and (IMF) conditions. We report new results from the two models. In both codes the Earth's bow shock position is found to be ≈14.8 R E along the Sun-Earth line, and ≈29 R E on the dusk side. Those findings are consistent with past in situ observations. Both simulations reproduce the theoretical jump conditions at the shock. However, the PIC code density and temperature distributions are inflated and slightly shifted sunward when compared to the MHD results. Kinetic electron motions and reflected ions upstream may cause this sunward shift. Species distributions in the foreshock region are depicted within the transition of the shock (measured ≈2 c/ ω pi for Θ Bn = 90° and M MS = 4.7) and in the downstream. The size of the foot jump in the magnetic field at the shock is measured to be (1.7 c/ ω pi ). In the foreshocked region, the thermal velocity is found equal to 213 km s-1 at 15 R E and is equal to 63 km s -1 at 12 R E (magnetosheath region). Despite the large cell size of the current version of the PIC code, it is powerful to retain macrostructure of planets magnetospheres in very short time, thus it can be used for pedagogical test purposes. It is also likely complementary with MHD to deepen our understanding of the large scale magnetosphere.

Effects of nitrogen seeding on core ion thermal transport in JET ILW L-mode plasmas

NASA Astrophysics Data System (ADS)

Bonanomi, N.; Mantica, P.; Citrin, J.; Giroud, C.; Lerche, E.; Sozzi, C.; Taylor, D.; Tsalas, M.; Van Eester, D.; contributors, JET

2018-02-01

A set of experiments was carried out in JET ILW (Joint European Torus with ITER-Like Wall) L-mode plasmas in order to study the effects of light impurities on core ion thermal transport. N was puffed into some discharges and its profile was measured by active Charge Exchange diagnostics, while ICRH power was deposited on- and off-axis in ({\\hspace{0pt}}3He)-D minority scheme in order to have a scan of local heat flux at constant total power with and without N injection. Experimentally, the ion temperature profiles are more peaked for similar heat fluxes when N is injected in the plasma. Gyro-kinetic simulations using the GENE code indicate that a stabilization of Ion Temperature Gradient driven turbulent transport due to main ion dilution and to changes in Te/Ti and s/q is responsible of the enhanced peaking. The quasi-linear models TGLF and QuaLiKiz are tested against the experimental and the gyro-kinetic results.

Comparing Turbulence Simulation with Experiment in DIII-D

NASA Astrophysics Data System (ADS)

Ross, D. W.; Bravenec, R. V.; Dorland, W.; Beer, M. A.; Hammett, G. W.; McKee, G. R.; Murakami, M.; Jackson, G. L.

2000-10-01

Gyrofluid simulations of DIII-D discharges with the GRYFFIN code(D. W. Ross et al.), Transport Task Force Workshop, Burlington, VT, (2000). are compared with transport and fluctuation measurements. The evolution of confinement-improved discharges(G. R. McKee et al.), Phys. Plasmas 7, 1870 (200) is studied at early times following impurity injection, when EXB rotational shear plays a small role. The ion thermal transport predicted by the code is consistent with the experimental values. Experimentally, changes in density profiles resulting from the injection of neon, lead to reduction in fluctuation levels and transport following the injection. This triggers subsequent changes in the shearing rate that further reduce the turbulence.(M. Murakami et al.), European Physical Society, Budapest (2000); M. Murakami et al., this meeting. Estimated uncertainties in the plasma profiles, however, make it difficult to simulate these reductions with the code. These cases will also be studied with the GS2 gyrokinetic code.

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

H.E. Mynick, P. Xanthopoulos and A.H. Boozer

Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes.

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.

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).

SciDAC Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas

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

Lin, Zhihong

2013-12-18

During the first year of the SciDAC gyrokinetic particle simulation (GPS) project, the GPS team (Zhihong Lin, Liu Chen, Yasutaro Nishimura, and Igor Holod) at the University of California, Irvine (UCI) studied the tokamak electron transport driven by electron temperature gradient (ETG) turbulence, and by trapped electron mode (TEM) turbulence and ion temperature gradient (ITG) turbulence with kinetic electron effects, extended our studies of ITG turbulence spreading to core-edge coupling. We have developed and optimized an elliptic solver using finite element method (FEM), which enables the implementation of advanced kinetic electron models (split-weight scheme and hybrid model) in the SciDACmore » GPS production code GTC. The GTC code has been ported and optimized on both scalar and vector parallel computer architectures, and is being transformed into objected-oriented style to facilitate collaborative code development. During this period, the UCI team members presented 11 invited talks at major national and international conferences, published 22 papers in peer-reviewed journals and 10 papers in conference proceedings. The UCI hosted the annual SciDAC Workshop on Plasma Turbulence sponsored by the GPS Center, 2005-2007. The workshop was attended by about fifties US and foreign researchers and financially sponsored several gradual students from MIT, Princeton University, Germany, Switzerland, and Finland. A new SciDAC postdoc, Igor Holod, has arrived at UCI to initiate global particle simulation of magnetohydrodynamics turbulence driven by energetic particle modes. The PI, Z. Lin, has been promoted to the Associate Professor with tenure at UCI.« less

MHD Advanced Power Train Phase I, Final Report, Volume 7

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

A. R. Jones

This appendix provides additional data in support of the MHD/Steam Power Plant Analyses reported in report Volume 5. The data is in the form of 3PA/SUMARY computer code printouts. The order of presentation in all four cases is as follows: (1) Overall Performance; (2) Component/Subsystem Information; (3) Plant Cost Accounts Summary; and (4) Plant Costing Details and Cost of Electricity.

Gyrokinetic equations and full f solution method based on Dirac's constrained Hamiltonian and inverse Kruskal iteration

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

Heikkinen, J. A.; Nora, M.

2011-02-15

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J= as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allowsmore » direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.« less

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

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.

Accelerating 3D Hall MHD Magnetosphere Simulations with Graphics Processing Units

NASA Astrophysics Data System (ADS)

Bard, C.; Dorelli, J.

2017-12-01

The resolution required to simulate planetary magnetospheres with Hall magnetohydrodynamics result in program sizes approaching several hundred million grid cells. These would take years to run on a single computational core and require hundreds or thousands of computational cores to complete in a reasonable time. However, this requires access to the largest supercomputers. Graphics processing units (GPUs) provide a viable alternative: one GPU can do the work of roughly 100 cores, bringing Hall MHD simulations of Ganymede within reach of modest GPU clusters ( 8 GPUs). We report our progress in developing a GPU-accelerated, three-dimensional Hall magnetohydrodynamic code and present Hall MHD simulation results for both Ganymede (run on 8 GPUs) and Mercury (56 GPUs). We benchmark our Ganymede simulation with previous results for the Galileo G8 flyby, namely that adding the Hall term to ideal MHD simulations changes the global convection pattern within the magnetosphere. Additionally, we present new results for the G1 flyby as well as initial results from Hall MHD simulations of Mercury and compare them with the corresponding ideal MHD runs.

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

Multi-dimensional computer simulation of MHD combustor hydrodynamics

NASA Astrophysics Data System (ADS)

Berry, G. F.; Chang, S. L.; Lottes, S. A.; Rimkus, W. A.

1991-04-01

Argonne National Laboratory is investigating the nonreacting jet gas mixing patterns in an MHD second stage combustor by using a 2-D multiphase hydrodynamics computer program and a 3-D single phase hydrodynamics computer program. The computer simulations are intended to enhance the understanding of flow and mixing patterns in the combustor, which in turn may lead to improvement of the downstream MHD channel performance. A 2-D steady state computer model, based on mass and momentum conservation laws for multiple gas species, is used to simulate the hydrodynamics of the combustor in which a jet of oxidizer is injected into an unconfined cross stream gas flow. A 3-D code is used to examine the effects of the side walls and the distributed jet flows on the non-reacting jet gas mixing patterns. The code solves the conservation equations of mass, momentum, and energy, and a transport equation of a turbulence parameter and allows permeable surfaces to be specified for any computational cell.

ECCD-induced tearing mode stabilization in coupled IPS/NIMROD/GENRAY HPC simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas; Kruger, S. E.; Held, E. D.; Harvey, R. W.; Elwasif, W. R.

2012-03-01

We summarize ongoing developments toward an integrated, predictive model for determining optimal ECCD-based NTM stabilization strategies in ITER. We demonstrate the capability of the SWIM Project's Integrated Plasma Simulator (IPS) framework to choreograph multiple executions of, and data exchanges between, physics codes modeling various spatiotemporal scales of this coupled RF/MHD problem on several thousand HPC processors. As NIMROD evolves fluid equations to model bulk plasma behavior, self-consistent propagation/deposition of RF power in the ensuing plasma profiles is calculated by GENRAY. Data from both codes is then processed by computational geometry packages to construct the RF-induced quasilinear diffusion tensor; moments of this tensor (entering as additional terms in NIMROD's fluid equations due to the disparity in RF/MHD spatiotemporal scales) influence the dynamics of current, momentum, and energy evolution as well as the MHD closures. Initial results are shown to correctly capture the physics of magnetic island stabilization; we also discuss the development of a numerical plasma control system for active feedback stabilization of tearing modes.

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.

Differential formulation of the gyrokinetic Landau operator

DOE PAGES

Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David

2017-01-05

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Mocz, Philip; Pakmor, Rüdiger; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars

2016-11-01

We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code AREPO. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a moving mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.

Advances in simulation of wave interactions with extended MHD phenomena

NASA Astrophysics Data System (ADS)

Batchelor, D.; Abla, G.; D'Azevedo, E.; Bateman, G.; Bernholdt, D. E.; Berry, L.; Bonoli, P.; Bramley, R.; Breslau, J.; Chance, M.; Chen, J.; Choi, M.; Elwasif, W.; Foley, S.; Fu, G.; Harvey, R.; Jaeger, E.; Jardin, S.; Jenkins, T.; Keyes, D.; Klasky, S.; Kruger, S.; Ku, L.; Lynch, V.; McCune, D.; Ramos, J.; Schissel, D.; Schnack, D.; Wright, J.

2009-07-01

The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.

XGC developments for a more efficient XGC-GENE code coupling

NASA Astrophysics Data System (ADS)

Dominski, Julien; Hager, Robert; Ku, Seung-Hoe; Chang, Cs

2017-10-01

In the Exascale Computing Program, the High-Fidelity Whole Device Modeling project initially aims at delivering a tightly-coupled simulation of plasma neoclassical and turbulence dynamics from the core to the edge of the tokamak. To permit such simulations, the gyrokinetic codes GENE and XGC will be coupled together. Numerical efforts are made to improve the numerical schemes agreement in the coupling region. One of the difficulties of coupling those codes together is the incompatibility of their grids. GENE is a continuum grid-based code and XGC is a Particle-In-Cell code using unstructured triangular mesh. A field-aligned filter is thus implemented in XGC. Even if XGC originally had an approximately field-following mesh, this field-aligned filter permits to have a perturbation discretization closer to the one solved in the field-aligned code GENE. Additionally, new XGC gyro-averaging matrices are implemented on a velocity grid adapted to the plasma properties, thus ensuring same accuracy from the core to the edge regions.

High beta and second stability region transport and stability analysis: Technical progress report

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

Hughes, M.H.; Phillips, M.W.

1995-03-01

This report summarizes MHD equilibrium and stability studies carried out at Northrop Grumman`s Advanced Technology and Development Center during the 12 month period starting March 1, 1994. Progress is reported in both ideal and resistive MHD modeling of TFTR plasmas. The development of codes to calculate the significant effects of highly anisotropic pressure distributions is discussed along with results from this model.

Three-dimensional global MHD modeling of a coronal mass ejection interacting with the solar wind

NASA Astrophysics Data System (ADS)

An, J.; Inoue, S.; Magara, T.; Lee, H.; Kang, J.; Hayashi, K.; Tanaka, T.; Den, M.

2013-12-01

We developed a three-dimensional (3D) magnetohydrodynamic (MHD) code to reproduce the structure of the solar wind, the propagation of a coronal mass ejection (CME), and the interaction between them. This MHD code is based on the finite volume method and total diminishing (TVD) scheme with an unstructured grid system. In particular, this grid system can avoid the singularity at the north and south poles and relax tight CFL conditions around the poles, both of which would arise in the spherical coordinate system (Tanaka 1995). In this study, we constructed a model of the solar wind driven by the physical values at 50 solar radii obtained from the MHD tomographic method (Hayashi et al. 2003) where an interplanetary scintillation (IPS) observational data is used. By comparing the result to the observational data obtained from the near-Earth OMNI dataset, we confirmed that our simulation reproduces the velocity, temperature and density profiles obtained from the near-Earth OMNI dataset. We then insert a spheromak-type CME (Kataoka et al. 2009) into our solar-wind model and investigate the propagation process of the CME interacting with the solar wind. In particular, we discuss how the magnetic twist accumulated in a CME affects the CME-solar wind interaction.

MHD Turbulence, div B = 0 and Lattice Boltzmann Simulations

NASA Astrophysics Data System (ADS)

Phillips, Nate; Keating, Brian; Vahala, George; Vahala, Linda

2006-10-01

The question of div B = 0 in MHD simulations is a crucial issue. Here we consider lattice Boltzmann simulations for MHD (LB-MHD). One introduces a scalar distribution function for the velocity field and a vector distribution function for the magnetic field. This asymmetry is due to the different symmetries in the tensors arising in the time evolution of these fields. The simple algorithm of streaming and local collisional relaxation is ideally parallelized and vectorized -- leading to the best sustained performance/PE of any code run on the Earth Simulator. By reformulating the BGK collision term, a simple implicit algorithm can be immediately transformed into an explicit algorithm that permits simulations at quite low viscosity and resistivity. However the div B is not an imposed constraint. Currently we are examining a new formulations of LB-MHD that impose the div B constraint -- either through an entropic like formulation or by introducing forcing terms into the momentum equations and permitting simpler forms of relaxation distributions.

Magnetohydrodynamic Modeling of the Jovian Magnetosphere

NASA Technical Reports Server (NTRS)

Walker, Raymond

2005-01-01

Under this grant we have undertaken a series of magnetohydrodynamic (MHD) simulation and data analysis studies to help better understand the configuration and dynamics of Jupiter's magnetosphere. We approached our studies of Jupiter's magnetosphere in two ways. First we carried out a number of studies using our existing MHD code. We carried out simulation studies of Jupiter s magnetospheric boundaries and their dependence on solar wind parameters, we studied the current systems which give the Jovian magnetosphere its unique configuration and we modeled the dynamics of Jupiter s magnetosphere following a northward turning of the interplanetary magnetic field (IMF). Second we worked to develop a new simulation code for studies of outer planet magnetospheres.

Edge-relevant plasma simulations with the continuum code COGENT

NASA Astrophysics Data System (ADS)

Dorf, M.; Dorr, M.; Ghosh, D.; Hittinger, J.; Rognlien, T.; Cohen, R.; Lee, W.; Schwartz, P.

2016-10-01

We describe recent advances in cross-separatrix and other edge-relevant plasma simulations with COGENT, a continuum gyro-kinetic code being developed by the Edge Simulation Laboratory (ESL) collaboration. The distinguishing feature of the COGENT code is its high-order finite-volume discretization methods, which employ arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. This paper discusses the 4D (axisymmetric) electrostatic version of the code, and the presented topics include: (a) initial simulations with kinetic electrons and development of reduced fluid models; (b) development and application of implicit-explicit (IMEX) time integration schemes; and (c) conservative modeling of drift-waves and the universal instability. Work performed for USDOE, at LLNL under contract DE-AC52-07NA27344 and at LBNL under contract DE-AC02-05CH11231.

Magnetosphere simulations with a high-performance 3D AMR MHD Code

NASA Astrophysics Data System (ADS)

Gombosi, Tamas; Dezeeuw, Darren; Groth, Clinton; Powell, Kenneth; Song, Paul

1998-11-01

BATS-R-US is a high-performance 3D AMR MHD code for space physics applications running on massively parallel supercomputers. In BATS-R-US the electromagnetic and fluid equations are solved with a high-resolution upwind numerical scheme in a tightly coupled manner. The code is very robust and it is capable of spanning a wide range of plasma parameters (such as β, acoustic and Alfvénic Mach numbers). Our code is highly scalable: it achieved a sustained performance of 233 GFLOPS on a Cray T3E-1200 supercomputer with 1024 PEs. This talk reports results from the BATS-R-US code for the GGCM (Geospace General Circularculation Model) Phase 1 Standard Model Suite. This model suite contains 10 different steady-state configurations: 5 IMF clock angles (north, south, and three equally spaced angles in- between) with 2 IMF field strengths for each angle (5 nT and 10 nT). The other parameters are: solar wind speed =400 km/sec; solar wind number density = 5 protons/cc; Hall conductance = 0; Pedersen conductance = 5 S; parallel conductivity = ∞.

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.

MHD stability analysis and global mode identification preparing for high beta operation in KSTAR

NASA Astrophysics Data System (ADS)

Park, Y. S.; Sabbagh, S. A.; Berkery, J. W.; Jiang, Y.; Ahn, J. H.; Han, H. S.; Bak, J. G.; Park, B. H.; Jeon, Y. M.; Kim, J.; Hahn, S. H.; Lee, J. H.; Ko, J. S.; in, Y. K.; Yoon, S. W.; Oh, Y. K.; Wang, Z.; Glasser, A. H.

2017-10-01

H-mode plasma operation in KSTAR has surpassed the computed n = 1 ideal no-wall stability limit in discharges exceeding several seconds in duration. The achieved high normalized beta plasmas are presently limited by resistive tearing instabilities rather than global kink/ballooning or RWMs. The ideal and resistive stability of these plasmas is examined by using different physics models. The observed m/ n = 2/1 tearing stability is computed by using the M3D-C1 code, and by the resistive DCON code. The global MHD stability modified by kinetic effects is examined using the MISK code. Results from the analysis explain the stabilization of the plasma above the ideal MHD no-wall limit. Equilibrium reconstructions used include the measured kinetic profiles and MSE data. In preparation for plasma operation at higher beta utilizing the planned second NBI system, three sets of 3D magnetic field sensors have been installed and will be used for RWM active feedback control. To accurately determine the dominant n-component produced by low frequency unstable RWMs, an algorithm has been developed that includes magnetic sensor compensation of the prompt applied field and the field from the induced current on the passive conductors. Supported by US DOE Contracts DE-FG02-99ER54524 and DE-SC0016614.

Short-scale turbulent fluctuations driven by the electron-temperature gradient in the national spherical torus experiment.

PubMed

Mazzucato, E; Smith, D R; Bell, R E; Kaye, S M; Hosea, J C; LeBlanc, B P; Wilson, J R; Ryan, P M; Domier, C W; Luhmann, N C; Yuh, H; Lee, W; Park, H

2008-08-15

Measurements with coherent scattering of electromagnetic waves in plasmas of the National Spherical Torus Experiment indicate the existence of turbulent fluctuations in the range of wave numbers k perpendicular rho(e)=0.1-0.4, corresponding to a turbulence scale length nearly equal to the collisionless skin depth. Experimental observations and agreement with numerical results from a linear gyrokinetic stability code support the conjecture that the observed turbulence is driven by the electron-temperature gradient.

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

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

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Fast Magnetotail Reconnection: Challenge to Global MHD Modeling

NASA Astrophysics Data System (ADS)

Kuznetsova, M. M.; Hesse, M.; Rastaetter, L.; Toth, G.; de Zeeuw, D.; Gombosi, T.

2005-05-01

Representation of fast magnetotail reconnection rates during substorm onset is one of the major challenges to global MHD modeling. Our previous comparative study of collisionless magnetic reconnection in GEM Challenge geometry demonstrated that the reconnection rate is controlled by ion nongyrotropic behavior near the reconnection site and that it can be described in terms of nongyrotropic corrections to the magnetic induction equation. To further test the approach we performed MHD simulations with nongyrotropic corrections of forced reconnection for the Newton Challenge setup. As a next step we employ the global MHD code BATSRUS and test different methods to model fast magnetotail reconnection rates by introducing non-ideal corrections to the induction equation in terms of nongyrotropic corrections, spatially localized resistivity, or current dependent resistivity. The BATSRUS adaptive grid structure allows to perform global simulations with spatial resolution near the reconnection site comparable with spatial resolution of local MHD simulations for the Newton Challenge. We select solar wind conditions which drive the accumulation of magnetic field in the tail lobes and subsequent magnetic reconnection and energy release. Testing the ability of global MHD models to describe magnetotail evolution during substroms is one of the elements of science based validation efforts at the Community Coordinated Modeling Center.

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

DOE PAGES

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

2018-03-26

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

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.

C-Mod MHD stability analysis with LHCD

NASA Astrophysics Data System (ADS)

Ebrahimi, Fatima; Bhattacharjee, A.; Delgado, L.; Scott, S.; Wilson, J. R.; Wallace, G. M.; Shiraiwa, S.; Mumgaard, R. T.

2016-10-01

In lower hybrid current drive (LHCD) experiments on the Alcator C-Mod, sawtooth activity could be suppressed as the safety factor q on axis is raised above unity. However, in some of these experiments, after applying LHCD, the onset of MHD mode activity caused the current drive efficiency to significantly drop. Here, we study the stability of these experiments by performing MHD simulations using the NIMROD code starting with experimental EFIT equilibria. First, consistent with the LHCD experiment with no signature of MHD activity, MHD mode activity was also absent in the simulations. Second, for experiments with MHD mode activity, we find that a core n=1 reconnecting mode with dominate poloidal modes of m=2,3 is unstable. This mode is a resistive current-driven mode as its growth rate scales with a negative power of the Lundquist number in the simulations. In addition, with further enhanced reversed-shear q profile in the simulations, a core double tearing mode is found to be unstable. This work is supported by U.S. DOE cooperative agreement DE-FC02-99ER54512 using the Alcator C-Mod tokamak, a DOE Office of Science user facility.

Two-fluid 2.5D code for simulations of small scale magnetic fields in the lower solar atmosphere

NASA Astrophysics Data System (ADS)

Piantschitsch, Isabell; Amerstorfer, Ute; Thalmann, Julia Katharina; Hanslmeier, Arnold; Lemmerer, Birgit

2015-08-01

Our aim is to investigate magnetic reconnection as a result of the time evolution of magnetic flux tubes in the solar chromosphere. A new numerical two-fluid code was developed, which will perform a 2.5D simulation of the dynamics from the upper convection zone up to the transition region. The code is based on the Total Variation Diminishing Lax-Friedrichs method and includes the effects of ion-neutral collisions, ionisation/recombination, thermal/resistive diffusivity as well as collisional/resistive heating. What is innovative about our newly developed code is the inclusion of a two-fluid model in combination with the use of analytically constructed vertically open magnetic flux tubes, which are used as initial conditions for our simulation. First magnetohydrodynamic (MHD) tests have already shown good agreement with known results of numerical MHD test problems like e.g. the Orszag-Tang vortex test, the Current Sheet test or the Spherical Blast Wave test. Furthermore, the single-fluid approach will also be applied to the initial conditions, in order to compare the different rates of magnetic reconnection in both codes, the two-fluid code and the single-fluid one.

An MHD Dynamo Experiment.

NASA Astrophysics Data System (ADS)

O'Connell, R.; Forest, C. B.; Plard, F.; Kendrick, R.; Lovell, T.; Thomas, M.; Bonazza, R.; Jensen, T.; Politzer, P.; Gerritsen, W.; McDowell, M.

1997-11-01

A MHD experiment is being constructed which will have the possibility of showing dynamo action: the self--generation of currents from fluid motion. The design allows sufficient experimental flexibility and diagnostic access to study a variety of issues central to dynamo theory, including mean--field electrodynamics and saturation (backreaction physics). Initially, helical flows required for dynamo action will be driven by propellers embedded in liquid sodium. The flow fields will first be measured using laser doppler velocimetry in a water experiment with an identical fluid Reynolds number. The magnetic field evolution will then be predicted using a MHD code, replacing the water with sodium; if growing magnetic fields are found, the experiment will be repeated with sodium.

Identifying microturbulence regimes in a TCV discharge making use of physical constraints on particle and heat fluxes

DOE PAGES

Mariani, Alberto; Brunner, S.; Dominski, J.; ...

2018-01-17

Reducing the uncertainty on physical input parameters derived from experimental measurements is essential towards improving the reliability of gyrokinetic turbulence simulations. This can be achieved by introducing physical constraints. Amongst them, the zero particle flux condition is considered here. A first attempt is also made to match as well the experimental ion/electron heat flux ratio. This procedure is applied to the analysis of a particular Tokamak à Configuration Variable discharge. A detailed reconstruction of the zero particle flux hyper-surface in the multi-dimensional physical parameter space at fixed time of the discharge is presented, including the effect of carbon as themore » main impurity. Both collisionless and collisional regimes are considered. Hyper-surface points within the experimental error bars are found. In conclusion, the analysis is done performing gyrokinetic simulations with the local version of the GENE code, computing the fluxes with a Quasi-Linear (QL) model and validating the QL results with non-linear simulations in a subset of cases.« less

Interaction between neoclassical effects and ion temperature gradient turbulence in gradient- and flux-driven gyrokinetic simulations

NASA Astrophysics Data System (ADS)

Oberparleiter, M.; Jenko, F.; Told, D.; Doerk, H.; Görler, T.

2016-04-01

Neoclassical and turbulent transport in tokamaks has been studied extensively over the past decades, but their possible interaction remains largely an open question. The two are only truly independent if the length scales governing each of them are sufficiently separate, i.e., if the ratio ρ* between ion gyroradius and the pressure gradient scale length is small. This is not the case in particularly interesting regions such as transport barriers. Global simulations of a collisional ion-temperature-gradient-driven microturbulence performed with the nonlinear global gyrokinetic code Gene are presented. In particular, comparisons are made between systems with and without neoclassical effects. In fixed-gradient simulations, the modified radial electric field is shown to alter the zonal flow pattern such that a significant increase in turbulent transport is observed for ρ*≳1 /300 . Furthermore, the dependency of the flux on the collisionality changes. In simulations with fixed power input, we find that the presence of neoclassical effects decreases the frequency and amplitude of intermittent turbulent transport bursts (avalanches) and thus plays an important role for the self-organisation behaviour.

Towards Multiscale Interactions Between Tearing Modes and Microturbulence

NASA Astrophysics Data System (ADS)

Williams, Z. R.; Pueschel, M. J.; Terry, P. W.

2017-10-01

Work on the Madison Symmetric Torus Reversed-Field Pinch (RFP) has shown that large-scale tearing modes present in standard operation are highly detrimental to confinement. These tearing modes, even when reduced in improved confinement regimes of operation, significantly affect zonal flow activity and play a large role in setting microturbulent-induced transport levels. Previous gyrokinetic work has shown that a small but finite tearing fluctuation amplitude is necessary to produce transport values in agreement with experimental observation. This has previously been implemented via an ad-hoc, constant-in-time A∥ perturbation. This work details self-consistent modeling of tearing fluctuations in the RFP using the Gene code via the inclusion of a current gradient drive incorporated into the background distribution function. Tearing mode growth rates calculated from gyrokinetic simulations are benchmarked with results from fluid theory. Additionally, first results from multiscale Gene simulations describing tearing mode interactions with RFP microturbulence are presented. This work is supported by the U.S. Department of Energy, Grant No. DE-FG02-85ER-53121.

Identifying microturbulence regimes in a TCV discharge making use of physical constraints on particle and heat fluxes

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

Mariani, Alberto; Brunner, S.; Dominski, J.

Reducing the uncertainty on physical input parameters derived from experimental measurements is essential towards improving the reliability of gyrokinetic turbulence simulations. This can be achieved by introducing physical constraints. Amongst them, the zero particle flux condition is considered here. A first attempt is also made to match as well the experimental ion/electron heat flux ratio. This procedure is applied to the analysis of a particular Tokamak à Configuration Variable discharge. A detailed reconstruction of the zero particle flux hyper-surface in the multi-dimensional physical parameter space at fixed time of the discharge is presented, including the effect of carbon as themore » main impurity. Both collisionless and collisional regimes are considered. Hyper-surface points within the experimental error bars are found. In conclusion, the analysis is done performing gyrokinetic simulations with the local version of the GENE code, computing the fluxes with a Quasi-Linear (QL) model and validating the QL results with non-linear simulations in a subset of cases.« less

Gyrokinetic Studies of Turbulence Reduction with Reverse Shear ETG Transport Barriers or Lithium Walls

NASA Astrophysics Data System (ADS)

Hammett, G. W.; Peterson, J. L.; Granstedt, E. M.; Bell, R.; Guttenfelder, W.; Kaye, S.; Leblanc, B.; Mikkelsen, D. R.; Smith, D. R.; Yuh, H. Y.; Candy, J.

2012-03-01

The National Spherical Torus Experiment (NSTX) can achieve high electron confinement regimes that are super-critically unstable to the electron temperature gradient (ETG) instability. These electron internal transport barriers (e-ITBs) occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO, the first nonlinear ETG simulations of NSTX e-ITB plasmas demonstrate reduced turbulence consistent with this observation. This is qualitatively consistent with a secondary instability picture of reduced ETG turbulence at negative shear (Jenko and Dorland PRL 2002). Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show that ETG-driven turbulence outside of the barrier is large enough to be experimentally relevant, but cannot propagate very far into the barrier. We also use GYRO to study turbulence in regimes that might be expected in the Lithium Torus eXperiment (LTX). While lithium has experimentally been shown to raise the edge temperature and improve performance, there can still be some turbulence from density-gradient-driven trapped electron modes, and a temperature pinch is found in some cases. (Supported by DOE.)

Gyrokinetic global three-dimensional simulations of linear ion-temperature-gradient modes in Wendelstein 7-X

NASA Astrophysics Data System (ADS)

Kornilov, V.; Kleiber, R.; Hatzky, R.; Villard, L.; Jost, G.

2004-06-01

Using a global approach for solving an ion gyrokinetic model in three-dimensional geometry the linear stability and structure of ion-temperature-gradient (ITG) modes in the configuration of the stellarator Wendelstein 7-X (W7-X) [G. Grieger et al., in Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525.] is studied. The time evolution of electrostatic perturbations is solved as an initial value problem with a particle-in-cell δf method. The vacuum magnetohydrodynamic equilibrium is calculated by the code VMEC [S. P. Hirshman and D. K. Lee, Comput. Phys. Commun. 39, 161 (1986)]. In this work the most unstable ITG mode in W7-X is presented. This mode has a pronounced ballooning-type structure; however, it is not tokamak-like. A driving mechanism analysis using the energy transfer shows that the contribution of curvature effects is non-negligible. The growth rate and the mixing-length estimate for transport are compared with those for ITG modes found in axisymmetric geometries.

Ideal MHD stability of double transport barrier plasmas in DIII-D

NASA Astrophysics Data System (ADS)

Li, G. Q.; Wang, S. J.; Lao, L. L.; Turnbull, A. D.; Chu, M. S.; Brennan, D. P.; Groebner, R. J.; Zhao, L.

2008-01-01

The ideal MHD stability for double transport barrier (DTB or DB) plasmas with varying edge and internal barrier width and height was investigated, using the ideal MHD stability code GATO. A moderate ratio of edge transport barriers (ETB) height to internal transport barriers (ITBs) height is found to be beneficial to MHD stability and the βN is limited by global low n instabilities. For moderate ITB width DB plasmas, if the ETB is weak, the stability is limited by n = 1 (n is the toroidal mode number) global mode; whereas if the ETB is strong it is limited by intermediate-n edge peeling-ballooning modes. Broadening the ITB can improve stability if the ITB half width wi lsim 0.3. For very broad ITB width plasmas the stability is limited by stability to a low n (n > 1) global mode.

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

Evolutionary Models of Cold, Magnetized, Interstellar Clouds

NASA Technical Reports Server (NTRS)

Gammie, Charles F.; Ostriker, Eve; Stone, James M.

2004-01-01

We modeled the long-term and small-scale evolution of molecular clouds using direct 2D and 3D magnetohydrodynamic (MHD) simulations. This work followed up on previous research by our group under auspices of the ATP in which we studied the energetics of turbulent, magnetized clouds and their internal structure on intermediate scales. Our new work focused on both global and smallscale aspects of the evolution of turbulent, magnetized clouds, and in particular studied the response of turbulent proto-cloud material to passage through the Galactic spiral potential, and the dynamical collapse of turbulent, magnetized (supercritical) clouds into fragments to initiate the formation of a stellar cluster. Technical advances under this program include developing an adaptive-mesh MHD code as a successor to ZEUS (ATHENA) in order to follow cloud fragmentation, developing a shearing-sheet MHD code which includes self-gravity and externally-imposed gravity to follow the evolution of clouds in the Galactic potential, and developing radiative transfer models to evaluate the internal ionization of clumpy clouds exposed to external photoionizing UV and CR radiation. Gammie's work at UIUC focused on the radiative transfer aspects of this program.

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 Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations

NASA Astrophysics Data System (ADS)

Abbott, Stephen; Germaschewski, Kai

2014-10-01

Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.

Particle tracing modeling of ion fluxes at geosynchronous orbit

DOE PAGES

Brito, Thiago V.; Woodroffe, Jesse; Jordanova, Vania K.; ...

2017-10-31

The initial results of a coupled MHD/particle tracing method to evaluate particle fluxes in the inner magnetosphere are presented. This setup is capable of capturing the earthward particle acceleration process resulting from dipolarization events in the tail region of the magnetosphere. On the period of study, the MHD code was able to capture a dipolarization event and the particle tracing algorithm was able to capture our results of these disturbances and calculate proton fluxes in the night side geosynchronous orbit region. The simulation captured dispersionless injections as well as the energy dispersion signatures that are frequently observed by satellites atmore » geosynchronous orbit. Currently, ring current models rely on Maxwellian-type distributions based on either empirical flux values or sparse satellite data for their boundary conditions close to geosynchronous orbit. In spite of some differences in intensity and timing, the setup presented here is able to capture substorm injections, which represents an improvement regarding a reverse way of coupling these ring current models with MHD codes through the use of boundary conditions.« less

Particle tracing modeling of ion fluxes at geosynchronous orbit

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

Brito, Thiago V.; Woodroffe, Jesse; Jordanova, Vania K.

The initial results of a coupled MHD/particle tracing method to evaluate particle fluxes in the inner magnetosphere are presented. This setup is capable of capturing the earthward particle acceleration process resulting from dipolarization events in the tail region of the magnetosphere. On the period of study, the MHD code was able to capture a dipolarization event and the particle tracing algorithm was able to capture our results of these disturbances and calculate proton fluxes in the night side geosynchronous orbit region. The simulation captured dispersionless injections as well as the energy dispersion signatures that are frequently observed by satellites atmore » geosynchronous orbit. Currently, ring current models rely on Maxwellian-type distributions based on either empirical flux values or sparse satellite data for their boundary conditions close to geosynchronous orbit. In spite of some differences in intensity and timing, the setup presented here is able to capture substorm injections, which represents an improvement regarding a reverse way of coupling these ring current models with MHD codes through the use of boundary conditions.« less

Modeling of Resistive Wall Modes in Tokamak and Reversed Field Pinch Configurations of KTX

NASA Astrophysics Data System (ADS)

Han, Rui; Zhu, Ping; Bai, Wei; Lan, Tao; Liu, Wandong

2016-10-01

Resistive wall mode is believed to be one of the leading causes for macroscopic degradation of plasma confinement in tokamaks and reversed field pinches (RFP). In this study, we evaluate the linear RWM instability of Keda Torus eXperiment (KTX) in both tokamak and RFP configurations. For the tokamak configuration, the extended MHD code NIMROD is employed for calculating the dependence of the RWM growth rate on the position and conductivity of the vacuum wall for a model tokamak equilibrium of KTX in the large aspect-ratio approximation. For the RFP configuration, the standard formulation of dispersion relation for RWM based on the MHD energy principle has been evaluated for a cylindrical α- Θ model of KTX plasma equilibrium, in an effort to investigate the effects of thin wall on the RWM in KTX. Full MHD calculations of RWM in the RFP configuration of KTX using the NIMROD code are also being developed. Supported by National Magnetic Confinement Fusion Science Program of China Grant Nos. 2014GB124002, 2015GB101004, 2011GB106000, and 2011GB106003.

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.

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.

Results from the OH-PT model: a Kinetic-MHD Model of the Outer Heliosphere within SWMF

NASA Astrophysics Data System (ADS)

Michael, A.; Opher, M.; Tenishev, V.; Borovikov, D.; Toth, G.

2017-12-01

We present an update of the OH-PT model, a kinetic-MHD model of the outer heliosphere. The OH-PT model couples the Outer Heliosphere (OH) and Particle Tracker (PT) components within the Space Weather Modeling Framework (SWMF). The OH component utilizes the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) MHD code, a highly parallel, 3D, and block-adaptive solver. As a stand-alone model, the OH component solves the ideal MHD equations for the plasma and a separate set of Euler's equations for the different populations of neutral atoms. The neutrals and plasma in the outer heliosphere are coupled through charge-exchange. While this provides an accurate solution for the plasma, it is an inaccurate description of the neutrals. The charge-exchange mean free path is on the order of the size of the heliosphere; therefore the neutrals cannot be described as a fluid. The PT component is based on the Adaptive Mesh Particle Simulator (AMPS) model, a 3D, direct simulation Monte Carlo model that solves the Boltzmann equation for the motion and interaction of multi-species plasma and is used to model the neutral distribution functions throughout the domain. The charge-exchange process occurs within AMPS, which handles each event on a particle-by-particle basis and calculates the resulting source terms to the MHD equations. The OH-PT model combines the MHD solution for the plasma with the kinetic solution for the neutrals to form a self-consistent model of the heliosphere. In this work, we present verification and validation of the model as well as demonstrate the codes capabilities. Furthermore we provide a comparison of the OH-PT model to our multi-fluid approximation and detail the differences between the models in both the plasma solution and neutral distribution functions.

GRADSPMHD: A parallel MHD code based on the SPH formalism

NASA Astrophysics Data System (ADS)

Vanaverbeke, S.; Keppens, R.; Poedts, S.

2014-03-01

We present GRADSPMHD, a completely Lagrangian parallel magnetohydrodynamics code based on the SPH formalism. The implementation of the equations of SPMHD in the “GRAD-h” formalism assembles known results, including the derivation of the discretized MHD equations from a variational principle, the inclusion of time-dependent artificial viscosity, resistivity and conductivity terms, as well as the inclusion of a mixed hyperbolic/parabolic correction scheme for satisfying the ∇ṡB→ constraint on the magnetic field. The code uses a tree-based formalism for neighbor finding and can optionally use the tree code for computing the self-gravity of the plasma. The structure of the code closely follows the framework of our parallel GRADSPH FORTRAN 90 code which we added previously to the CPC program library. We demonstrate the capabilities of GRADSPMHD by running 1, 2, and 3 dimensional standard benchmark tests and we find good agreement with previous work done by other researchers. The code is also applied to the problem of simulating the magnetorotational instability in 2.5D shearing box tests as well as in global simulations of magnetized accretion disks. We find good agreement with available results on this subject in the literature. Finally, we discuss the performance of the code on a parallel supercomputer with distributed memory architecture. Catalogue identifier: AERP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 620503 No. of bytes in distributed program, including test data, etc.: 19837671 Distribution format: tar.gz Programming language: FORTRAN 90/MPI. Computer: HPC cluster. Operating system: Unix. Has the code been vectorized or parallelized?: Yes, parallelized using MPI. RAM: ˜30 MB for a Sedov test including 15625 particles on a single CPU. Classification: 12. Nature of problem: Evolution of a plasma in the ideal MHD approximation. Solution method: The equations of magnetohydrodynamics are solved using the SPH method. Running time: The test provided takes approximately 20 min using 4 processors.

A Nonlinear Gyrokinetic Vlasov-Maxwell System for High-frequency Simulation in Toroidal Geometry

NASA Astrophysics Data System (ADS)

Liu, Pengfei; Zhang, Wenlu; Lin, Jingbo; Li, Ding; Dong, Chao

2016-10-01

A nonlinear gyrokinetic Vlasov equation is derived through the Lie-perturbation method to the Lagrangian and Hamiltonian systems in extanded phase space. The gyrokinetic Maxwell equations are derived in terms of the moments of gyrocenter phase-space distribution through the push-forward and pull-back representations, where the polarization and magnetization effects of gyrocenter are retained. The goal of this work is to construct a global nonlinear gyrokinetic vlasov-maxwell system for high-frequency simulation in toroidal geometry relevent for ion cyclotron range of frequencies (ICRF) waves heating and lower hybrid wave current driven (LHCD). Supported by National Special Research Program of China For ITER and National Natural Science Foundation of China.

Gyrokinetic simulation of ITG modes in a three-mode coupling model

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Lee, W. W.

2004-11-01

A three-mode coupling model of ITG modes with adiabatic electrons is studied both analytically and numerically in 2-dimensional slab geometry using the gyrokinetic formalism. It can be shown analytically that the (quasilinear) saturation amplitude of the waves in the system should be enhanced by the inclusion of the parallel velocity nonlinearity in the governing gyrokinetic equation. The effect of this (frequently neglected) nonlinearity on the steady-state transport properties of the plasma is studied numerically using standard gyrokinetic particle simulation techniques. The balance [1] between various steady-state transport properties of the model (particle and heat flux, entropy production, and collisional dissipation) is examined. Effects resulting from the inclusion of nonadiabatic electrons in the model are also considered numerically, making use of the gyrokinetic split-weight scheme [2] in the simulations. [1] W. W. Lee and W. M. Tang, Phys. Fluids 31, 612 (1988). [2] I. Manuilskiy and W. W. Lee, Phys. Plasmas 7, 1381 (2000).

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.

Gyroaveraging operations using adaptive matrix operators

NASA Astrophysics Data System (ADS)

Dominski, Julien; Ku, Seung-Hoe; Chang, Choong-Seock

2018-05-01

A new adaptive scheme to be used in particle-in-cell codes for carrying out gyroaveraging operations with matrices is presented. This new scheme uses an intermediate velocity grid whose resolution is adapted to the local thermal Larmor radius. The charge density is computed by projecting marker weights in a field-line following manner while preserving the adiabatic magnetic moment μ. These choices permit to improve the accuracy of the gyroaveraging operations performed with matrices even when strong spatial variation of temperature and magnetic field is present. Accuracy of the scheme in different geometries from simple 2D slab geometry to realistic 3D toroidal equilibrium has been studied. A successful implementation in the gyrokinetic code XGC is presented in the delta-f limit.

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).

Simulations of initial MHD experiments on the Madison Dynamo Experiment

NASA Astrophysics Data System (ADS)

O'Connell, R.; Forest, C. B.; Goldwin, J. M.; Kendrick, R. D.; Canary, H. W.; Nornberg, M. D.; Jaun, A.

1999-11-01

Initial experiments for a liquid metal MHD device have been modelled using measurements from geometrically similar water experiments. In the low B limit the water flows are the same as sodium flows. Two codes have been written to predict 1) linear stability of the system and 2) the response of the system to an externally applied vertical magnetic field, using measured velocity profiles. Predictions are made for a first set of MHD experiments, including: a) demonstration of the distortion and amplification of externally applied magnetic fields by sheared flows, b) demonstration of the β-effect by measurement of the turbulent conductivity, c) demonstration of a turbulent α effect and d) characterization of magnetic eigenmodes.

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

Viktor K. Decyk

The UCLA work on this grant was to design and help implement an object-oriented version of the GTC code, which is written in Fortran90. The GTC code is the main global gyrokinetic code used in this project, and over the years multiple, incompatible versions have evolved. The reason for this effort is to allow multiple authors to work together on GTC and to simplify future enhancements to GTC. The effort was designed to proceed incrementally. Initially, an upper layer of classes (derived types and methods) was implemented which called the original GTC code 'under the hood.' The derived types pointedmore » to data in the original GTC code, and the methods called the original GTC subroutines. The original GTC code was modified only very slightly. This allowed one to define (and refine) a set of classes which described the important features of the GTC code in a new, more abstract way, with a minimum of implementation. Furthermore, classes could be added one at a time, and at the end of the each day, the code continued to work correctly. This work was done in close collaboration with Y. Nishimura from UC Irvine and Stefan Ethier from PPPL. Ten classes were ultimately defined and implemented: gyrokinetic and drift kinetic particles, scalar and vector fields, a mesh, jacobian, FLR, equilibrium, interpolation, and particles species descriptors. In the second state of this development, some of the scaffolding was removed. The constructors in the class objects now allocated the data and the array data in the original GTC code was removed. This isolated the components and now allowed multiple instantiations of the objects to be created, in particular, multiple ion species. Again, the work was done incrementally, one class at a time, so that the code was always working properly. This work was done in close collaboration with Y. Nishimura and W. Zhang from UC Irvine and Stefan Ethier from PPPL. The third stage of this work was to integrate the capabilities of the various versions of the GTC code into one flexible and extensible version. To do this, we developed a methodology to implement Design Patterns in Fortran90. Design Patterns are abstract solutions to generic programming problems, which allow one to handle increased complexity. This work was done in collaboration with Henry Gardner, a computer scientist (and former plasma physicist) from the Australian National University. As an example, the Strategy Pattern is being used in GTC to support multiple solvers. This new code is currently being used in the study of energetic particles. A document describing the evolution of the GTC code to this new object-oriented version is available to users of GTC.« less

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

Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches

DOE PAGES

Seyler, C. E.; Martin, M. R.

2011-01-14

In this study, it is shown that the two-fluid model under a generalized Ohm’s law formulation and the resistive magnetohydrodynamics (MHD) can both be described as relaxation systems. In the relaxation model, the under-resolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional two-fluid model, the relaxation of fast time scales associated with displacement current and finite electron mass allows for a natural transition from a system where Ohm’s law determines the current density to a system where Ohm’s law determines the electric field. This resultmore » is used to derive novel algorithms, which allow for multiscale simulation of low and high frequency extended-MHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasma-vacuum interface without invoking phenomenological models. The relaxation model is implemented as an extended-MHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Two-dimensional simulations of pulsed power loads are compared for extended-MHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistive-MHD limit.« less

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

Electromagnetic nonlinear gyrokinetics with polarization drift

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

Duthoit, F.-X.; Hahm, T. S., E-mail: tshahm@snu.ac.kr; Wang, Lu

2014-08-15

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen,more » Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.« less

Electromagnetic nonlinear gyrokinetics with polarization drift

NASA Astrophysics Data System (ADS)

Duthoit, F.-X.; Hahm, T. S.; Wang, Lu

2014-08-01

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.

Parabolized Navier-Stokes Code for Computing Magneto-Hydrodynamic Flowfields

NASA Technical Reports Server (NTRS)

Mehta, Unmeel B. (Technical Monitor); Tannehill, J. C.

2003-01-01

This report consists of two published papers, 'Computation of Magnetohydrodynamic Flows Using an Iterative PNS Algorithm' and 'Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm'.

Implementation of an anomalous radial transport model for continuum kinetic edge codes

NASA Astrophysics Data System (ADS)

Bodi, K.; Krasheninnikov, S. I.; Cohen, R. H.; Rognlien, T. D.

2007-11-01

Radial plasma transport in magnetic fusion devices is often dominated by plasma turbulence compared to neoclassical collisional transport. Continuum kinetic edge codes [such as the (2d,2v) transport version of TEMPEST and also EGK] compute the collisional transport directly, but there is a need to model the anomalous transport from turbulence for long-time transport simulations. Such a model is presented and results are shown for its implementation in the TEMPEST gyrokinetic edge code. The model includes velocity-dependent convection and diffusion coefficients expressed as a Hermite polynominals in velocity. The specification of the Hermite coefficients can be set, e.g., by specifying the ratio of particle and energy transport as in fluid transport codes. The anomalous transport terms preserve the property of no particle flux into unphysical regions of velocity space. TEMPEST simulations are presented showing the separate control of particle and energy anomalous transport, and comparisons are made with neoclassical transport also included.

Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

NASA Astrophysics Data System (ADS)

Marx, Alain; Lütjens, Hinrich

2017-03-01

A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

Multi-scale gyrokinetic simulation of Alcator C-Mod tokamak discharges

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

Howard, N. T., E-mail: nthoward@psfc.mit.edu; White, A. E.; Greenwald, M.

2014-03-15

Alcator C-Mod tokamak discharges have been studied with nonlinear gyrokinetic simulation simultaneously spanning both ion and electron spatiotemporal scales. These multi-scale simulations utilized the gyrokinetic model implemented by GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and the approximation of reduced electron mass (μ = (m{sub D}/m{sub e}){sup .5} = 20.0) to qualitatively study a pair of Alcator C-Mod discharges: a low-power discharge, previously demonstrated (using realistic mass, ion-scale simulation) to display an under-prediction of the electron heat flux and a high-power discharge displaying agreement with both ion and electron heat flux channels [N. T. Howard et al.,more » Nucl. Fusion 53, 123011 (2013)]. These multi-scale simulations demonstrate the importance of electron-scale turbulence in the core of conventional tokamak discharges and suggest it is a viable candidate for explaining the observed under-prediction of electron heat flux. In this paper, we investigate the coupling of turbulence at the ion (k{sub θ}ρ{sub s}∼O(1.0)) and electron (k{sub θ}ρ{sub e}∼O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (k{sub θ}ρ{sub s} < 1.0) turbulence. It is found that reduced mass simulation of the plasma exhibiting marginally stable low-k turbulence fails to provide even qualitative insight into the turbulence present in the realistic plasma conditions. In contrast, multi-scale simulation of the plasma condition exhibiting strong turbulence provides valuable insight into the coupling of the ion and electron scales.« less

The influence of the Hall term on the development of magnetized laser-produced plasma jets

NASA Astrophysics Data System (ADS)

Hamlin, N. D.; Seyler, C. E.; Khiar, B.

2018-04-01

We present 2D axisymmetric simulation results describing the influence of the Hall term on laser-produced plasma jets and their interaction with an applied magnetic field parallel to the laser axis. Bending of the poloidal B-field lines produces an MHD shock structure surrounding a conical cavity, and a jet is produced from the convergence of the shock envelope. Both the jet and the conical cavity underneath it are bound by fast MHD shocks. We compare the MHD results generated using the extended-MHD code Physics as an Extended-MHD Relaxation System with an Efficient Upwind Scheme (PERSEUS) with MHD results generated using GORGON and find reasonable agreement. We then present extended-MHD results generated using PERSEUS, which show that the Hall term has several effects on the plasma jet evolution. A hot low-density current-carrying layer of plasma develops just outside the plume, which results in a helical rather than a purely poloidal B-field, and reduces magnetic stresses, resulting in delayed flow convergence and jet formation. The flow is partially frozen into the helical field, resulting in azimuthal rotation of the jet. The Hall term also produces field-aligned current in strongly magnetized regions. In particular, we find the influence of Hall physics on this problem to be scale-dependent. This points to the importance of mitigating the Hall effect in a laboratory setup, by increasing the jet density and system dimensions, in order to avoid inaccurate extrapolation to astrophysical scales.

Global MHD modeling of an ICME focused on the physics involved in an ICME interacting with a solar wind

NASA Astrophysics Data System (ADS)

An, Jun-Mo; Magara, Tetsuya; Inoue, Satoshi; Hayashi, Keiji; Tanaka, Takashi

2015-04-01

We developed a three-dimensional (3D) magnetohydrodynamic (MHD) code to investigate the structure of a solar wind, the properties of a coronal mass ejection (CME) and the interaction between them. This MHD code is based on the finite volume method incorporating total variation diminishing (TVD) scheme with an unstructured grid system. In particular, this grid system can avoid the singularity at the north and south poles and relax tight CFL conditions around the poles, both of which would arise in a spherical coordinate system (Tanaka 1994). In this model, we first apply an MHD tomographic method (Hayashi et al. 2003) to interplanetary scintillation (IPS) observational data and derive a solar wind from the physical values obtained at 50 solar radii away from the Sun. By comparing the properties of this solar wind to observational data obtained near the Earth orbit, we confirmed that our model captures the velocity, temperature and density profiles of a solar wind near the Earth orbit. We then insert a spheromak-type CME (Kataoka et al. 2009) into the solar wind to reproduce an actual CME event occurred on 29 September 2013. This has been done by introducing a time-dependent boundary condition to the inner boundary of our simulation domain (50rs < r < 300rs). On the basis of a comparison between the properties of a simulated CME and observations near the Earth, we discuss the physics involved in an ICME interacting with a solar wind.

Radial Diffusion study of the 1 June 2013 CME event using MHD simulations.

NASA Astrophysics Data System (ADS)

Patel, M.; Hudson, M.; Wiltberger, M. J.; Li, Z.; Boyd, A. J.

2016-12-01

The June 1, 2013 storm was a CME-shock driven geomagnetic storm (Dst = -119 nT) that caused a dropout affecting all radiation belt electron energies measured by the Energetic Particle, Composition and Thermal Plasma Suite (ECT) instrument on Van Allen Probes at higher L-shells following dynamic pressure enhancement in the solar wind. Lower energies (up to about 700 keV) were enhanced by the storm while MeV electrons were depleted throughout the belt. We focus on depletion through radial diffusion caused by the enhanced ULF wave activity due to the CME-shock. This study utilities the Lyon-Fedder-Mobarry (LFM) model, a 3D global magnetospheric simulation code based on the ideal MHD equations, coupled with the Magnetosphere Ionosphere Coupler (MIX) and Rice Convection Model (RCM). The MHD electric and magnetic fields with equations described by Fei et al. [JGR, 2006] are used to calculate radial diffusion coefficients (DLL). These DLL values are input into a radial diffusion code to recreate the dropouts observed by the Van Allen Probes. The importance of understanding the complex role that ULF waves play in radial transport and the effects of CME-driven storms on the relativistic energy electrons in the radiation belts can be accomplished using MHD simulations to obtain diffusion coefficients, initial phase space density and the outer boundary condition from the ECT instrument suite and a radial diffusion model to reproduce observed fluxes which compare favorably with Van Allen Probes ECT measurements.

The build-up of energetic electrons triggering electron cyclotron emission bursts due to a magnetohydrodynamic mode at the edge of tokamaks

DOE PAGES

Li, Erzhong; Austin, Max E.; White, R. B.; ...

2017-08-21

Intense bursts of electron cyclotron emission (ECE) triggered by magnetohydrodynamic (MHD) instabilities such as edge localized modes (ELMs) have been observed on many tokamaks. On the DIII-D tokamak, it is found that an MHD mode is observed to trigger the ECE bursts in the low collisionality regime at the plasma edge. ORBIT-code simulations have shown that energetic electrons build up due to an interaction between barely trapped electrons with an MHD mode (f = 50 kHz for current case). The energetic tail of the electron distribution function develops a bump within several microseconds for this collisionless case. This behavior dependsmore » on the competition between the perturbing MHD mode and slowing down and pitch angle scattering due to collisions. As a result, for typical DIII-D parameters, the calculated ECE radiation transport predicted by ORBIT is in excellent agreement with ECE measurements, clarifying the electron dynamics of the ECE bursts for the first time.« less

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

NASA Astrophysics Data System (ADS)

Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie; Bohm, Marvin

2018-07-01

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme).

An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.

1994-01-01

An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.

Modeling of flow-dominated MHD instabilities at WiPPAL using NIMROD

NASA Astrophysics Data System (ADS)

Flanagan, K.; McCollam, K. J.; Milhone, J.; Mirnov, V. V.; Nornberg, M. D.; Peterson, E. E.; Siller, R.; Forest, C. B.

2017-10-01

Using the NIMROD (non-ideal MHD with rotation - open discussion) code developed at UW-Madison, we model two different flow scenarios to study the onset of MHD instabilities in flow-dominated plasmas in the Big Red Ball (BRB) and the Plasma Couette Experiment (PCX). Both flows rely on volumetric current drive, where a large current is drawn through the plasma across a weak magnetic field, injecting J × B torque across the whole volume. The first scenario uses a vertical applied magnetic field and a mostly radial injected current to create Couette-like flows which may excite the magnetorotational instability (MRI). In the other scenario, a quadrupolar field is applied to create counter-rotating von Karman-like flow that demonstrates a dynamo-like instability. For both scenarios, the differences between Hall and MHD Ohm's laws are explored. The implementation of BRB geometry in NIMROD, details of the observed flows, and instability results are shown. This work was funded by DoE and NSF.

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.

Fluctuations, noise, and numerical methods in gyrokinetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Jenkins, Thomas Grant

In this thesis, the role of the "marker weight" (or "particle weight") used in gyrokinetic particle-in-cell (PIC) simulations is explored. Following a review of the foundations and major developments of gyrokinetic theory, key concepts of the Monte Carlo methods which form the basis for PIC simulations are set forth. Consistent with these methods, a Klimontovich representation for the set of simulation markers is developed in the extended phase space {R, v||, v ⊥, W, P} (with the additional coordinates representing weight fields); clear distinctions are consequently established between the marker distribution function and various physical distribution functions (arising from diverse moments of the marker distribution). Equations describing transport in the simulation are shown to be easily derivable using the formalism. The necessity of a two-weight model for nonequilibrium simulations is demonstrated, and a simple method for calculating the second (background-related) weight is presented. Procedures for arbitrary marker loading schemes in gyrokinetic PIC simulations are outlined; various initialization methods for simulations are compared. Possible effects of inadequate velocity-space resolution in gyrokinetic continuum simulations are explored. The "partial-f" simulation method is developed and its limitations indicated. A quasilinear treatment of electrostatic drift waves is shown to correctly predict nonlinear saturation amplitudes, and the relevance of the gyrokinetic fluctuation-dissipation theorem in assessing the effects of discrete-marker-induced statistical noise on the resulting marginally stable states is demonstrated.

Understanding Accretion Disks through Three Dimensional Radiation MHD Simulations

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei

I study the structures and thermal properties of black hole accretion disks in the radiation pressure dominated regime. Angular momentum transfer in the disk is provided by the turbulence generated by the magneto-rotational instability (MRI), which is calculated self-consistently with a recently developed 3D radiation magneto-hydrodynamics (MHD) code based on Athena. This code, developed by my collaborators and myself, couples both the radiation momentum and energy source terms with the ideal MHD equations by modifying the standard Godunov method to handle the stiff radiation source terms. We solve the two momentum equations of the radiation transfer equations with a variable Eddington tensor (VET), which is calculated with a time independent short characteristic module. This code is well tested and accurate in both optically thin and optically thick regimes. It is also accurate for both radiation pressure and gas pressure dominated flows. With this code, I find that when photon viscosity becomes significant, the ratio between Maxwell stress and Reynolds stress from the MRI turbulence can increase significantly with radiation pressure. The thermal instability of the radiation pressure dominated disk is then studied with vertically stratified shearing box simulations. Unlike the previous results claiming that the radiation pressure dominated disk with MRI turbulence can reach a steady state without showing any unstable behavior, I find that the radiation pressure dominated disks always either collapse or expand until we have to stop the simulations. During the thermal runaway, the heating and cooling rates from the simulations are consistent with the general criterion of thermal instability. However, details of the thermal runaway are different from the predictions of the standard alpha disk model, as many assumptions in that model are not satisfied in the simulations. We also identify the key reasons why previous simulations do not find the instability. The thermal instability has many important implications for understanding the observations of both X-ray binaries and Active Galactic Nuclei (AGNs). However, direct comparisons between observations and the simulations require global radiation MHD simulations, which will be the main focus of my future work.

User's manual for the FLORA equilibrium and stability code

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

Freis, R.P.; Cohen, B.I.

1985-04-01

This document provides a user's guide to the content and use of the two-dimensional axisymmetric equilibrium and stability code FLORA. FLORA addresses the low-frequency MHD stability of long-thin axisymmetric tandem mirror systems with finite pressure and finite-larmor-radius effects. FLORA solves an initial-value problem for interchange, rotational, and ballooning stability.

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.

Effects of stochastic field lines on the pressure driven MHD instabilities in the Large Helical Device

NASA Astrophysics Data System (ADS)

Ohdachi, Satoshi; Watanabe, Kiyomasa; Sakakibara, Satoru; Suzuki, Yasuhiro; Tsuchiya, Hayato; Ming, Tingfeng; Du, Xiaodi; LHD Expriment Group Team

2014-10-01

In the Large Helical Device (LHD), the plasma is surrounded by the so-called magnetic stochastic region, where the Kolmogorov length of the magnetic field lines is very short, from several tens of meters and to thousands meters. Finite pressure gradient are formed in this region and MHD instabilities localized in this region is observed since the edge region of the LHD is always unstable against the pressure driven mode. Therefore, the saturation level of the instabilities is the key issue in order to evaluate the risk of this kind of MHD instabilities. The saturation level depends on the pressure gradient and on the magnetic Reynolds number; there results are similar to the MHD mode in the closed magnetic surface region. The saturation level in the stochastic region is affected also by the stocasticity itself. Parameter dependence of the saturation level of the MHD activities in the region is discussed in detail. It is supported by NIFS budget code ULPP021, 028 and is also partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research 26249144, by the JSPS-NRF-NSFC A3 Foresight Program NSFC: No. 11261140328.

Advanced MHD Algorithm for Solar and Space Science: lst Year Semi Annual Progress Report

NASA Technical Reports Server (NTRS)

Schnack, Dalton D.; Lionello, Roberto

2003-01-01

We report progress for the development of MH4D for the first and second quarters of FY2004, December 29, 2002 - June 6, 2003. The present version of MH4D can now solve the full viscous and resistive MHD equations using either an explicit or a semi-implicit time advancement algorithm. In this report we describe progress in the following areas. During the two last quarters we have presented poster at the EGS-AGU-EUG Joint Assembly in Nice, France, April 6-11, 2003, and a poster at the 2003 International Sherwood Theory Conference in Corpus Christi, Texas, April 28-30 2003. In the area of code development, we have implemented the MHD equations and the semi-implicit algorithm. The new features have been tested.

QUANTITATIVE TESTS OF ELMS AS INTERMEDIATE N PEELING-BALOONING MODES

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

LAO,LL; SNYDER,PB; LEONARD,AW

2003-03-01

A271 QUANTITATIVE TESTS OF ELMS AS INTERMEDIATE N PEELING-BALOONING MODES. Several testable features of the working model of edge localized modes (ELMs) as intermediate toroidal mode number peeling-ballooning modes are evaluated quantitatively using DIII-D and JT-60U experimental data and the ELITE MHD stability code. These include the hypothesis that ELM sizes are related to the radial widths of the unstable MHD modes, the unstable modes have a strong ballooning character localized in the outboard bad curvature region, and ELM size generally becomes smaller at high edge collisionality. ELMs are triggered when the growth rates of the unstable MHD modes becomemore » significantly large. These testable features are consistent with many ELM observations in DIII-D and JT-60U discharges.« less

Pressure profiles of plasmas confined in the field of a dipole magnet

NASA Astrophysics Data System (ADS)

Davis, Matthew Stiles

Understanding the maintenance and stability of plasma pressure confined by a strong magnetic field is a fundamental challenge in both laboratory and space plasma physics. Using magnetic and X-ray measurements on the Levitated Dipole Experiment (LDX), the equilibrium plasma pressure has been reconstructed, and variations of the plasma pressure for different plasma conditions have been examined. The relationship of these profiles to the magnetohydrodynamic (MHD) stability limit, and to the enhanced stability limit that results from a fraction of energetic trapped electrons, has been analyzed. In each case, the measured pressure profiles and the estimated fractional densities of energetic electrons were qualitatively consistent with expectations of plasma stability. LDX confines high temperature and high pressure plasma in the field of a superconducting dipole magnet. The strong dipole magnet can be either mechanically supported or magnetically levitated. When the dipole was mechanically supported, the plasma density profile was generally uniform while the plasma pressure was highly peaked. The uniform density was attributed to the thermal plasma being rapidly lost along the field to the mechanical supports. In contrast, the strongly peaked plasma pressure resulted from a fraction of energetic, mirror trapped electrons created by microwave heating at the electron cyclotron resonance (ECRH). These hot electrons are known to be gyrokinetically stabilized by the background plasma and can adopt pressure profiles steeper than the MHD limit. X-ray measurements indicated that this hot electron population could be described by an energy distribution in the range 50-100 keV. Combining information from the magnetic reconstruction of the pressure profile, multi-chord interferometer measurements of the electron density profile, and X-ray measurements of the hot electron energy distribution, the fraction of energetic electrons at the pressure peak was estimated to be ˜ 35% of the total electron population. When the dipole was magnetically levitated the plasma density increased substantially because particle losses to the mechanical supports were eliminated so particles could only be lost via slower cross-field transport processes. The pressure profile was observed to be broader during levitated operation than it was during supported operation, and the pressure appeared to be contained in both a thermal population and an energetic electron population. X-ray spectra indicated that the X-rays came from a similar hot electron population during levitated and supported operation; however, the hot electron fraction was an order of magnitude smaller during levitated operation (<3% of the total electron population). Pressure gradients for both supported and levitated plasmas were compared to the MHD limit. Levitated plasmas had pressure profiles that were (i) steeper than, (ii) shallower than, or (iii) near the MHD limit dependent on plasma conditions. However, those profiles that exceeded the MHD limit were observed to have larger fractions of energetic electrons. When the dipole magnet was supported, high pressure plasmas always had profiles that exceeded the MHD interchange stability limit, but the high pressure in these plasmas appeared to arise entirely from a population of energetic trapped electrons.

Electron Scale Turbulence and Transport in an NSTX H-mode Plasma Using a Synthetic Diagnostic for High-k Scattering Measurements

NASA Astrophysics Data System (ADS)

Ruiz Ruiz, Juan; Guttenfelder, Walter; Loureiro, Nuno; Ren, Yang; White, Anne; MIT/PPPL Collaboration

2017-10-01

Turbulent fluctuations on the electron gyro-radius length scale are thought to cause anomalous transport of electron energy in spherical tokamaks such as NSTX and MAST in some parametric regimes. In NSTX, electron-scale turbulence is studied through a combination of experimental measurements from a high-k scattering system and gyrokinetic simulations. Until now most comparisons between experiment and simulation of electron scale turbulence have been qualitative, with recent work expanding to more quantitative comparisons via synthetic diagnostic development. In this new work, we propose two alternate, complementary ways to perform a synthetic diagnostic using the gyrokinetic code GYRO. The first approach builds on previous work and is based on the traditional selection of wavenumbers using a wavenumber filter, for which a new wavenumber mapping was implemented for general axisymmetric geometry. A second alternate approach selects wavenumbers in real-space to compute the power spectra. These approaches are complementary, and recent results from both synthetic diagnostic approaches applied to NSTX plasmas will be presented. Work supported by U.S. DOE contracts DE-AC02-09CH11466 and DE-AC02-05CH11231.

Continuum Gyrokinetic Simulations of Turbulence in a Helical Model SOL with NSTX-type parameters

NASA Astrophysics Data System (ADS)

Hammett, G. W.; Shi, E. L.; Hakim, A.; Stoltzfus-Dueck, T.

2017-10-01

We have developed the Gkeyll code to carry out 3D2V full- F gyrokinetic simulations of electrostatic plasma turbulence in open-field-line geometries, using special versions of discontinuous-Galerkin algorithms to help with the computational challenges of the edge region. (Higher-order algorithms can also be helpful for exascale computing as they reduce the ratio of communications to computations.) Our first simulations with straight field lines were done for LAPD-type cases. Here we extend this to a helical model of an SOL plasma and show results for NSTX-type parameters. These simulations include the basic elements of a scrape-off layer: bad-curvature/interchange drive of instabilities, narrow sources to model plasma leaking from the core, and parallel losses with model sheath boundary conditions (our model allows currents to flow in and out of the walls). The formation of blobs is observed. By reducing the strength of the poloidal magnetic field, the heat flux at the divertor plate is observed to broaden. Supported by the Max-Planck/Princeton Center for Plasma Physics, the SciDAC Center for the Study of Plasma Microturbulence, and DOE Contract DE-AC02-09CH11466.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing'' terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k'‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Gyrokinetic simulations of DIII-D near-edge L-mode plasmas

NASA Astrophysics Data System (ADS)

Neiser, Tom; Jenko, Frank; Carter, Troy; Schmitz, Lothar; Merlo, Gabriele; Told, Daniel; Banon Navarro, Alejandro; McKee, George; Yan, Zheng

2017-10-01

In order to understand the L-H transition, a good understanding of the L-mode edge region is necessary. We perform nonlinear gyrokinetic simulations of a DIII-D L-mode discharge with the GENE code in the near-edge, which we define as ρtor >= 0.8 . At ρ = 0.9 , ion-scale simulations reproduce experimental heat fluxes within the uncertainty of the experiment. At ρ = 0 . 8 , electron-scale simulations reproduce the experimental electron heat flux while ion-scale simulations do not reproduce the respective ion heat flux due to a strong poloidal zonal flow. However, we reproduce both electron and ion heat fluxes by increasing the local ion temperature gradient by 80 % . Local fitting to the CER data in the domain 0.7 <= ρ <= 0.9 is compatible with such an increase in ion temperature gradient within the error bars. Ongoing multi-scale simulations are investigating whether radial electron streamers could dampen the poloidal zonal flows at ρ = 0.8 and increase the radial ion-scale flux. Supported by U.S. DOE under Contract Numbers DE-FG02-08ER54984, DE-FC02-04ER54698, and DE-AC02-05CH11231.

Effects of plasma shaping on nonlinear gyrokinetic turbulence

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

Belli, E. A.; Hammett, G. W.; Dorland, W.

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on bothmore » the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of {chi}{approx}{kappa}{sup -1.5} or {kappa}{sup -2.0}, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.« less

MHD simulation of transition process from the magneto-rotational instability to magnetic turbulence by using a high-order MHD simulation scheme

NASA Astrophysics Data System (ADS)

Hirai, K.; Katoh, Y.; Terada, N.; Kawai, S.

2016-12-01

In accretion disks, magneto-rotational instability (MRI; Balbus & Hawley, 1991) makes the disk gas in the magnetic turbulent state and drives efficient mass accretion into a central star. MRI drives turbulence through the evolution of the parasitic instability (PI; Goodman & Xu, 1994), which is related to both Kelvin-Helmholtz (K-H) instability and magnetic reconnection. The wave number vector of PI is strongly affected by both magnetic diffusivity and fluid viscosity (Pessah, 2010). This fact makes MHD simulation of MRI difficult, because we need to employ the numerical diffusivity for treating discontinuities in compressible MHD simulation schemes. Therefore, it is necessary to use an MHD scheme that has both high-order accuracy so as to resolve MRI driven turbulence and small numerical diffusivity enough to treat discontinuities. We have originally developed an MHD code by employing the scheme proposed by Kawai (2013). This scheme focuses on resolving turbulence accurately by using a high-order compact difference scheme (Lele, 1992), and meanwhile, the scheme treats discontinuities by using the localized artificial diffusivity method (Kawai, 2013). Our code also employs the pipeline algorithm (Matsuura & Kato, 2007) for MPI parallelization without diminishing the accuracy of the compact difference scheme. We carry out a 3-dimensional ideal MHD simulation with a net vertical magnetic field in the local shearing box disk model. We use 256x256x128 grids. Simulation results show that the spatially averaged turbulent stress induced by MRI linearly grows until around 2.8 orbital periods, and decreases after the saturation. We confirm the strong enhancement of the K-H mode PI at a timing just before the saturation, identified by the enhancement of its anisotropic wavenumber spectra in the 2-dimensional wavenumber space. The wave number of the maximum growth of PI reproduced in the simulation result is larger than the linear analysis. This discrepancy is explained by the simulation result that a shear flow created by MRI locally becomes thinner and faster due to interactions between antiparallel vortices induced by K-H mode PI, and this structure induces small scale waves which break the shear flow itself. We report the results of the simulation, and discuss how the saturation amplitude of MRI is determined.

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

Final Report for "Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing"

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

Srinath Vadlamani; Scott Kruger; Travis Austin

Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems.more » For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.« less

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

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

Cloning and characterization of the SERK1 gene in triploid Pingyi Tiancha [Malus hupehensis (Pamp.) Rehd. var. pingyiensis Jiang] and a tetraploid hybrid strain.

PubMed

Zhang, L J; Dong, W X; Guo, S M; Wang, Y X; Wang, A D; Lu, X J

2015-11-19

This study aims to explore the roles of somatic embryogenesis receptor-like kinase (SERK) in Malus hupehensis (Pingyi Tiancha). The full-length sequences of SERK1 in triploid Pingyi Tiancha (3n) and a tetraploid hybrid strain 33# (4n) were cloned, sequenced, and designated as MhSERK1 and MhdSERK1, respectively. Multiple alignments of amino acid sequences were conducted to identify similarity between MhSERK1 and MhdSERK1 and SERK sequences in other species, and a neighbor-joining phylogenetic tree was constructed to elucidate their phylogenetic relations. Expression levels of MhSERK1 and MhdSERK1 in different tissues and developmental stages were investigated using quantitative real-time PCR. The coding sequence lengths of MhSERK1 and MhdSERK1 were 1899 bp (encoding 632 amino acids) and 1881 bp (encoding 626 amino acids), respectively. Sequence analysis demonstrated that MhSERK1 and MhdSERK1 display high similarity to SERKs in other species, with a conserved intron/exon structure that is unique to members of the SERK family. Additionally, the phylogenetic tree showed that MhSERK1 and MhdSERK1 clustered with orange CitSERK (93%). Furthermore, MhSERK1 and MhdSERK1 were mainly expressed in the reproductive organs, in particular the ovary. Their expression levels were highest in young flowers and they differed among different tissues and organs. Our results suggest that MhSERK1 and MhdSERK1 are related to plant reproduction, and that MhSERK1 is related to apomixis in triploid Pingyi Tiancha.

NIMROD simulations of HIT-SI plasmas

NASA Astrophysics Data System (ADS)

Akcay, Cihan; Jarboe, Thomas; Nelson, Brian; Kim, Charlson

2011-10-01

HIT-SI (Steady Inductive Helicity Injected Torus) is a current drive experiment that uses two semi-toroidal helicity injectors driven at 5-15 kHz to generate steady inductive helicity injection (SIHI). All the plasma-facing walls of the experiment are coated with an insulating material to guarantee an inductive discharge. NIMROD is a 3-D extended MHD code that can only model toroidally-uniform geometries. The helicity injectors of the experiment are simulated as flux and voltage boundary conditions with odd toroidal symmetry. A highly resistive, thin edge-layer approximates the insulating walls. The simulations are initial-value calculations that use a zero β resistive MHD (rMHD) model with uniform density. The Prandtl number (Pr = 10), and Lundquist number (S = 5 - 50) closely match the experimental values. rMHD calculations at S ~ 10 show no growth of an n = 0 mode and only a few kA of toroidal current whereas HIT-SI has demonstrated toroidal currents greater than 50 kA with a current amplification of 3. At higher S (>= 20) the simulations exhibit significant n = 0 magnetic energy growth and a current amplification exceeding unity: Itor/Iinj >= 1 . While HIT-SI has shown evidence for separatrix formation, rMHD calculations indicate an entirely stochastic magnetic structure during sustainment. Results will also presented for Hall MHD, anticipated to play a crucial role in the physics of SIHI.

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

Ivanov, A. A., E-mail: aai@a5.kiam.ru; Martynov, A. A., E-mail: martynov@a5.kiam.ru; Medvedev, S. Yu., E-mail: medvedev@a5.kiam.ru

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (withmore » arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.« less

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

Gyroaveraging operations using adaptive matrix operators

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

Dominski, Julien; Ku, Seung -Hoe; Chang, Choong -Seock

A new adaptive scheme to be used in particle-in-cell codes for carrying out gyroaveraging operations with matrices is presented. This new scheme uses an intermediate velocity grid whose resolution is adapted to the local thermal Larmor radius. The charge density is computed by projecting marker weights in a field-line following manner while preserving the adiabatic magnetic moment μ. These choices permit to improve the accuracy of the gyroaveraging operations performed with matrices even when strong spatial variation of temperature and magnetic field is present. Accuracy of the scheme in different geometries from simple 2D slab geometry to realistic 3D toroidalmore » equilibrium has been studied. As a result, a successful implementation in the gyrokinetic code XGC is presented in the delta-f limit.« less

Gyroaveraging operations using adaptive matrix operators

DOE PAGES

Dominski, Julien; Ku, Seung -Hoe; Chang, Choong -Seock

2018-05-17

A new adaptive scheme to be used in particle-in-cell codes for carrying out gyroaveraging operations with matrices is presented. This new scheme uses an intermediate velocity grid whose resolution is adapted to the local thermal Larmor radius. The charge density is computed by projecting marker weights in a field-line following manner while preserving the adiabatic magnetic moment μ. These choices permit to improve the accuracy of the gyroaveraging operations performed with matrices even when strong spatial variation of temperature and magnetic field is present. Accuracy of the scheme in different geometries from simple 2D slab geometry to realistic 3D toroidalmore » equilibrium has been studied. As a result, a successful implementation in the gyrokinetic code XGC is presented in the delta-f limit.« less

Investigation of the plasma shaping effects on the H-mode pedestal structure using coupled kinetic neoclassical/MHD stability simulations

NASA Astrophysics Data System (ADS)

Pankin, A. Y.; Rafiq, T.; Kritz, A. H.; Park, G. Y.; Snyder, P. B.; Chang, C. S.

2017-06-01

The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas. The neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] is used in carrying out a scan over plasma elongation and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)]. Simulations with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed. For the discharges with higher elongation, it is found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states. In these simulations, the pedestal slowly continues to evolve to higher pedestal pressures and bootstrap currents until the peeling-ballooning stability conditions are satisfied. The discharges with lower elongation do not reach the semi-steady state, and ELM crashes are triggered at earlier times. The plasma elongation is found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency is large, and the H-mode pedestal evolves rapidly. It is found that the temperature of neutrals in the scrape-off-layer (SOL) region can affect the dynamics of the H-mode pedestal buildup. However, the final pedestal profiles are nearly independent of the neutral temperature. The elongation and triangularity affect the pedestal widths of plasma density and electron temperature profiles differently. This provides a new mechanism of controlling the pedestal bootstrap current and the pedestal stability.

Investigation of the plasma shaping effects on the H-mode pedestal structure using coupled kinetic neoclassical/MHD stability simulations

DOE PAGES

Pankin, A. Y.; Rafiq, T.; Kritz, A. H.; ...

2017-06-08

The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas. We use the neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] to carry out a scan over plasma elongation and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)]. In simulationsmore » with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed. For the discharges with higher elongation, it is found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states. In these simulations, the pedestal slowly continues to evolve to higher pedestal pressures and bootstrap currents until the peeling-ballooning stability conditions are satisfied. The discharges with lower elongation do not reach the semi-steady state, and ELM crashes are triggered at earlier times. The plasma elongation is found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency is large, and the H-mode pedestal evolves rapidly. It is found that the temperature of neutrals in the scrape-off-layer (SOL) region can affect the dynamics of the H-mode pedestal buildup. But the final pedestal profiles are nearly independent of the neutral temperature. The elongation and triangularity affect the pedestal widths of plasma density and electron temperature profiles differently. This provides a new mechanism of controlling the pedestal bootstrap current and the pedestal stability.« less

Investigation of the plasma shaping effects on the H-mode pedestal structure using coupled kinetic neoclassical/MHD stability simulations

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

Pankin, A. Y.; Rafiq, T.; Kritz, A. H.

The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas. We use the neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] to carry out a scan over plasma elongation and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)]. In simulationsmore » with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed. For the discharges with higher elongation, it is found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states. In these simulations, the pedestal slowly continues to evolve to higher pedestal pressures and bootstrap currents until the peeling-ballooning stability conditions are satisfied. The discharges with lower elongation do not reach the semi-steady state, and ELM crashes are triggered at earlier times. The plasma elongation is found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency is large, and the H-mode pedestal evolves rapidly. It is found that the temperature of neutrals in the scrape-off-layer (SOL) region can affect the dynamics of the H-mode pedestal buildup. But the final pedestal profiles are nearly independent of the neutral temperature. The elongation and triangularity affect the pedestal widths of plasma density and electron temperature profiles differently. This provides a new mechanism of controlling the pedestal bootstrap current and the pedestal stability.« less

Conservation Laws for Gyrokinetic Equations for Large Perturbations and Flows

NASA Astrophysics Data System (ADS)

Dimits, Andris

2017-10-01

Gyrokinetic theory has proved to be very useful for the understanding of magnetized plasmas, both to simplify analytical treatments and as a basis for efficient numerical simulations. Gyrokinetic theories were previously developed in two extended orderings that are applicable to large fluctuations and flows as may arise in the tokamak edge and scrapeoff layer. In the present work, we cast the resulting equations in a field-theoretical variational form, and derive, up to second order in the respective orderings, the associated global and local energy and (linear and toroidal) momentum conservation relations that result from Noether's theorem. The consequences of these for the various possible choices of numerical discretization used in gyrokinetic simulations are considered. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and supported by the U.S. DOE, OFES.

A hybrid numerical fluid dynamics code for resistive magnetohydrodynamics

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

Johnson, Jeffrey

2006-04-01

Spasmos is a computational fluid dynamics code that uses two numerical methods to solve the equations of resistive magnetohydrodynamic (MHD) flows in compressible, inviscid, conducting media[1]. The code is implemented as a set of libraries for the Python programming language[2]. It represents conducting and non-conducting gases and materials with uncomplicated (analytic) equations of state. It supports calculations in 1D, 2D, and 3D geometry, though only the 1D configuation has received significant testing to date. Because it uses the Python interpreter as a front end, users can easily write test programs to model systems with a variety of different numerical andmore » physical parameters. Currently, the code includes 1D test programs for hydrodynamics (linear acoustic waves, the Sod weak shock[3], the Noh strong shock[4], the Sedov explosion[5], magnetic diffusion (decay of a magnetic pulse[6], a driven oscillatory "wine-cellar" problem[7], magnetic equilibrium), and magnetohydrodynamics (an advected magnetic pulse[8], linear MHD waves, a magnetized shock tube[9]). Spasmos current runs only in a serial configuration. In the future, it will use MPI for parallel computation.« less

Linear and nonlinear verification of gyrokinetic microstability codes

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

Bravenec, R. V.; Candy, J.; Barnes, M.

2011-12-15

Verification of nonlinear microstability codes is a necessary step before comparisons or predictions of turbulent transport in toroidal devices can be justified. By verification we mean demonstrating that a code correctly solves the mathematical model upon which it is based. Some degree of verification can be accomplished indirectly from analytical instability threshold conditions, nonlinear saturation estimates, etc., for relatively simple plasmas. However, verification for experimentally relevant plasma conditions and physics is beyond the realm of analytical treatment and must rely on code-to-code comparisons, i.e., benchmarking. The premise is that the codes are verified for a given problem or set ofmore » parameters if they all agree within a specified tolerance. True verification requires comparisons for a number of plasma conditions, e.g., different devices, discharges, times, and radii. Running the codes and keeping track of linear and nonlinear inputs and results for all conditions could be prohibitive unless there was some degree of automation. We have written software to do just this and have formulated a metric for assessing agreement of nonlinear simulations. We present comparisons, both linear and nonlinear, between the gyrokinetic codes GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and GS2[W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. We do so at the mid-radius for the same discharge as in earlier work [C. Holland, A. E. White, G. R. McKee, M. W. Shafer, J. Candy, R. E. Waltz, L. Schmitz, and G. R. Tynan, Phys. Plasmas 16, 052301 (2009)]. The comparisons include electromagnetic fluctuations, passing and trapped electrons, plasma shaping, one kinetic impurity, and finite Debye-length effects. Results neglecting and including electron collisions (Lorentz model) are presented. We find that the linear frequencies with or without collisions agree well between codes, as do the time averages of the nonlinear fluxes without collisions. With collisions, the differences between the time-averaged fluxes are larger than the uncertainties defined as the oscillations of the fluxes, with the GS2 fluxes consistently larger (or more positive) than those from GYRO. However, the electrostatic fluxes are much smaller than those without collisions (the electromagnetic energy flux is negligible in both cases). In fact, except for the electron energy fluxes, the absolute magnitudes of the differences in fluxes with collisions are the same or smaller than those without. None of the fluxes exhibit large absolute differences between codes. Beyond these results, the specific linear and nonlinear benchmarks proposed here, as well as the underlying methodology, provide the basis for a wide variety of future verification efforts.« less

Characterization of open-cycle coal-fired MHD generators. Quarterly technical summary report No. 6, October 1--December 31, 1977. [PACKAGE code

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

Kolb, C.E.; Yousefian, V.; Wormhoudt, J.

1978-01-30

Research has included theoretical modeling of important plasma chemical effects such as: conductivity reductions due to condensed slag/electron interactions; conductivity and generator efficiency reductions due to the formation of slag-related negative ion species; and the loss of alkali seed due to chemical combination with condensed slag. A summary of the major conclusions in each of these areas is presented. A major output of the modeling effort has been the development of an MHD plasma chemistry core flow model. This model has been formulated into a computer program designated the PACKAGE code (Plasma Analysis, Chemical Kinetics, And Generator Efficiency). The PACKAGEmore » code is designed to calculate the effect of coal rank, ash percentage, ash composition, air preheat temperatures, equivalence ratio, and various generator channel parameters on the overall efficiency of open-cycle, coal-fired MHD generators. A complete description of the PACKAGE code and a preliminary version of the PACKAGE user's manual are included. A laboratory measurements program involving direct, mass spectrometric sampling of the positive and negative ions formed in a one atmosphere coal combustion plasma was also completed during the contract's initial phase. The relative ion concentrations formed in a plasma due to the methane augmented combustion of pulverized Montana Rosebud coal with potassium carbonate seed and preheated air are summarized. Positive ions measured include K/sup +/, KO/sup +/, Na/sup +/, Rb/sup +/, Cs/sup +/, and CsO/sup +/, while negative ions identified include PO/sub 3//sup -/, PO/sub 2//sup -/, BO/sub 2//sup -/, OH/sup -/, SH/sup -/, and probably HCrO/sub 3/, HMoO/sub 4//sup -/, and HWO/sub 3//sup -/. Comparison of the measurements with PACKAGE code predictions are presented. Preliminary design considerations for a mass spectrometric sampling probe capable of characterizing coal combustion plasmas from full scale combustors and flow trains are presented and discussed.« less

The Influence of the Hall Term on the Development of Magnetized Laser-Produced Plasma Jets

DOE PAGES

Hamlin, N.D.; Seyler, C. E.; Khiar, B.

2018-04-29

We present 2D axisymmetric simulation results describing the influence of the Hall term on laser-produced plasma jets and their interaction with an applied magnetic field parallel to the laser axis. Bending of the poloidal B-field lines produces an MHD shock structure surrounding a conical cavity, and a jet is produced from the convergence of the shock envelope. Both the jet and the conical cavity underneath it are bound by fast MHD shocks. We compare the MHD results generated using the extended-MHD code Physics as an Extended-MHD Relaxation System with an Efficient Upwind Scheme (PERSEUS) with MHD results generated using GORGONmore » and find reasonable agreement. We then present extended-MHD results generated using PERSEUS, which show that the Hall term has several effects on the plasma jet evolution. A hot low-density current-carrying layer of plasma develops just outside the plume, which results in a helical rather than a purely poloidal B-field, and reduces magnetic stresses, resulting in delayed flow convergence and jet formation. The flow is partially frozen into the helical field, resulting in azimuthal rotation of the jet. The Hall term also produces field-aligned current in strongly magnetized regions. In particular, we find the influence of Hall physics on this problem to be scale-dependent. In conclusion, this points to the importance of mitigating the Hall effect in a laboratory setup, by increasing the jet density and system dimensions, in order to avoid inaccurate extrapolation to astrophysical scales.« less

The Influence of the Hall Term on the Development of Magnetized Laser-Produced Plasma Jets

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

Hamlin, N.D.; Seyler, C. E.; Khiar, B.

We present 2D axisymmetric simulation results describing the influence of the Hall term on laser-produced plasma jets and their interaction with an applied magnetic field parallel to the laser axis. Bending of the poloidal B-field lines produces an MHD shock structure surrounding a conical cavity, and a jet is produced from the convergence of the shock envelope. Both the jet and the conical cavity underneath it are bound by fast MHD shocks. We compare the MHD results generated using the extended-MHD code Physics as an Extended-MHD Relaxation System with an Efficient Upwind Scheme (PERSEUS) with MHD results generated using GORGONmore » and find reasonable agreement. We then present extended-MHD results generated using PERSEUS, which show that the Hall term has several effects on the plasma jet evolution. A hot low-density current-carrying layer of plasma develops just outside the plume, which results in a helical rather than a purely poloidal B-field, and reduces magnetic stresses, resulting in delayed flow convergence and jet formation. The flow is partially frozen into the helical field, resulting in azimuthal rotation of the jet. The Hall term also produces field-aligned current in strongly magnetized regions. In particular, we find the influence of Hall physics on this problem to be scale-dependent. In conclusion, this points to the importance of mitigating the Hall effect in a laboratory setup, by increasing the jet density and system dimensions, in order to avoid inaccurate extrapolation to astrophysical scales.« less

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

Analytical investigation of critical phenomena in MHD power generators

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

Not Available

1980-07-31

Critical phenomena in the Arnold Engineering Development Center (AEDC) High Performance Demonstration Experiment (HPDE) and the US U-25 Experiment, are analyzed. Also analyzed are the performance of a NASA-specified 500 MW(th) flow train and computations concerning critica issues for the scale-up of MHD Generators. The HPDE is characterized by computational simulations of both the nominal conditions and the conditions during the experimental runs. The steady-state performance is discussed along with the Hall voltage overshoots during the start-up and shutdown transients. The results of simulations of the HPDE runs with codes from the Q3D and TRANSIENT code families are compared tomore » the experimental results. The results of the simulations are in good agreement with the experimental data. Additional critica phenomena analyzed in the AEDC/HPDE are the optimal load schedules, parametric variations, the parametric dependence of the electrode voltage drops, the boundary layer behavior, near electrode phenomena with finite electrode segmentation, and current distribution in the end regions. The US U-25 experiment is characterized by computational simulations of the nominal operating conditions. The steady-state performance for the nominal design of the US U-25 experiment is analyzed, as is the dependence of performance on the mass flow rate. A NASA-specified 500 MW(th) MHD flow train is characterized for computer simulation and the electrical, transport, and thermodynamic properties at the inlet plane are analyzed. Issues for the scale-up of MHD power trains are discussed. The AEDC/HPDE performance is analyzed to compare these experimental results to scale-up rules.« less

Bringing global gyrokinetic turbulence simulations to the transport timescale using a multiscale approach

NASA Astrophysics Data System (ADS)

Parker, Jeffrey B.; LoDestro, Lynda L.; Told, Daniel; Merlo, Gabriele; Ricketson, Lee F.; Campos, Alejandro; Jenko, Frank; Hittinger, Jeffrey A. F.

2018-05-01

The vast separation dividing the characteristic times of energy confinement and turbulence in the core of toroidal plasmas makes first-principles prediction on long timescales extremely challenging. Here we report the demonstration of a multiple-timescale method that enables coupling global gyrokinetic simulations with a transport solver to calculate the evolution of the self-consistent temperature profile. This method, which exhibits resiliency to the intrinsic fluctuations arising in turbulence simulations, holds potential for integrating nonlocal gyrokinetic turbulence simulations into predictive, whole-device models.

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.

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.

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.

Low-Frequency Microinstabilities in Rotating Tokamak Plasmas.

NASA Astrophysics Data System (ADS)

Artun, Mehmet

1994-01-01

Low-frequency drift-type microinstabilities have often been suggested as the leading candidates to account for the anomalously large transport; observed in tokamak plasmas. The effects of sheared equilibrium flows on this important class of instabilities is systematically investigated in the present thesis. In particular, the analysis is carried out in two parts. In order to gain some insight into the key elements of this problem, the first part deals with the stability properties of the kinetic ion temperature gradient mode under the influence of parallel and perpendicular shear flows in a simplified sheared magnetic slab geometry. The eigenmode analysis is performed using a shooting code for long-wavelength modes (k_|rho _{i} << 1), and an integral eigenmode code for short-wavelength modes (k_ |rho_{i} ~ 1). Numerical results are cross-checked with analytical estimates in the fluid regime. While the differential analysis is mostly limited to ground state modes of the system--due to the requirement that the average perpendicular wavenumber be small--the integral eigenmode code has been used to calculate higher radial eigenmodes with confidence. New features observed through the introduction of shear flows are discussed. In the second part we present the shear flow generalization of the nonlinear electromagnetic gyrokinetic equation for realistic toroidal geometry. In accordance with the most natural choice for such studies, the coordinate frame is chosen to be shifted in velocity space and unchanged in configuration space. The natural equilibrium constraints of the toroidal problem limits the choice of the flow profile to that in which the angular velocity is a function of the flux surface. The general form of the gyrokinetic equation obtained is then used to derive the two-dimensional linear electrostatic eigenmode equation in circular toroidal geometry including trapped particle effects. In addition to magnetic trapping, electrostatic and centrifugal trapping are also found to play an important role here. A modified version of a finite element code is utilized to analyze shear flow effects on the trapped ion mode (TIM) in the long wavelength limit. Numerical results for fully coupled as well as single poloidal harmonic cases are presented. Implications of the results obtained in the present investigation are discussed and suggestions are given for future studies.

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

D'Azevedo, Eduardo; Abbott, Stephen; Koskela, Tuomas

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

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

Xu, X. Q.; Xiong, Z.; Nevins, W. M.

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon} scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Gao, Z.; Nevins, W. M.; McKee, G. R.

2008-05-01

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio γ scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

TEMPEST simulations of collisionless damping of the geodesic-acoustic mode in edge-plasma pedestals.

PubMed

Xu, X Q; Xiong, Z; Gao, Z; Nevins, W M; McKee, G R

2008-05-30

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Impact of energetic-particle-driven geodesic acoustic modes on turbulence.

PubMed

Zarzoso, D; Sarazin, Y; Garbet, X; Dumont, R; Strugarek, A; Abiteboul, J; Cartier-Michaud, T; Dif-Pradalier, G; Ghendrih, Ph; Grandgirard, V; Latu, G; Passeron, C; Thomine, O

2013-03-22

The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.

MHD work related to a self-cooled Pb-17Li blanket with poloidal-radial-toroidal ducts

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

Reimann, J.; Barleon, L.; Buehler, L.

1994-12-31

For self cooled liquid metal blankets MHD pressure drop and velocity distributions are considered as critical issues. This paper summarizes MHD work performed for a DEMO-relevant Pb-17Li blanket which uses essential characteristics of a previous ANL design: The coolant flows downwards in the rear poloidal ducts, turns by 180{degrees} at the blanket bottom and is distributed from the ascending poloidal ducts into short radial channels which feed the toroidal First Wall coolant ducts (aligned with the main magnetic field direction). The flow through the subsequent radial channels is collected again in poloidal channels and the coolant leaves the blanket segmentmore » at the top. The blanket design is based on the use of flow channel inserts (FCIs) (which means electrically thin conducting walls for MHD) for all ducts except for the toroidal FW coolant channels. MHD related issues were defined and estimations of corresponding pressure drops were performed. Previous experimental work included a proof of principle of FCIs and a detailed experiment with a single {open_quotes}poloidal{sm_bullet}toroidal{sm_bullet}poloidal{close_quotes} duct (cooperation with ANL). In parallel, a numerical code based on the Core Flow Approximation (CFA) was developed to predict pressure drop and velocity distributions for arbitrary single duct geometries.« less

GPU Particle Tracking and MHD Simulations with Greatly Enhanced Computational Speed

NASA Astrophysics Data System (ADS)

Ziemba, T.; O'Donnell, D.; Carscadden, J.; Cash, M.; Winglee, R.; Harnett, E.

2008-12-01

GPUs are intrinsically highly parallelized systems that provide more than an order of magnitude computing speed over a CPU based systems, for less cost than a high end-workstation. Recent advancements in GPU technologies allow for full IEEE float specifications with performance up to several hundred GFLOPs per GPU, and new software architectures have recently become available to ease the transition from graphics based to scientific applications. This allows for a cheap alternative to standard supercomputing methods and should increase the time to discovery. 3-D particle tracking and MHD codes have been developed using NVIDIA's CUDA and have demonstrated speed up of nearly a factor of 20 over equivalent CPU versions of the codes. Such a speed up enables new applications to develop, including real time running of radiation belt simulations and real time running of global magnetospheric simulations, both of which could provide important space weather prediction tools.

Application of electron closures in extended MHD

NASA Astrophysics Data System (ADS)

Held, Eric; Adair, Brett; Taylor, Trevor

2017-10-01

Rigorous closure of the extended MHD equations in plasma fluid codes includes the effects of electron heat conduction along perturbed magnetic fields and contributions of the electron collisional friction and stress to the extended Ohms law. In this work we discuss application of a continuum numerical solution to the Chapman-Enskog-like electron drift kinetic equation using the NIMROD code. The implementation is a tightly-coupled fluid/kinetic system that carefully addresses time-centering in the advance of the fluid variables with their kinetically-computed closures. Comparisons of spatial accuracy, computational efficiency and required velocity space resolution are presented for applications involving growing magnetic islands in cylindrical and toroidal geometry. The reduction in parallel heat conduction due to particle trapping in toroidal geometry is emphasized. Work supported by DOE under Grant Nos. DE-FC02-08ER54973 and DE-FG02-04ER54746.

PerSEUS: Ultra-Low-Power High Performance Computing for Plasma Simulations

NASA Astrophysics Data System (ADS)

Doxas, I.; Andreou, A.; Lyon, J.; Angelopoulos, V.; Lu, S.; Pritchett, P. L.

2017-12-01

Peta-op SupErcomputing Unconventional System (PerSEUS) aims to explore the use for High Performance Scientific Computing (HPC) of ultra-low-power mixed signal unconventional computational elements developed by Johns Hopkins University (JHU), and demonstrate that capability on both fluid and particle Plasma codes. We will describe the JHU Mixed-signal Unconventional Supercomputing Elements (MUSE), and report initial results for the Lyon-Fedder-Mobarry (LFM) global magnetospheric MHD code, and a UCLA general purpose relativistic Particle-In-Cell (PIC) code.

Continued Development and Validation of Methods for Spheromak Simulation

NASA Astrophysics Data System (ADS)

Benedett, Thomas

2015-11-01

The HIT-SI experiment has demonstrated stable sustainment of spheromaks; determining how the underlying physics extrapolate to larger, higher-temperature regimes is of prime importance in determining the viability of the inductively-driven spheromak. It is thus prudent to develop and validate a computational model that can be used to study current results and provide an intermediate step between theory and future experiments. A zero-beta Hall-MHD model has shown good agreement with experimental data at 14.5 kHz injector operation. Experimental observations at higher frequency, where the best performance is achieved, indicate pressure effects are important and likely required to attain quantitative agreement with simulations. Efforts to extend the existing validation to high frequency (~ 36-68 kHz) using an extended MHD model implemented in the PSI-TET arbitrary-geometry 3D MHD code will be presented. Results from verification of the PSI-TET extended MHD model using the GEM magnetic reconnection challenge will also be presented along with investigation of injector configurations for future SIHI experiments using Taylor state equilibrium calculations. Work supported by DoE.

A Computational Study of a Circular Interface Richtmyer-Meshkov Instability in MHD

NASA Astrophysics Data System (ADS)

Maxon, William; Black, Wolfgang; Denissen, Nicholas; McFarland, Jacob; Los Alamos National Laboratory Collaboration; University of Missouri Shock Tube Laboratory Team

2017-11-01

The Richtmyer-Meshkov instability (RMI) is a hydrodynamic instability that appears in several high energy density applications such as inertial confinement fusion (ICF). In ICF, as the thermonuclear fuel is being compressed it begins to mix due to fluid instabilities including the RMI. This mixing greatly decreases the energy output. The RMI occurs when two fluids of different densities are impulsively accelerated and the pressure and density gradients are misaligned. In magnetohydrodynamics (MHD), the RMI may be suppressed by introducing a magnetic field in an electrically conducting fluid, such as a plasma. This suppression has been studied as a possible mechanism for improving confinement in ICF targets. In this study,ideal MHD simulations are performed with a circular interface impulsively accelerated by a shock wave in the presence of a magnetic field. These simulations are executed with the research code FLAG, a multiphysics, arbitrary Lagrangian/Eulerian, hydrocode developed and utilized at Los Alamos National Laboratory. The simulation results will be assessed both quantitatively and qualitatively to examine the stabilization mechanism. These simulations will guide ongoing MHD experiments at the University of Missouri Shock Tube Facility.

The numerical modelling of MHD astrophysical flows with chemistry

NASA Astrophysics Data System (ADS)

Kulikov, I.; Chernykh, I.; Protasov, V.

2017-10-01

The new code for numerical simulation of magnetic hydrodynamical astrophysical flows with consideration of chemical reactions is given in the paper. At the heart of the code - the new original low-dissipation numerical method based on a combination of operator splitting approach and piecewise-parabolic method on the local stencil. The chemodynamics of the hydrogen while the turbulent formation of molecular clouds is modeled.

Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

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

Post, R.F.; Fowler, T.K.; Bulmer, R.

2005-01-15

The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma.At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies have employedmore » a low-beta code written especially to analyze the beam injection/stabilization process,and a new code SYMTRAN (by Hua and Fowler)that solves the coupled radial and axial particle and energy transport in a K-S T-M. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values.The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma.Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging.Our studies have confirmed the viability of the K-S T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution.In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M.« less

Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies

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

Post, R F; Fowler, T K; Bulmer, R

2004-07-15

The 'Kinetic Stabilizer' has been proposed as a means of MHD stabilizing an axisymmetric tandem mirror system. The K-S concept is based on theoretical studies by Ryutov, confirmed experimentally in the Gas Dynamic Trap experiment in Novosibirsk. In the K-S beams of ions are directed into the end of an 'expander' region outside the outer mirror of a tandem mirror. These ions, slowed, stagnated, and reflected as they move up the magnetic gradient, produce a low-density stabilizing plasma. At the Lawrence Livermore National Laboratory we have been conducting theoretical and computational studies of the K-S Tandem Mirror. These studies havemore » employed a low-beta code written especially to analyze the beam injection/stabilization process, and a new code SYMTRAN (by Hua and Fowler) that solves the coupled radial and axial particle and energy transport in a K-S TM. Also, a 'legacy' MHD stability code, FLORA, has been upgraded and employed to benchmark the injection/stabilization code and to extend its results to high beta values. The FLORA code studies so far have confirmed the effectiveness of the K-S in stabilizing high-beta (40%) plasmas with stabilizer plasmas the peak pressures of which are several orders of magnitude smaller than those of the confined plasma. Also the SYMTRAN code has shown D-T plasma ignition from alpha particle energy deposition in T-M regimes with strong end plugging. Our studies have confirmed the viability of the K-S-T-M concept with respect to MHD stability and radial and axial confinement. We are continuing these studies in order to optimize the parameters and to examine means for the stabilization of possible residual instability modes, such as drift modes and 'trapped-particle' modes. These modes may in principle be controlled by tailoring the stabilizer plasma distribution and/or the radial potential distribution. In the paper the results to date of our studies are summarized and projected to scope out possible fusion-power versions of the K-S T-M« less

Steady State Global Simulations of Microturbulence

NASA Astrophysics Data System (ADS)

Lee, W. W.

2004-11-01

Critical physics issues for the steady state simulation of ion temperature gradient (ITG) drift instabilities are associated with collisionless and collisional dissipation processes. In this paper, we will report on recent investigations involving the inclusion of velocity-space nonlinearity term in our global Gyrokinetic Toroidal Code (GTC) [1]. It is important to point out that this term has not been critically examined in the turbulence simulation community [2], although it has attracted some recent interest for energy conservation considerations as well as for its effect on transport [3]. The nonlinearity in question is actually of the same order as the nonlinear zonal flow, and it can also play an interesting role in entropy balance for steady state transport [4]. Our initial results with adiabatic electrons have shown that the velocity-space nonlinearity for the ions can have a small but non-negligible effect at the early nonlinear stage of the ITG simulation. In the later stage, it can actually enhance the level of zonal flow and, in turn, can reduce the steady state thermal flux. The enhanced fluctuation of (n=0, m=1) mode has also been observed. More detailed simulation results including also collisions [5] as well as the theoretical attempt to understand the nonlinear physics of mode-coupling and entropy balance will be reported. The implication of the present work on transport time scale simulation including Alfven kinetic-MHD physics [6] will also be discussed. [1] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang and R. White, Science, <281>, 1835 (1998). [2] W. M. Nevins et al., Plasma Microturbulence Project, this conference. [3] L. Villard et al., Nuclear Fusion <44>, 172 (2004). [4] W. W. Lee and W. M. Tang, Phys. Fluids <31>, 612 (1988). [5] Z. Lin, T. S. Hahm, W. W. Lee, W. M. Tang and R. White, Phys. Plasmas <7>, 1857 (2000). [6] W. W. Lee and H. Qin, Phys. Plasmas <10>, 3196 (2003).

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.

Poloidal structure of the plasma response to n = 1 Resonant Magnetic Perturbations in ASDEX Upgrade

NASA Astrophysics Data System (ADS)

Marrelli, L.; Bettini, P.; Piovesan, P.; Terranova, D.; Giannone, L.; Igochine, V.; Maraschek, M.; Suttrop, W.; Teschke, M.; Liu, Y. Q.; Ryan, D.; Eurofusion Mst1 Team; ASDEX Upgrade Team

2017-10-01

The hybrid scenario, a candidate for high-beta steady-state tokamak operations, becomes highly sensitive to 3D magnetic field near the no-wall limit. A predictive understanding of the plasma response to 3D fields near ideal MHD limits in terms of validated MHD stability codes is therefore important in order to safely operate future devices. Slowly rotating (5 - 10 Hz) n = 1 external magnetic fields have been applied in hybrid discharges in ASDEX Upgrade for an experimental characterization: the global n = 1 kink response has been measured by means of SXR and complete poloidal arrays of bθ probes located at different toroidal angles and compared to predictions of MHD codes such as MARS-F and V3FIT-VMEC. A Least-Squares Spectral Analysis approach has been developed together with a Monte Carlo technique to extract the small plasma response and its confidence interval from the noisy magnetic signals. MARS-F correctly reproduces the poloidal structure of the n = 1 measurements: for example, the dependence of the dominant poloidal mode number at the plasma edge from q95 is the same as in the experiment. Similar comparisons with V3FIT-VMEC and will be presented. See author list of ``H. Meyer et al. 2017 Nucl. Fusion 57 102014''.

Modeling extreme (Carrington-type) space weather events using three-dimensional MHD code simulations

NASA Astrophysics Data System (ADS)

Ngwira, C. M.; Pulkkinen, A. A.; Kuznetsova, M. M.; Glocer, A.

2013-12-01

There is growing concern over possible severe societal consequences related to adverse space weather impacts on man-made technological infrastructure and systems. In the last two decades, significant progress has been made towards the modeling of space weather events. Three-dimensional (3-D) global magnetohydrodynamics (MHD) models have been at the forefront of this transition, and have played a critical role in advancing our understanding of space weather. However, the modeling of extreme space weather events is still a major challenge even for existing global MHD models. In this study, we introduce a specially adapted University of Michigan 3-D global MHD model for simulating extreme space weather events that have a ground footprint comparable (or larger) to the Carrington superstorm. Results are presented for an initial simulation run with ``very extreme'' constructed/idealized solar wind boundary conditions driving the magnetosphere. In particular, we describe the reaction of the magnetosphere-ionosphere system and the associated ground induced geoelectric field to such extreme driving conditions. We also discuss the results and what they might mean for the accuracy of the simulations. The model is further tested using input data for an observed space weather event to verify the MHD model consistence and to draw guidance for future work. This extreme space weather MHD model is designed specifically for practical application to the modeling of extreme geomagnetically induced electric fields, which can drive large currents in earth conductors such as power transmission grids.

An MHD simulation of By-dependent magnetospheric convection and field-aligned currents during northward IMF

NASA Technical Reports Server (NTRS)

Ogino, T.; Walker, R. J.; Ashour-Abdalla, M.; Dawson, J. M.

1985-01-01

A three-dimensional MHD simulation code is used to model the magnetospheric configuration when the IMF has both a northward B(z) component and a B(y) component in the east-west direction. Projections of the plasma pressure, the field-aligned velocity, the field-aligned vorticity, and the field-aligned current along the magnetic field lines into the northern ionosphere are shown and discussed. Cross-sectional patterns of these parameters are shown. The results demonstrate that the B(y) component of the IMF strongly influences the plasma sheet configuration and the magnetospheric convection pattern.

MHD Simulation of the HIT-SI Experiment

NASA Astrophysics Data System (ADS)

Marklin, George

2003-10-01

The Helicity Injected Torus (HIT) experiment at the University of Washington has been reconfigured into a high beta spheromak with steady state AC current drive [1]. Helicity is injected by two half torus Reversed Field Pinches (RFP's) connected to the ends of the cylindrically symmetric flux conserver, rotated by 90 degrees from each other. The RFP's are driven with sinusoidally varying voltage and flux. Each side has its voltage and flux in phase, but is 90 degrees out of phase from the other side. The helicity injection rate, which is proportional to the voltage times the flux, goes like sin(wt)^2 on one side and cos(wt)^2 on the other, making the total injection rate constant in time. The complex multiply connected 3-dimensional geometry of this device make it difficult to simulate with existing codes that typically use a structured mesh. This poster will describe a new 3D MHD simulation code and a new 3D Taylor state code which both use an unstructured finite element mesh. The mesh is generated from a CAD-like description of an arbitrary arrangement of 3D geometrical objects. Taylor states in the HIT-SI geometry will be shown for different combinations of fluxes in the two injectors. MHD simulation results will be shown starting from a Taylor state with uniform density and temperature and continuing through several cycles of time dependent helicity injection. Field line tracing plots will show the quality of the flux surfaces at various stages in the injection cycle. [1] T. R. Jarboe, Fusion Technology, vol. 36, p. 85, 1999

Cross-verification of the GENE and XGC codes in preparation for their coupling

NASA Astrophysics Data System (ADS)

Jenko, Frank; Merlo, Gabriele; Bhattacharjee, Amitava; Chang, Cs; Dominski, Julien; Ku, Seunghoe; Parker, Scott; Lanti, Emmanuel

2017-10-01

A high-fidelity Whole Device Model (WDM) of a magnetically confined plasma is a crucial tool for planning and optimizing the design of future fusion reactors, including ITER. Aiming at building such a tool, in the framework of the Exascale Computing Project (ECP) the two existing gyrokinetic codes GENE (Eulerian delta-f) and XGC (PIC full-f) will be coupled, thus enabling to carry out first principle kinetic WDM simulations. In preparation for this ultimate goal, a benchmark between the two codes is carried out looking at ITG modes in the adiabatic electron limit. This verification exercise is also joined by the global Lagrangian PIC code ORB5. Linear and nonlinear comparisons have been carried out, neglecting for simplicity collisions and sources. A very good agreement is recovered on frequency, growth rate and mode structure of linear modes. A similarly excellent agreement is also observed comparing the evolution of the heat flux and of the background temperature profile during nonlinear simulations. Work supported by the US DOE under the Exascale Computing Project (17-SC-20-SC).

Measurements of Impurity Particle Transport Associated with Drift-Wave Turbulence in MST

NASA Astrophysics Data System (ADS)

Nishizawa, Takashi; Nornberg, Mark; Boguski, John; Craig, Darren; den Hartog, Daniel; Pueschel, M. J.; Sarff, John; Terry, Paul; Williams, Zach; Xing, Zichuan

2017-10-01

Understanding and controlling impurity transport in a toroidal magnetized plasma is one of the critical issues that need to be addressed in order to achieve controlled fusion. Gyrokinetic modeling shows turbulence can drive impurity transport, but direct measurements of the turbulent flux have not been made. Particle balance is typically used to infer the presence of turbulent impurity transport. We report, for the first time in a toroidal plasma, direct measurements of turbulence-driven impurity transport. Trapped electron mode (TEM) turbulence appears in MST plasmas when MHD tearing fluctuations are suppressed. Impurity ion-Doppler spectroscopy is used to correlate impurity density and radial velocity fluctuations associated with TEM. Small Doppler shifts associated with the radial velocity fluctuations (rms 1km/s) are resolved with the use of a new linearized spectrum correlation analysis method, which improves the rejection of Poisson noise. The method employs frequency-domain correlation analysis to expose the fluctuation and transport spectrum. The C+ 2 impurity transport velocity driven by turbulence is found to be 48m/s (inward), which is sufficiently large to impact an impurity flux balance in MST improved-confinement plasmas. This work is supported by the US DOE.

Overview of MST Research

NASA Astrophysics Data System (ADS)

Sarff, J. S.

2016-10-01

MST progress in advancing the RFP for (1) fusion plasma confinement with ohmic heating and minimal external magnetization, (2) predictive capability in toroidal confinement physics, and (3) basic plasma physics is summarized. Validation of key plasma models is a program priority. Programmable power supplies (PPS) are being developed to maximize inductive capability. Well-controlled flattops with current as low as 0.02 MA are produced with an existing PPS, and Ip <= 0.8 MA is anticipated with a second PPS under construction. The Lundquist number spans S =10(4 - 9) for 0.02-0.8 MA, allowing nonlinear MHD validation using NIMROD and DEBS at low S to be connected to highest S experiments. The PPS also enables MST tokamak operation for studying transients and runaway electron suppression with RMPs. Gyrokinetic modeling with GENE predicts unstable TEM in improved-confinement plasmas. Fluctuations are measured with TEM properties including a density-gradient threshold larger than for tokamak plasmas. Probe measurements hint that drift waves are also excited via the turbulent cascade in standard RFP plasmas. Turbulent energization of an electron tail occurs during sawtooth reconnection. New diagnostics are being developed to measure the energetic ion profile and transport from EP instabilities with NBI. Supported by US DoE and NSF.

Metriplectic Gyrokinetics and Discretization Methods for the Landau Collision Integral

NASA Astrophysics Data System (ADS)

Hirvijoki, Eero; Burby, Joshua W.; Kraus, Michael

2017-10-01

We present two important results for the kinetic theory and numerical simulation of warm plasmas: 1) We provide a metriplectic formulation of collisional electrostatic gyrokinetics that is fully consistent with the First and Second Laws of Thermodynamics. 2) We provide a metriplectic temporal and velocity-space discretization for the particle phase-space Landau collision integral that satisfies the conservation of energy, momentum, and particle densities to machine precision, as well as guarantees the existence of numerical H-theorem. The properties are demonstrated algebraically. These two result have important implications: 1) Numerical methods addressing the Vlasov-Maxwell-Landau system of equations, or its reduced gyrokinetic versions, should start from a metriplectic formulation to preserve the fundamental physical principles also at the discrete level. 2) The plasma physics community should search for a metriplectic reduction theory that would serve a similar purpose as the existing Lagrangian and Hamiltonian reduction theories do in gyrokinetics. The discovery of metriplectic formulation of collisional electrostatic gyrokinetics is strong evidence in favor of such theory and, if uncovered, the theory would be invaluable in constructing reduced plasma models. Supported by U.S. DOE Contract Nos. DE-AC02-09-CH11466 (EH) and DE-AC05-06OR23100 (JWB) and by European Union's Horizon 2020 research and innovation Grant No. 708124 (MK).

Numerical analysis of real gas MHD flow on two-dimensional self-field MPD thrusters

NASA Astrophysics Data System (ADS)

Xisto, Carlos M.; Páscoa, José C.; Oliveira, Paulo J.

2015-07-01

A self-field magnetoplasmadynamic (MPD) thruster is a low-thrust electric propulsion space-system that enables the usage of magnetohydrodynamic (MHD) principles for accelerating a plasma flow towards high speed exhaust velocities. It can produce an high specific impulse, making it suitable for long duration interplanetary space missions. In this paper numerical results obtained with a new code, which is being developed at C-MAST (Centre for Mechanical and Aerospace Technologies), for a two-dimensional self-field MPD thruster are presented. The numerical model is based on the macroscopic MHD equations for compressible and electrically resistive flow and is able to predict the two most important thrust mechanisms that are associated with this kind of propulsion system, namely the thermal thrust and the electromagnetic thrust. Moreover, due to the range of very high temperatures that could occur during the operation of the MPD, it also includes a real gas model for argon.

High fidelity studies of exploding foil initiator bridges, Part 3: ALEGRA MHD simulations

NASA Astrophysics Data System (ADS)

Neal, William; Garasi, Christopher

2017-01-01

Simulations of high voltage detonators, such as Exploding Bridgewire (EBW) and Exploding Foil Initiators (EFI), have historically been simple, often empirical, one-dimensional models capable of predicting parameters such as current, voltage, and in the case of EFIs, flyer velocity. Experimental methods have correspondingly generally been limited to the same parameters. With the advent of complex, first principles magnetohydrodynamic codes such as ALEGRA and ALE-MHD, it is now possible to simulate these components in three dimensions, and predict a much greater range of parameters than before. A significant improvement in experimental capability was therefore required to ensure these simulations could be adequately verified. In this third paper of a three part study, the experimental results presented in part 2 are compared against 3-dimensional MHD simulations. This improved experimental capability, along with advanced simulations, offer an opportunity to gain a greater understanding of the processes behind the functioning of EBW and EFI detonators.

Gas Core Reactor Numerical Simulation Using a Coupled MHD-MCNP Model

NASA Technical Reports Server (NTRS)

Kazeminezhad, F.; Anghaie, S.

2008-01-01

Analysis is provided in this report of using two head-on magnetohydrodynamic (MHD) shocks to achieve supercritical nuclear fission in an axially elongated cylinder filled with UF4 gas as an energy source for deep space missions. The motivation for each aspect of the design is explained and supported by theory and numerical simulations. A subsequent report will provide detail on relevant experimental work to validate the concept. Here the focus is on the theory of and simulations for the proposed gas core reactor conceptual design from the onset of shock generations to the supercritical state achieved when the shocks collide. The MHD model is coupled to a standard nuclear code (MCNP) to observe the neutron flux and fission power attributed to the supercritical state brought about by the shock collisions. Throughout the modeling, realistic parameters are used for the initial ambient gaseous state and currents to ensure a resulting supercritical state upon shock collisions.

MHD simulation of plasma compression experiments

NASA Astrophysics Data System (ADS)

Reynolds, Meritt; Barsky, Sandra; de Vietien, Peter

2017-10-01

General Fusion (GF) is working to build a magnetized target fusion (MTF) power plant based on compression of magnetically-confined plasma by liquid metal. GF is testing this compression concept by collapsing solid aluminum liners onto plasmas formed by coaxial helicity injection in a series of experiments called PCS (Plasma Compression, Small). We simulate the PCS experiments using the finite-volume MHD code VAC. The single-fluid plasma model includes temperature-dependent resistivity and anisotropic heat transport. The time-dependent curvilinear mesh for MHD simulation is derived from LS-DYNA simulations of actual field tests of liner implosion. We will discuss how 3D simulations reproduced instability observed in the PCS13 experiment and correctly predicted stabilization of PCS14 by ramping the shaft current during compression. We will also present a comparison of simulated Mirnov and x-ray diagnostics with experimental measurements indicating that PCS14 compressed well to a linear compression ratio of 2.5:1.

Damping Rate Measurements of Medium n Alfv'en Eigenmodes in JET

NASA Astrophysics Data System (ADS)

Klein, Alexander; Testa, Duccio; Snipes, Joseph; Fasoli, Ambrogio; Carfantan, Hervé

2007-11-01

Alfv'en Eigenmodes (AE's) with mode numbers 5 < n < 20 are expected to be unstable in burning tokamaks and may lead to loss of fast particle confinement. The active MHD spectroscopy program at JET has already provided a wealth of information about low n (n <= 2) AE's in the past decade, but a recently installed array of four antennas is capable of driving higher mode numbered (n < 100, 30 < f < 350 kHz) perturbations. In the latest JET campaign, the damping rates for several types of AE's were measured parasitically in a wide range of tokamak scenarios. We review the active MHD diagnostic and present the first measurements of medium-n AE stability on JET, then describe future plans for the active MHD spectroscopy project. The data analysis involves a novel method for resolving multiple AE's that exist at identical frequencies, which uses techniques based on the SparSpec code.

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.

3D Equilibrium Effects Due to RMP Application on DIII-D

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

S. Lazerson, E. Lazarus, S. Hudson, N. Pablant and D. Gates

2012-06-20

The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon [1]. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC [2] and SPEC [3] codes have been performed for an up-down symmetric shot (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nestedmore » family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.« less

3D Equilibrium Effects Due to RMP Application on DIII-D

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

Lazerson, S.; Lazarus, E.; Hudson, S.

2012-06-20

The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon. Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC and SPEC codes have been performed for an up-down symmetric shot in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfacesmore » is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete "ideal-interfaces" at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.« less

Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

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

Miller, D S

In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.

Calculation of Eddy Currents In the CTH Vacuum Vessel and Coil Frame

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

A. Zolfaghari, A. Brooks, A. Michaels, J. Hanson, and G. Hartwell

2012-09-25

Knowledge of eddy currents in the vacuum vessel walls and nearby conducting support structures can significantly contribute to the accuracy of Magnetohydrodynamics (MHD) equilibrium reconstruction in toroidal plasmas. Moreover, the magnetic fields produced by the eddy currents could generate error fields that may give rise to islands at rational surfaces or cause field lines to become chaotic. In the Compact Toroidal Hybrid (CTH) device (R0 = 0.75 m, a = 0.29 m, B ≤ 0.7 T), the primary driver of the eddy currents during the plasma discharge is the changing flux of the ohmic heating transformer. Electromagnetic simulations are usedmore » to calculate eddy current paths and profile in the vacuum vessel and in the coil frame pieces with known time dependent currents in the ohmic heating coils. MAXWELL and SPARK codes were used for the Electromagnetic modeling and simulation. MAXWELL code was used for detailed 3D finite-element analysis of the eddy currents in the structures. SPARK code was used to calculate the eddy currents in the structures as modeled with shell/surface elements, with each element representing a current loop. In both cases current filaments representing the eddy currents were prepared for input into VMEC code for MHD equilibrium reconstruction of the plasma discharge. __________________________________________________« less

Fully non-linear multi-species Fokker-Planck-Landau collisions for gyrokinetic particle-in-cell simulations of fusion plasma

NASA Astrophysics Data System (ADS)

Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.

2015-11-01

We describe the implementation, and application of a time-dependent, fully nonlinear multi-species Fokker-Planck-Landau collision operator based on the single-species work of Yoon and Chang [Phys. Plasmas 21, 032503 (2014)] in the full-function gyrokinetic particle-in-cell codes XGC1 [Ku et al., Nucl. Fusion 49, 115021 (2009)] and XGCa. XGC simulations include the pedestal and scrape-off layer, where significant deviations of the particle distribution function from a Maxwellian can occur. Thus, in order to describe collisional effects on neoclassical and turbulence physics accurately, the use of a non-linear collision operator is a necessity. Our collision operator is based on a finite volume method using the velocity-space distribution functions sampled from the marker particles. Since the same fine configuration space mesh is used for collisions and the Poisson solver, the workload due to collisions can be comparable to or larger than the workload due to particle motion. We demonstrate that computing time spent on collisions can be kept affordable by applying advanced parallelization strategies while conserving mass, momentum, and energy to reasonable accuracy. We also show results of production scale XGCa simulations in the H-mode pedestal and compare to conventional theory. Work supported by US DOE OFES and OASCR.

Collisional Ion and Electron Scale Gyrokinetic Simulations in the Tokamak Pedestal

NASA Astrophysics Data System (ADS)

Belli, E. A.; Candy, J.; Snyder, P. B.

2016-10-01

A new gyrokinetic solver, CGYRO, has been developed for precise studies of high collisionality regimes, such as the H-mode pedestal and L-mode edge. Building on GYRO and NEO, CGYRO uses the same velocity-space coordinates as NEO to optimize the accuracy of the collision dynamics and allow for advanced operators beyond the standard Lorentz pitch-angle scattering model. These advanced operators include energy diffusion and finite-FLR collisional effects. The code is optimized for multiscale (coupled electron and ion turbulence scales) simulations, employing a new spatial discretization and array distribution scheme that targets scalability on next-generation (exascale) HPC systems. In this work, CGYRO is used to study the complex spectrum of modes in the pedestal region. The onset of the linear KBM with full collisional effects is assessed to develop an improved KBM/RBM model for EPED. The analysis is extended to high k to explore the role of electron-scale (ETG-range) physics. Comparisons with new analytic collisional theories are made. Inclusion of sonic toroidal rotation (including full centrifugal effects) for studies including heavy wall impurities is also reported. Work supported in part by the US DOE under DE-FC02-06ER54873 and DE-FC02-08ER54963.

Internal transport barriers in the National Spherical Torus Experimenta)

NASA Astrophysics Data System (ADS)

Yuh, H. Y.; Levinton, F. M.; Bell, R. E.; Hosea, J. C.; Kaye, S. M.; LeBlanc, B. P.; Mazzucato, E.; Peterson, J. L.; Smith, D. R.; Candy, J.; Waltz, R. E.; Domier, C. W.; Luhmann, N. C.; Lee, W.; Park, H. K.

2009-05-01

In the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)], internal transport barriers (ITBs) are observed in reversed (negative) shear discharges where diffusivities for electron and ion thermal channels and momentum are reduced. While neutral beam heating can produce ITBs in both electron and ion channels, high harmonic fast wave heating can also produce electron ITBs (e-ITBs) under reversed magnetic shear conditions without momentum input. Interestingly, the location of the e-ITB does not necessarily match that of the ion ITB (i-ITB). The e-ITB location correlates best with the magnetic shear minima location determined by motional Stark effect constrained equilibria, whereas the i-ITB location better correlates with the location of maximum E ×B shearing rate. Measured electron temperature gradients in the e-ITB can exceed critical gradients for the onset of electron thermal gradient microinstabilities calculated by linear gyrokinetic codes. A high-k microwave scattering diagnostic shows locally reduced density fluctuations at wave numbers characteristic of electron turbulence for discharges with strongly negative magnetic shear versus weakly negative or positive magnetic shear. Reductions in fluctuation amplitude are found to be correlated with the local value of magnetic shear. These results are consistent with nonlinear gyrokinetic simulations predicting a reduction in electron turbulence under negative magnetic shear conditions despite exceeding critical gradients.

Non-linear gyrokinetic simulations of microturbulence in TCV electron internal transport barriers

NASA Astrophysics Data System (ADS)

Lapillonne, X.; Brunner, S.; Sauter, O.; Villard, L.; Fable, E.; Görler, T.; Jenko, F.; Merz, F.

2011-05-01

Using the local (flux-tube) version of the Eulerian code GENE (Jenko et al 2000 Phys. Plasmas 7 1904), gyrokinetic simulations of microturbulence were carried out considering parameters relevant to electron-internal transport barriers (e-ITBs) in the TCV tokamak (Sauter et al 2005 Phys. Rev. Lett. 94 105002), generated under conditions of low or negative shear. For typical density and temperature gradients measured in such barriers, the corresponding simulated fluctuation spectra appears to simultaneously contain longer wavelength trapped electron modes (TEMs, for typically k⊥ρi < 0.5, k⊥ being the characteristic perpendicular wavenumber and ρi the ion Larmor radius) and shorter wavelength ion temperature gradient modes (ITG, k⊥ρi > 0.5). The contributions to the electron particle flux from these two types of modes are, respectively, outward/inward and may cancel each other for experimentally realistic gradients. This mechanism may partly explain the feasibility of e-ITBs. The non-linear simulation results confirm the predictions of a previously developed quasi-linear model (Fable et al 2010 Plasma Phys. Control. Fusion 52 015007), namely that the stationary condition of zero particle flux is obtained through the competitive contributions of ITG and TEM. A quantitative comparison of the electron heat flux with experimental estimates is presented as well.

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

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

Bass, Eric M.; Waltz, R. E.

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

DOE PAGES

Bass, Eric M.; Waltz, R. E.

2017-12-08

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Dynamics of kinetic geodesic-acoustic modes and the radial electric field in tokamak neoclassical plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Belli, E.; Bodi, K.; Candy, J.; Chang, C. S.; Cohen, R. H.; Colella, P.; Dimits, A. M.; Dorr, M. R.; Gao, Z.; Hittinger, J. A.; Ko, S.; Krasheninnikov, S.; McKee, G. R.; Nevins, W. M.; Rognlien, T. D.; Snyder, P. B.; Suh, J.; Umansky, M. V.

2009-06-01

We present edge gyrokinetic simulations of tokamak plasmas using the fully non-linear (full-f) continuum code TEMPEST. A non-linear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson equation. We demonstrate the following. (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high q (tokamak safety factor), and are necessary to explain the damping observed in our TEMPEST q-scans and consistent with the experimental measurements of the scaling of the GAM amplitude with edge q95 in the absence of obvious evidence that there is a strong q-dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and parallel flow characteristics qualitatively like those observed in experiments.

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.

Numerical analysis on the cutting and finishing efficiency of MRAFF process

NASA Astrophysics Data System (ADS)

Lih, F. L.

2016-03-01

The aim of the present research is to conduct a numerical study of the characteristic of a two-phase magnetorheological fluid with different operation conditions by the finite volume method called SIMPLE with an add-on MHD code.

Extended MHD Effects in High Energy Density Experiments

NASA Astrophysics Data System (ADS)

Seyler, Charles

2016-10-01

The MHD model is the workhorse for computational modeling of HEDP experiments. Plasma models are inheritably limited in scope, but MHD is expected to be a very good model for studying plasmas at the high densities attained in HEDP experiments. There are, however, important ways in which MHD fails to adequately describe the results, most notably due to the omission of the Hall term in the Ohm's law (a form of extended MHD or XMHD). This talk will discuss these failings by directly comparing simulations of MHD and XMHD for particularly relevant cases. The methodology is to simulate HEDP experiments using a Hall-MHD (HMHD) code based on a highly accurate and robust Discontinuous Galerkin method, and by comparison of HMHD to MHD draw conclusions about the impact of the Hall term. We focus on simulating two experimental pulsed power machines under various scenarios. We examine the MagLIF experiment on the Z-machine at Sandia National Laboratories and liner experiments on the COBRA machine at Cornell. For the MagLIF experiment we find that power flow in the feed leads to low density plasma ablation into the region surrounding the liner. The inflow of this plasma compresses axial magnetic flux onto the liner. In MHD this axial flux tends to resistively decay, whereas in HMHD a force-free current layer sustains the axial flux on the liner leading to a larger ratio of axial to azimuthal flux. During the liner compression the magneto-Rayleigh-Taylor instability leads to helical perturbations due to minimization of field line bending. Simulations of a cylindrical liner using the COBRA machine parameters can under certain conditions exhibit amplification of an axial field due to a force-free low-density current layer separated by some distance from the liner. This results in a configuration in which there is predominately axial field on the liner inside the current layer and azimuthal field outside the layer. We are currently attempting to experimentally verify the simulation results. Collaborator: Nathaniel D. Hamlin, School of Electrical and Computer Engineering, Cornell University, Ithaca, New York.

CISM: Modeling the Sun-Earth Connection

NASA Astrophysics Data System (ADS)

Hughes, W. J.; Team, T. C.

2003-12-01

The Center for Integrated SpaceWeather Modeling (CISM), an NSF Science and Technology Center that is a consortium of ten institutions headed by Boston University, has as its primary goal the development of a series of ever improving versions of a comprehensive physics-based simulation model that describes the space environment from the Sun to the Earth. CISM will do this by coupling existing models of components of the system. In this paper we review our progress to date and summarize our plans. We discuss results of initial coupling of MHD models of the corona and solar wind, and of a global magnetospheric MHD model with a global ionosphere/thermosphere model, a radiation belt model, and a ring current particle model. Coupling the SAIC coronal MHD model and the U Colorado/SEC solar wind MHD codes allows us to track CMEs from the base of the corona to 1 AU. The results show how shocks form and develop in the heliosphere, and how the CME flattens into a pancake shape by the time it reaches earth. Coupling the Lyon/Fedder/Mobarry global MHD model with the Rice Convection Model and the NCAR TIE-GCM/TING model allows full dynamic coupling between the magnetosphere, the ionosphere/thermosphere, and the hot plasma in the inner magnetosphere. Including the Dartmouth radiation belt model shows how the radiation belts evolve in a realistic magnetosphere.

An Iterative Interplanetary Scintillation (IPS) Analysis Using Time-dependent 3-D MHD Models as Kernels

NASA Astrophysics Data System (ADS)

Jackson, B. V.; Yu, H. S.; Hick, P. P.; Buffington, A.; Odstrcil, D.; Kim, T. K.; Pogorelov, N. V.; Tokumaru, M.; Bisi, M. M.; Kim, J.; Yun, J.

2017-12-01

The University of California, San Diego has developed an iterative remote-sensing time-dependent three-dimensional (3-D) reconstruction technique which provides volumetric maps of density, velocity, and magnetic field. We have applied this technique in near real time for over 15 years with a kinematic model approximation to fit data from ground-based interplanetary scintillation (IPS) observations. Our modeling concept extends volumetric data from an inner boundary placed above the Alfvén surface out to the inner heliosphere. We now use this technique to drive 3-D MHD models at their inner boundary and generate output 3-D data files that are fit to remotely-sensed observations (in this case IPS observations), and iterated. These analyses are also iteratively fit to in-situ spacecraft measurements near Earth. To facilitate this process, we have developed a traceback from input 3-D MHD volumes to yield an updated boundary in density, temperature, and velocity, which also includes magnetic-field components. Here we will show examples of this analysis using the ENLIL 3D-MHD and the University of Alabama Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) heliospheric codes. These examples help refine poorly-known 3-D MHD variables (i.e., density, temperature), and parameters (gamma) by fitting heliospheric remotely-sensed data between the region near the solar surface and in-situ measurements near Earth.

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.

Transport Barriers in Bootstrap Driven Tokamaks

NASA Astrophysics Data System (ADS)

Staebler, Gary

2017-10-01

Maximizing the bootstrap current in a tokamak, so that it drives a high fraction of the total current, reduces the external power required to drive current by other means. Improved energy confinement, relative to empirical scaling laws, enables a reactor to more fully take advantage of the bootstrap driven tokamak. Experiments have demonstrated improved energy confinement due to the spontaneous formation of an internal transport barrier in high bootstrap fraction discharges. Gyrokinetic analysis, and quasilinear predictive modeling, demonstrates that the observed transport barrier is due to the suppression of turbulence primarily due to the large Shafranov shift. ExB velocity shear does not play a significant role in the transport barrier due to the high safety factor. It will be shown, that the Shafranov shift can produce a bifurcation to improved confinement in regions of positive magnetic shear or a continuous reduction in transport for weak or negative magnetic shear. Operation at high safety factor lowers the pressure gradient threshold for the Shafranov shift driven barrier formation. The ion energy transport is reduced to neoclassical and electron energy and particle transport is reduced, but still turbulent, within the barrier. Deeper into the plasma, very large levels of electron transport are observed. The observed electron temperature profile is shown to be close to the threshold for the electron temperature gradient (ETG) mode. A large ETG driven energy transport is qualitatively consistent with recent multi-scale gyrokinetic simulations showing that reducing the ion scale turbulence can lead to large increase in the electron scale transport. A new saturation model for the quasilinear TGLF transport code, that fits these multi-scale gyrokinetic simulations, can match the data if the impact of zonal flow mixing on the ETG modes is reduced at high safety factor. This work was supported by the U.S. Department of Energy under DE-FG02-95ER54309 and DE-FC02-04ER54698.

Gyrokinetic simulations with external resonant magnetic perturbations: Island torque and nonambipolar transport with plasma rotation

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Waelbroeck, F. L.

2012-03-01

Static external resonant magnetic field perturbations (RMPs) have been added to the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)]. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding j→×B→ plasma torque (density) R[jrBp/c], induced by magnetic islands that break the toroidal symmetry of a tokamak. This extends the previous GYRO formulation for the transport of toroidal angular momentum (TAM) [R. E. Waltz, G. M. Staebler, J. Candy, and F. L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)]. The focus is on electrostatic full torus radial slice simulations of externally induced q =m/n=6/3 islands with widths 5% of the minor radius or about 20 ion gyroradii. Up to moderately strong E ×B rotation, the island torque scales with the radial electric field at the resonant surface Er, the island width w, and the intensity I of the high-n micro-turbulence, as Erw√I . The radial current inside the island is carried (entirely in the n =3 component) and almost entirely by the ion E ×B flux, since the electron E ×B and magnetic flutter particle fluxes are cancelled. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that while the expected magnetic braking of the toroidal plasma rotation occurs at strong co- and counter-current rotation, at null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic (ion pressure gradient driven) co-rotation corresponding to the zero Er and null torque. This could be called the residual stress from an externally induced island. At zero Er, the only effect is the expected partial flattening of the electron temperature gradient within the island. Finite-beta GYRO simulations demonstrate almost complete RMP field screening and n =3 mode unlocking at strong Er.

Alternative modeling methods for plasma-based Rf ion sources

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

Veitzer, Seth A., E-mail: veitzer@txcorp.com; Kundrapu, Madhusudhan, E-mail: madhusnk@txcorp.com; Stoltz, Peter H., E-mail: phstoltz@txcorp.com

Rf-driven ion sources for accelerators and many industrial applications benefit from detailed numerical modeling and simulation of plasma characteristics. For instance, modeling of the Spallation Neutron Source (SNS) internal antenna H{sup −} source has indicated that a large plasma velocity is induced near bends in the antenna where structural failures are often observed. This could lead to improved designs and ion source performance based on simulation and modeling. However, there are significant separations of time and spatial scales inherent to Rf-driven plasma ion sources, which makes it difficult to model ion sources with explicit, kinetic Particle-In-Cell (PIC) simulation codes. Inmore » particular, if both electron and ion motions are to be explicitly modeled, then the simulation time step must be very small, and total simulation times must be large enough to capture the evolution of the plasma ions, as well as extending over many Rf periods. Additional physics processes such as plasma chemistry and surface effects such as secondary electron emission increase the computational requirements in such a way that even fully parallel explicit PIC models cannot be used. One alternative method is to develop fluid-based codes coupled with electromagnetics in order to model ion sources. Time-domain fluid models can simulate plasma evolution, plasma chemistry, and surface physics models with reasonable computational resources by not explicitly resolving electron motions, which thereby leads to an increase in the time step. This is achieved by solving fluid motions coupled with electromagnetics using reduced-physics models, such as single-temperature magnetohydrodynamics (MHD), extended, gas dynamic, and Hall MHD, and two-fluid MHD models. We show recent results on modeling the internal antenna H{sup −} ion source for the SNS at Oak Ridge National Laboratory using the fluid plasma modeling code USim. We compare demonstrate plasma temperature equilibration in two-temperature MHD models for the SNS source and present simulation results demonstrating plasma evolution over many Rf periods for different plasma temperatures. We perform the calculations in parallel, on unstructured meshes, using finite-volume solvers in order to obtain results in reasonable time.« less

Alternative modeling methods for plasma-based Rf ion sources.

PubMed

Veitzer, Seth A; Kundrapu, Madhusudhan; Stoltz, Peter H; Beckwith, Kristian R C

2016-02-01

Rf-driven ion sources for accelerators and many industrial applications benefit from detailed numerical modeling and simulation of plasma characteristics. For instance, modeling of the Spallation Neutron Source (SNS) internal antenna H(-) source has indicated that a large plasma velocity is induced near bends in the antenna where structural failures are often observed. This could lead to improved designs and ion source performance based on simulation and modeling. However, there are significant separations of time and spatial scales inherent to Rf-driven plasma ion sources, which makes it difficult to model ion sources with explicit, kinetic Particle-In-Cell (PIC) simulation codes. In particular, if both electron and ion motions are to be explicitly modeled, then the simulation time step must be very small, and total simulation times must be large enough to capture the evolution of the plasma ions, as well as extending over many Rf periods. Additional physics processes such as plasma chemistry and surface effects such as secondary electron emission increase the computational requirements in such a way that even fully parallel explicit PIC models cannot be used. One alternative method is to develop fluid-based codes coupled with electromagnetics in order to model ion sources. Time-domain fluid models can simulate plasma evolution, plasma chemistry, and surface physics models with reasonable computational resources by not explicitly resolving electron motions, which thereby leads to an increase in the time step. This is achieved by solving fluid motions coupled with electromagnetics using reduced-physics models, such as single-temperature magnetohydrodynamics (MHD), extended, gas dynamic, and Hall MHD, and two-fluid MHD models. We show recent results on modeling the internal antenna H(-) ion source for the SNS at Oak Ridge National Laboratory using the fluid plasma modeling code USim. We compare demonstrate plasma temperature equilibration in two-temperature MHD models for the SNS source and present simulation results demonstrating plasma evolution over many Rf periods for different plasma temperatures. We perform the calculations in parallel, on unstructured meshes, using finite-volume solvers in order to obtain results in reasonable time.

Minerva: Cylindrical coordinate extension for Athena

NASA Astrophysics Data System (ADS)

Skinner, M. Aaron; Ostriker, Eve C.

2013-02-01

Minerva is a cylindrical coordinate extension of the Athena astrophysical MHD code of Stone, Gardiner, Teuben, and Hawley. The extension follows the approach of Athena's original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport (CT), a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully.

Proceedings of the STRESS Data Review Meeting, 29-30 November 1977

DTIC Science & Technology

1978-06-01

INSULATORS MAGNETOMETER BEACON ANTENNA fe?^ S-BAND ANTENNA- -DC PROBE SENSING ELEMENT PLASMA FREQUENCY PROBE MONOPOLE -GUARD ELECTRODE PLASMA...have demonstrated, using calculational results from MICE and MRHYDE (MHD computer codes), that the gradient-drift instability is the one primarily

Continuum kinetic modeling of the tokamak plasma edge

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

Dorf, M. A.; Dorr, M. R.; Hittinger, J. A.

2016-05-15

The first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasma transport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalous radial transport.

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

Ku, S.; Chang, C. S.; Hager, R.

Here, a fast edge turbulence suppression event has been simulated in the electrostatic version of the gyrokinetic particle-in-cell code XGC1 in a realistic diverted tokamak edge geometry under neutral particle recycling. The results show that the sequence of turbulent Reynolds stress followed by neoclassical ion orbit-loss driven together conspire to form the sustaining radial electric field shear and to quench turbulent transport just inside the last closed magnetic flux surface. As a result, the main suppression action is located in a thin radial layer around ψ N≃0.96–0.98, where ψ N is the normalized poloidal flux, with the time scale ~0.1more » ms.« less

Effects of magnetic islands on drift wave instability

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

Jiang, P., E-mail: jiangp@pku.edu.cn; Department of Physics and Astronomy, University of California, Irvine, California 92697; Lin, Z., E-mail: zhihongl@uci.edu

2014-12-15

Magnetic islands have been implemented in the gyrokinetic toroidal code to study the effects of the islands on microturbulence. The pressure profile flattening is verified in the simulation with the islands. Simulations of ion temperature gradient instability find that different toroidal modes are linearly coupled together and that toroidal spectra become broader when the island width increases. The real frequencies and growth rates of different toroidal modes approach each other with the averaged value independent of the island width. The linear mode structures are enhanced at the island separatrices and weakened at the island centers, consistent with the flattening ofmore » the pressure profile inside the islands.« less

TEMPEST Simulations of Collisionless Damping of Geodesic-Acoustic Mode in Edge Plasma Pedestal

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

Xu, X Q; Xiong, Z; Nevins, W M

The fully nonlinear (full-f) 4D TEMPEST gyrokinetic continuum code produces frequency, collisionless damping of GAM and zonal flow with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon}-scan and the tokamak safety factor q-scan in homogeneous plasmas. The TEMPEST simulation shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude.

TEMPEST Simulations of Collisionless Damping of Geodesic-Acoustic Mode in Edge Plasma Pedestal

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

Xu, X; Xiong, Z; Nevins, W

The fully nonlinear 4D TEMPEST gyrokinetic continuum code produces frequency, collisionless damping of geodesic-acoustic mode (GAM) and zonal flow with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon}-scan and the tokamak safety factor q-scan in homogeneous plasmas. The TEMPEST simulation shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude.

A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem

NASA Astrophysics Data System (ADS)

Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.

2009-04-01

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.

Non-ideal magnetohydrodynamics on a moving mesh

NASA Astrophysics Data System (ADS)

Marinacci, Federico; Vogelsberger, Mark; Kannan, Rahul; Mocz, Philip; Pakmor, Rüdiger; Springel, Volker

2018-05-01

In certain astrophysical systems, the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

NASA Astrophysics Data System (ADS)

Banerjee, Debabrata; Zhu, Ping; Maingi, Rajesh

2017-07-01

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. The purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Z eff after Li-conditioning in ELM-free H-mode. Unlike an earlier conclusion from an eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Z eff, the complete stabilization could be explained. A thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.

Kinetic-MHD simulations of gyroresonance instability driven by CR pressure anisotropy

NASA Astrophysics Data System (ADS)

Lebiga, O.; Santos-Lima, R.; Yan, H.

2018-05-01

The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs (≲100 GeV) in the interstellar and intracluster medium of galaxies has been shown in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this, we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient Dμμ produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasi-linear theory (QLT). Our results support the applicability of the QLT for modelling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.

Modeling of 3D magnetic equilibrium effects on edge turbulence stability during RMP ELM suppression in tokamaks

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

Wilcox, R. S.; Wingen, Andreas; Cianciosa, Mark R.

Some recent experimental observations have found turbulent fluctuation structures that are non-axisymmetric in a tokamak with applied 3D fields. Here, two fluid resistive effects are shown to produce changes relevant to turbulent transport in the modeled 3D magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied. Ideal MHD models are insufficient to reproduce the relevant effects. By calculating the ideal 3D equilibrium using the VMEC code, the geometric shaping parameters that determine linear turbulence stability, including the normal curvature and local magnetic shear, are shown to be only weakly modified by applied 3D fields in the DIII-D tokamak.more » These ideal MHD effects are therefore not sufficient to explain the observed changes to fluctuations and transport. Using the M3D-C1 code to model the 3D equilibrium, density is shown to be redistributed on flux surfaces in the pedestal when resistive two fluid effects are included, while islands are screened by rotation in this region. Furthermore, the redistribution of density results in density and pressure gradient scale lengths that vary within pedestal flux surfaces between different helically localized flux tubes. This would produce different drive terms for trapped electron mode and kinetic ballooning mode turbulence, the latter of which is expected to be the limiting factor for pedestal pressure gradients in DIII-D.« less

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.

Modeling of 3D magnetic equilibrium effects on edge turbulence stability during RMP ELM suppression in tokamaks

DOE PAGES

Wilcox, R. S.; Wingen, Andreas; Cianciosa, Mark R.; ...

2017-07-28

Some recent experimental observations have found turbulent fluctuation structures that are non-axisymmetric in a tokamak with applied 3D fields. Here, two fluid resistive effects are shown to produce changes relevant to turbulent transport in the modeled 3D magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied. Ideal MHD models are insufficient to reproduce the relevant effects. By calculating the ideal 3D equilibrium using the VMEC code, the geometric shaping parameters that determine linear turbulence stability, including the normal curvature and local magnetic shear, are shown to be only weakly modified by applied 3D fields in the DIII-D tokamak.more » These ideal MHD effects are therefore not sufficient to explain the observed changes to fluctuations and transport. Using the M3D-C1 code to model the 3D equilibrium, density is shown to be redistributed on flux surfaces in the pedestal when resistive two fluid effects are included, while islands are screened by rotation in this region. Furthermore, the redistribution of density results in density and pressure gradient scale lengths that vary within pedestal flux surfaces between different helically localized flux tubes. This would produce different drive terms for trapped electron mode and kinetic ballooning mode turbulence, the latter of which is expected to be the limiting factor for pedestal pressure gradients in DIII-D.« less

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)

H.E. Mynick, N. Pomphrey and P. Xanthopoulos

Recent progress in reducing turbulent transport in stellarators and tokamaks by 3D shaping using a stellarator optimization code in conjunction with a gyrokinetic code is presented. The original applications of the method focussed on ion temperature gradient transport in a quasi-axisymmetric stellarator design. Here, an examination of both other turbulence channels and other starting configurations is initiated. It is found that the designs evolved for transport from ion temperature gradient turbulence also display reduced transport from other transport channels whose modes are also stabilized by improved curvature, such as electron temperature gradient and ballooning modes. The optimizer is also appliedmore » to evolving from a tokamak, finding appreciable turbulence reduction for these devices as well. From these studies, improved understanding is obtained of why the deformations found by the optimizer are beneficial, and these deformations are related to earlier theoretical work in both stellarators and tokamaks.« less

Global simulation of edge pedestal micro-instabilities

NASA Astrophysics Data System (ADS)

Wan, Weigang; Parker, Scott; Chen, Yang

2011-10-01

We study micro turbulence of the tokamak edge pedestal with global gyrokinetic particle simulations. The simulation code GEM is an electromagnetic δf code. Two sets of DIII-D experimental profiles, shot #131997 and shot #136051 are used. The dominant instabilities appear to be two kinds of modes both propagating in the electron diamagnetic direction, with comparable linear growth rates. The low n mode is at the Alfven frequency range and driven by density and ion temperature gradients. The high n mode is driven by electron temperature gradient and has a low real frequency. A β scan shows that the low n mode is electromagnetic. Frequency analysis shows that the high n mode is sometimes mixed with an ion instability. Experimental radial electric field is applied and its effects studied. We will also show some preliminary nonlinear results. We thank R. Groebner, P. Snyder and Y. Zheng for providing experimental profiles and helpful discussions.

Nonlinear 3D MHD verification study: SpeCyl and PIXIE3D codes for RFP and Tokamak plasmas

NASA Astrophysics Data System (ADS)

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

2010-11-01

A strong emphasis is presently placed in the fusion community on reaching predictive capability of computational models. An essential requirement of such endeavor is the process of assessing the mathematical correctness of computational tools, termed verification [1]. We present here a successful nonlinear cross-benchmark verification study between the 3D nonlinear MHD codes SpeCyl [2] and PIXIE3D [3]. Excellent quantitative agreement is obtained in both 2D and 3D nonlinear visco-resistive dynamics for reversed-field pinch (RFP) and tokamak configurations [4]. RFP dynamics, in particular, lends itself as an ideal non trivial test-bed for 3D nonlinear verification. Perspectives for future application of the fully-implicit parallel code PIXIE3D to RFP physics, in particular to address open issues on RFP helical self-organization, will be provided. [4pt] [1] M. Greenwald, Phys. Plasmas 17, 058101 (2010) [0pt] [2] S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996) [0pt] [3] L. Chac'on, Phys. Plasmas 15, 056103 (2008) [0pt] [4] D. Bonfiglio, L. Chac'on and S. Cappello, Phys. Plasmas 17 (2010)

Inclusion of pressure and flow in a new 3D MHD equilibrium code

NASA Astrophysics Data System (ADS)

Raburn, Daniel; Fukuyama, Atsushi

2012-10-01

Flow and nonsymmetric effects can play a large role in plasma equilibria and energy confinement. A concept for such a 3D equilibrium code was developed and presented in 2011. The code is called the Kyoto ITerative Equilibrium Solver (KITES) [1], and the concept is based largely on the PIES code [2]. More recently, the work-in-progress KITES code was used to calculate force-free equilibria. Here, progress and results on the inclusion of pressure and flow in the code are presented. [4pt] [1] Daniel Raburn and Atsushi Fukuyama, Plasma and Fusion Research: Regular Articles, 7:240381 (2012).[0pt] [2] H. S. Greenside, A. H. Reiman, and A. Salas, J. Comput. Phys, 81(1):102-136 (1989).

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.

Experiments and numerical modeling of fast flowing liquid metal thin films under spatially varying magnetic field conditions

NASA Astrophysics Data System (ADS)

Narula, Manmeet Singh

Innovative concepts using fast flowing thin films of liquid metals (like lithium) have been proposed for the protection of the divertor surface in magnetic fusion devices. However, concerns exist about the possibility of establishing the required flow of liquid metal thin films because of the presence of strong magnetic fields which can cause flow disrupting MHD effects. A plan is underway to design liquid lithium based divertor protection concepts for NSTX, a small spherical torus experiment at Princeton. Of these, a promising concept is the use of modularized fast flowing liquid lithium film zones, as the divertor (called the NSTX liquid surface module concept or NSTX LSM). The dynamic response of the liquid metal film flow in a spatially varying magnetic field configuration is still unknown and it is suspected that some unpredicted effects might be lurking. The primary goal of the research work being reported in this dissertation is to provide qualitative and quantitative information on the liquid metal film flow dynamics under spatially varying magnetic field conditions, typical of the divertor region of a magnetic fusion device. The liquid metal film flow dynamics have been studied through a synergic experimental and numerical modeling effort. The Magneto Thermofluid Omnibus Research (MTOR) facility at UCLA has been used to design several experiments to study the MHD interaction of liquid gallium films under a scaled NSTX outboard divertor magnetic field environment. A 3D multi-material, free surface MHD modeling capability is under development in collaboration with HyPerComp Inc., an SBIR vendor. This numerical code called HIMAG provides a unique capability to model the equations of incompressible MHD with a free surface. Some parts of this modeling capability have been developed in this research work, in the form of subroutines for HIMAG. Extensive code debugging and benchmarking exercise has also been carried out. Finally, HIMAG has been used to study the MHD interaction of fast flowing liquid metal films under various divertor relevant magnetic field configurations through numerical modeling exercises.

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.

An MHD Code for the Study of Magnetic Structures in the Solar Wind

NASA Technical Reports Server (NTRS)

Allred, J. C.; MacNeice, P. J.

2015-01-01

We have developed a 2.5D MHD code designed to study how the solar wind influences the evolution of transient events in the solar corona and inner heliosphere. The code includes thermal conduction, coronal heating and radiative cooling. Thermal conduction is assumed to be magnetic field-aligned in the inner corona and transitions to a collisionless formulation in the outer corona. We have developed a stable method to handle field-aligned conduction around magnetic null points. The inner boundary is placed in the upper transition region, and the mass flux across the boundary is determined from 1D field-aligned characteristics and a 'radiative energy balance' condition. The 2.5D nature of this code makes it ideal for parameter studies not yet possible with 3D codes. We have made this code publicly available as a tool for the community. To this end we have developed a graphical interface to aid in the selection of appropriate options and a graphical interface that can process and visualize the data produced by the simulation. As an example, we show a simulation of a dipole field stretched into a helmet streamer by the solar wind. Plasmoids periodically erupt from the streamer, and we perform a parameter study of how the frequency and location of these eruptions changed in response to different levels of coronal heating. As a further example, we show the solar wind stretching a compact multi-polar flux system. This flux system will be used to study breakout coronal mass ejections in the presence of the solar wind.

Development of the PARVMEC Code for Rapid Analysis of 3D MHD Equilibrium

NASA Astrophysics Data System (ADS)

Seal, Sudip; Hirshman, Steven; Cianciosa, Mark; Wingen, Andreas; Unterberg, Ezekiel; Wilcox, Robert; ORNL Collaboration

2015-11-01

The VMEC three-dimensional (3D) MHD equilibrium has been used extensively for designing stellarator experiments and analyzing experimental data in such strongly 3D systems. Recent applications of VMEC include 2D systems such as tokamaks (in particular, the D3D experiment), where application of very small (delB/B ~ 10-3) 3D resonant magnetic field perturbations render the underlying assumption of axisymmetry invalid. In order to facilitate the rapid analysis of such equilibria (for example, for reconstruction purposes), we have undertaken the task of parallelizing the VMEC code (PARVMEC) to produce a scalable and temporally rapidly convergent equilibrium code for use on parallel distributed memory platforms. The parallelization task naturally splits into three distinct parts 1) radial surfaces in the fixed-boundary part of the calculation; 2) two 2D angular meshes needed to compute the Green's function integrals over the plasma boundary for the free-boundary part of the code; and 3) block tridiagonal matrix needed to compute the full (3D) pre-conditioner near the final equilibrium state. Preliminary results show that scalability is achieved for tasks 1 and 3, with task 2 still nearing completion. The impact of this work on the rapid reconstruction of D3D plasmas using PARVMEC in the V3FIT code will be discussed. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

A unified radiative magnetohydrodynamics code for lightning-like discharge simulations

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

Chen, Qiang, E-mail: cq0405@126.com; Chen, Bin, E-mail: emcchen@163.com; Xiong, Run

2014-03-15

A two-dimensional Eulerian finite difference code is developed for solving the non-ideal magnetohydrodynamic (MHD) equations including the effects of self-consistent magnetic field, thermal conduction, resistivity, gravity, and radiation transfer, which when combined with specified pulse current models and plasma equations of state, can be used as a unified lightning return stroke solver. The differential equations are written in the covariant form in the cylindrical geometry and kept in the conservative form which enables some high-accuracy shock capturing schemes to be equipped in the lightning channel configuration naturally. In this code, the 5-order weighted essentially non-oscillatory scheme combined with Lax-Friedrichs fluxmore » splitting method is introduced for computing the convection terms of the MHD equations. The 3-order total variation diminishing Runge-Kutta integral operator is also equipped to keep the time-space accuracy of consistency. The numerical algorithms for non-ideal terms, e.g., artificial viscosity, resistivity, and thermal conduction, are introduced in the code via operator splitting method. This code assumes the radiation is in local thermodynamic equilibrium with plasma components and the flux limited diffusion algorithm with grey opacities is implemented for computing the radiation transfer. The transport coefficients and equation of state in this code are obtained from detailed particle population distribution calculation, which makes the numerical model is self-consistent. This code is systematically validated via the Sedov blast solutions and then used for lightning return stroke simulations with the peak current being 20 kA, 30 kA, and 40 kA, respectively. The results show that this numerical model consistent with observations and previous numerical results. The population distribution evolution and energy conservation problems are also discussed.« less

Gyrokinetic statistical absolute equilibrium and turbulence

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

Zhu Jianzhou; Hammett, Gregory W.

2010-12-15

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperaturemore » states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less

Gyrokinetics with Advanced Collision Operators

NASA Astrophysics Data System (ADS)

Belli, E. A.; Candy, J.

2014-10-01

For gyrokinetic studies in the pedestal region, collisions are expected to play a more critical role than in the core and there is concern that more advanced collision operators, as well as numerical methods optimized for the strong collisionality regime, are needed. For this purpose, a new gyrokinetic solver CGYRO has been developed for precise studies of high collisionality regimes. Building on GYRO and NEO, CGYRO uses the NEO pitch angle and energy velocity-space coordinate system to optimize the accuracy of the collision dynamics, particularly for multi-species collisions and including energy diffusion. With implementation of the reduced Hirshman-Sigmar collision operator with full cross-species coupling, CGYRO recovers linear ITG growth rates and the collisional GAM test at moderate collision frequency. Methods to improve the behavior in the collisionless regime, particularly for the trapped/passing particle boundary physics for kinetic electrons, are studied. Extensions to advanced model operators with finite-k⊥ corrections, e.g., the Sugama operator, and the impact of high collisionality on linear gyrokinetic stability in the edge are explored. Work supported by the US DOE under DE-FG02-95ER54309.

Numerical simulation of surface wave dynamics of liquid metal MHD flow on an inclined plane in a magnetic field with spatial variation

NASA Astrophysics Data System (ADS)

Gao, Donghong

Interest in utilizing liquid metal film flows to protect the plasma-facing solid structures places increasing demand on understanding the magnetohydrodynamics (MHD) of such flows in a magnetic field with spatial variation. The field gradient effect is studied by a two-dimensional (2D) model in Cartesian coordinates. The thin film flow down an inclined plane in spanwise (z-direction) magnetic field with constant streamwise gradient and applied current is analyzed. The solution to the equilibrium flow shows forcefully the M-shaped velocity profile and dependence of side layer thickness on Ha-1/2 whose definition is based on field gradient. The major part of the dissertation is the numerical simulation of free surface film flows and understanding the results. The VOF method is employed to track the free surface, and the CSF model is combined with VOF method to account for surface dynamics condition. The code is validated with respect to Navier-Stokes solver and MHD implementation by computations of ordinary wavy films, MHD flat films and a colleague proposed film flow. The comparisons are performed against respective experimental, theoretical or numerical solutions, and the results are well matched with them. It is found for the ordinary water falling films, at low frequency and high flowrate, the small forcing disturbance at inlet flowrate develops into big roll waves preceded by small capillary bow waves; at high frequency and low Re, it develops into nearly sinusoidal waves with small amplitude and without fore-running capillary waves. The MHD surface instability is investigated for two kinds of film flows in constant streamwise field gradient: one with spatial disturbance and without surface tension, the other with inlet forcing disturbance and with surface tension. At no surface tension condition, the finite amplitude disturbance is rapidly amplified and degrades to irregular shape. With surface tension to maintain smooth interface, finite amplitude regular waves can be established only on near inlet region and they decay to nearly zero amplitude ripple on the far downstream region. At both film conditions, the wave traveling velocity is reduced by the MHD drag from field gradient. The code is also used to explore the exit-pipe and first wall conceptual designs for fusion reactor being proposed in the APEX program. It is seen that the field gradient restrains and lifts up the flow to the whole channel in the exit-pipe high field gradient condition, but an applied streamwise current can propel the flow through the gradient region. The Sn jet flow with high inertia is able to overcome the inverted gravity and MHD induction to form the desired protection liquid layer on top of the first wall.

Center for the Study of Plasma Microturbulence

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

Parker, Scott E.

We have discovered a possible "natural fueling" mechanism in tokamak fusion reactors using large scale gyrokinetic turbulence simulation. In the presence of a heat flux dominated tokamak plasma, cold ions naturally pinch radially inward. If cold DT fuel is introduced near the edge using shallow pellet injection, the cold fuel will pinch inward, at the expense of hot helium ash going radially outward. By adjusting the cold DT fuel concentration, the core DT density profiles can be maintained. We have also shown that cold source ions from edge recycling of cold neutrals are pinched radially inward. This mechanism may bemore » important for fully understanding the edge pedestal buildup after an ELM crash. Work includes benchmarking the gyrokinetic turbulence codes in the electromagnetic regime. This includes cyclone base case parameters with an increasing plasma beta. The code comparisons include GEM, GYRO and GENE. There is good linear agreement between the codes using the Cyclone base case, but including electromagnetics and scanning the plasma beta. All the codes have difficulty achieving nonlinear saturation as the kinetic ballooning limit is approached. GEM does not saturate well when beta gets above about 1/2 of the ideal ballooning limit. We find that the lack of saturation is due to the long wavelength k{sub y} modes being nonlinearly pumped to high levels. If the fundamental k{sub y} mode is zeroed out, higher values of beta nonlinearly saturate well. Additionally, there have been studies to better understand CTEM nonlinear saturation and the importance of zonal flows. We have continued our investigation of trapped electron mode (TEM) turbulence. More recently, we have focused on the nonlinear saturation of TEM turbulence. An important feature of TEM is that in many parameter regimes, the zonal flow is unimportant. We find that when zonal flows are unimportant, zonal density is the dominant saturation mechanism. We developed a simple theory that agrees with the simulation and predicts zonal density generation and feedback stabilization of the most unstable mode even in the absence of zonal flow. We are using GEM to simulate NSTX discharges. We have also done verification and validation on DIII-D. Good agreement with GYRO and DIII-D flux levels were reported in the core region.« less

Design Considerations of a Virtual Laboratory for Advanced X-ray Sources

NASA Astrophysics Data System (ADS)

Luginsland, J. W.; Frese, M. H.; Frese, S. D.; Watrous, J. J.; Heileman, G. L.

2004-11-01

The field of scientific computation has greatly advanced in the last few years, resulting in the ability to perform complex computer simulations that can predict the performance of real-world experiments in a number of fields of study. Among the forces driving this new computational capability is the advent of parallel algorithms, allowing calculations in three-dimensional space with realistic time scales. Electromagnetic radiation sources driven by high-voltage, high-current electron beams offer an area to further push the state-of-the-art in high fidelity, first-principles simulation tools. The physics of these x-ray sources combine kinetic plasma physics (electron beams) with dense fluid-like plasma physics (anode plasmas) and x-ray generation (bremsstrahlung). There are a number of mature techniques and software packages for dealing with the individual aspects of these sources, such as Particle-In-Cell (PIC), Magneto-Hydrodynamics (MHD), and radiation transport codes. The current effort is focused on developing an object-oriented software environment using the Rational© Unified Process and the Unified Modeling Language (UML) to provide a framework where multiple 3D parallel physics packages, such as a PIC code (ICEPIC), a MHD code (MACH), and a x-ray transport code (ITS) can co-exist in a system-of-systems approach to modeling advanced x-ray sources. Initial software design and assessments of the various physics algorithms' fidelity will be presented.

A Radiation Transfer Solver for Athena Using Short Characteristics

NASA Astrophysics Data System (ADS)

Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei

2012-03-01

We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.

Enhanced understanding of the MHD dynamics and ELM control experiments in KSTAR

NASA Astrophysics Data System (ADS)

Park, Hyeon K.

2013-10-01

In KSTAR, H-mode discharges have been achieved reliably at toroidal fields from 1.4 to 3.5 T with a heating power of ~ 5 MW. Using real-time plasma shape control the flattop time in H-mode has been extended to over ~ 16 s at 600 kA in the 2012 campaign and the extended plasma operation boundary has surpassed the n = 1 no-wall limit with βN /li up to 4.1. In order to achieve a high beta steady state operation in KSTAR, establishment of predictive MHD simulation and first-principle-based control of the harmful MHD are the first steps. Visualization of MHD dynamics via a 2-D Electron Cyclotron Emission Imaging (ECEI) has significantly enhanced the level of understanding of the MHD dynamics. Following the first 2-D ELM measurements in H-mode plasmas in KSTAR the measured 2-D ELM images were compared with synthetic images from the BOUT + + code. The physics of ELMs is characterized based on a wide range of measured mode numbers (n, m) local magnetic shear and pressure gradients. The observed ELM dynamics during control experiments have been enlightening and consistent with the stability models. Near the q ~ 2 surface, the island width and Δ' of the m = 2 tearing mode have been verified through the modified Rutherford model based on the 2-D images. With the aid of a second (toroidally separated) ECEI system installed in the 2012 KSTAR campaign, a 3-D reconstruction of the MHD instabilities has allowed further validation of the computed magnetic field pitch angles, rotation speeds, and toroidal asymmetries of the MHDs Work supported by NRF of Korea under contract No. 20120005920 and the U.S. DoE under contract No. DE-FG-02-99ER54531.

Numerical Simulation of Coronal Waves Interacting with Coronal Holes. III. Dependence on Initial Amplitude of the Incoming Wave

NASA Astrophysics Data System (ADS)

Piantschitsch, Isabell; Vršnak, Bojan; Hanslmeier, Arnold; Lemmerer, Birgit; Veronig, Astrid; Hernandez-Perez, Aaron; Čalogović, Jaša

2018-06-01

We performed 2.5D magnetohydrodynamic (MHD) simulations showing the propagation of fast-mode MHD waves of different initial amplitudes and their interaction with a coronal hole (CH), using our newly developed numerical code. We find that this interaction results in, first, the formation of reflected, traversing, and transmitted waves (collectively, secondary waves) and, second, in the appearance of stationary features at the CH boundary. Moreover, we observe a density depletion that is moving in the opposite direction of the incoming wave. We find a correlation between the initial amplitude of the incoming wave and the amplitudes of the secondary waves as well as the peak values of the stationary features. Additionally, we compare the phase speed of the secondary waves and the lifetime of the stationary features to observations. Both effects obtained in the simulation, the evolution of secondary waves, as well as the formation of stationary fronts at the CH boundary, strongly support the theory that coronal waves are fast-mode MHD waves.

Surface currents on the plasma-vacuum interface in MHD equilibria

NASA Astrophysics Data System (ADS)

Hanson, James D.

2016-10-01

The VMEC non-axisymmetric MHD equilibrium code can compute free-boundary equilibria. Since VMEC assumes that magnetic fields within the plasma form closed and nested flux surfaces, the plasma-vacuum interface is a flux surface, and the total magnetic field there has no normal component. VMEC imposes this condition of zero normal field using the potential formulation of Merkel, and solves a Neumann problem for the magnetic potential in the exterior region. This boundary condition necessarily admits the possibility of a surface current on the plasma-vacuum interface. While this current may be small in MHD equilibrium, this current may be readily computed in terms of a magnetic potential in both the interior and exterior regions. Examples of the surface current for VMEC equilibria will be shown. This material is based upon work supported by Auburn University and the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Award Number DE-FG02-03ER54692.

Toroidal Simulations of Sawteeth with Diamagnetic Effects

NASA Astrophysics Data System (ADS)

Beidler, Matthew; Cassak, Paul; Jardin, Stephen

2014-10-01

The sawtooth crash in tokamaks limits the core temperature, adversely impacts confinement, and seeds disruptions. Adequate knowledge of the physics governing the sawtooth crash and a predictive capability of its ramifications has been elusive, including an understanding of incomplete reconnection, i.e., why sawteeth often cease prematurely before processing all available magnetic flux. There is an indication that diamagnetic suppression could play an important role in this phenomenon. While computational tools to study toroidal plasmas have existed for some time, extended-MHD physics have only recently been integrated. Interestingly, incomplete reconnection has been observed in simulations when diamagnetic effects are present. In the current study, we employ the three-dimensional, extended-MHD code M3D-C1 to study the sawtooth crash in a toroidal geometry. In particular, we describe how magnetic reconnection at the q = 1 rational surface evolves when self-consistently increasing diamagnetic effects are present. We also explore how the termination of reconnection may lead to core-relaxing ideal-MHD instabilities.

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

Renormalization-group theory of plasma microturbulence

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

Carati, D.; Chriaa, K.; Balescu, R.

1994-08-01

The dynamical renormalization-group methods are applied to the gyrokinetic equation describing drift-wave turbulence in plasmas. As in both magnetohydrodynamic and neutral turbulence, small-scale fluctuations appear to act as effective dissipative processes on large-scale phenomena. A linear renormalized gyrokinetic equation is derived. No artificial forcing is introduced into the equations and all the renormalized corrections are expressed in terms of the fluctuating electric potential. The link with the quasilinear limit and the direct interaction approximation is investigated. Simple analytical expressions for the anomalous transport coefficients are derived by using the linear renormalized gyrokinetic equation. Examples show that both quasilinear and Bohmmore » scalings can be recovered depending on the spectral amplitude of the electric potential fluctuations.« less

Transport, noise, and conservation properties in gyrokinetic plasmas

NASA Astrophysics Data System (ADS)

Jenkins, Thomas

2005-10-01

The relationship between various transport properties (such as particle and heat flux, entropy production, heating, and collisional dissipation) [1] is examined in electrostatic gyrokinetic simulations of ITG modes in simple geometry. The effect of the parallel velocity nonlinearity on the achievement of steady-state solutions and the transport properties of these solutions is examined; the effects of nonadiabatic electrons are also considered. We also examine the effectiveness of the electromagnetic split-weight scheme [2] in reducing the noise and improving the conservation properties (energy, momentum, particle number, etc.) of gyrokinetic plasmas. [1] W. W. Lee and W. M. Tang, Phys. Fluids 31, 612 (1988). [2] W. W. Lee, J. L. V. Lewandowski, T. S. Hahm, and Z.Lin, Phys. Plasmas 8, 4435 (2001).

Fluctuations and discrete particle noise in gyrokinetic simulation of drift waves

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Lee, W. W.

2007-03-01

The relevance of the gyrokinetic fluctuation-dissipation theorem (FDT) to thermal equilibrium and nonequilibrium states of the gyrokinetic plasma is explored, with particular focus being given to the contribution of weakly damped normal modes to the fluctuation spectrum. It is found that the fluctuation energy carried in the normal modes exhibits the proper scaling with particle count (as predicted by the FDT in thermal equilibrium) even in the presence of drift waves, which grow linearly and attain a nonlinearly saturated steady state. This favorable scaling is preserved, and the saturation amplitude of the drift wave unaffected, for parameter regimes in which the normal modes become strongly damped and introduce a broad spectrum of discreteness-induced background noise in frequency space.

A gyrokinetic perspective on the JET-ILW pedestal

NASA Astrophysics Data System (ADS)

Hatch, D. R.; Kotschenreuther, M.; Mahajan, S.; Valanju, P.; Liu, X.

2017-03-01

JET has been unable to recover historical confinement levels when operating with an ITER-like wall (ILW) due largely to the inaccessibility of high pedestal temperatures. Finding a path to overcome this challenge is of utmost importance for both a prospective JET DT campaign and for future ITER operation. Gyrokinetic simulations (using the Gene code) quantitatively capture experimental transport levels for a representative experimental discharge and qualitatively recover the major experimental trends. Microtearing turbulence is a major transport mechanisms for the low-temperature pedestals characteristic of unseeded JET-ILW discharges. At higher temperatures and/or lower {ρ\\ast} , we identify electrostatic ITG transport of a type that is strongly shear-suppressed on smaller machines. Consistent with observations, this transport mechanism is strongly reduced by the presence of a low-Z impurity (e.g. carbon or nitrogen at the level of {{Z}\\text{eff}}∼ 2 ), recovering the accessibility of high pedestal temperatures. Notably, simulations based on dimensionless {ρ\\ast} scans recover historical scaling behavior except in the unique JET-ILW parameter regime where ITG turbulence becomes important. Our simulations also elucidate the observed degradation of confinement caused by gas puffing, emphasizing the important role of the density pedestal structure. This study maps out important regions of parameter space, providing insights that may point to optimal physical regimes that can enable the recovery of high pedestal temperatures on JET.

Influence of the parallel nonlinearity on zonal flows and heat transport in global gyrokinetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.

2009-07-01

In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Könies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.

Multi-field/-scale interactions of turbulence with neoclassical tearing mode magnetic islands in the DIII-D tokamak

DOE PAGES

Bardoczi, Laszlo; Rhodes, Terry L.; Navarro, Alejandro Banon; ...

2017-03-03

We present the first localized measurements of long and intermediate wavelength turbulent density fluctuations (more » $$\\sim\\atop{n}$$) and long wavelength turbulent electron temperature fluctuations ($$\\sim\\atop{T}$$ e) modified by m/n = 2/1 Neoclassical Tearing Mode (NTM) islands (m and n are the poloidal and toroidal mode numbers, respectively). These long and intermediate wavelengths correspond to the expected Ion Temperature Gradient and Trapped Electron Mode scales, respectively. Two regimes have been observed when tracking $$\\sim\\atop{n}$$ during NTM evolution: (1) small islands are characterized by a steep T e radial profile and turbulence levels comparable to those of the background; (2) large islands have a flat T e profile and reduced turbulence level at the O-point. Radially outside the large island, the T e profile is steeper and the turbulence level increased compared to the no or small island case. Reduced turbulence at the O-point compared to the X-point leads to a 15% modulation of $$\\sim\\atop{n}$$ 2 across the island that is nearly in phase with the T e modulation. Qualitative comparisons to the GENE non-linear gyrokinetic code are promising with GENE replicating the observed scaling of turbulence modification with island size. Furthermore, these results are significant as they allow the validation of gyrokinetic simulations modeling the interaction of these multi-scale phenomena.« less

Proceedings of the 14th International Conference on the Numerical Simulation of Plasmas

NASA Astrophysics Data System (ADS)

Partial Contents are as follows: Numerical Simulations of the Vlasov-Maxwell Equations by Coupled Particle-Finite Element Methods on Unstructured Meshes; Electromagnetic PIC Simulations Using Finite Elements on Unstructured Grids; Modelling Travelling Wave Output Structures with the Particle-in-Cell Code CONDOR; SST--A Single-Slice Particle Simulation Code; Graphical Display and Animation of Data Produced by Electromagnetic, Particle-in-Cell Codes; A Post-Processor for the PEST Code; Gray Scale Rendering of Beam Profile Data; A 2D Electromagnetic PIC Code for Distributed Memory Parallel Computers; 3-D Electromagnetic PIC Simulation on the NRL Connection Machine; Plasma PIC Simulations on MIMD Computers; Vlasov-Maxwell Algorithm for Electromagnetic Plasma Simulation on Distributed Architectures; MHD Boundary Layer Calculation Using the Vortex Method; and Eulerian Codes for Plasma Simulations.

Comparison of Magnetospheric Magnetic Field Variations at Quasi-Zenith Orbit Based on Michibiki Observation and REPPU Global MHD Simulation

NASA Astrophysics Data System (ADS)

Kubota, Y.; Nagatsuma, T.; Den, M.; Nakamizo, A.; Matsumoto, H.; Tanaka, T.

2017-12-01

We are developing a numerical simulator for future space weather forecast using magnetosphere-ionosphere coupling global MHD simulation called REPPU (REProduce Plasma Universe) code. We investigate the validity of the MHD simulation result as compared with observation. In this study we simulate some events including both quiet and disturbed geomagnetic conditions using OMNIWeb solar wind data. The simulation results are compared with magnetic field observations from Michibiki satellite, which is on the quasi-zenith orbit (QZO). In quiet geomagnetic condition, magnetic field variations at QZO obtained from simulation results have good consistency as compared correspondence with those from Michibiki observation. In disturbed geomagnetic condition in which the Dst < -20 nT, however, V component of magnetic field variations from simulation results tend to deviate from observations especially at the night side. We consider that this deviation during disturbed geomagnetic condition might be due to tail and/or ring current enhancement which is already suggested by many other MHD simulation studies as compared with the magnetic field observation at geosynchronous orbit. In this presentation, we will discuss the cause of this discrepancy in more detail with studying the relationship between the magnetic field deviation and some parameters such as Dst and solar wind.

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

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

Banerjee, Debabrata; Zhu, Ping; Maingi, Rajesh

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. Our purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Z eff after Li-conditioning in ELM-free H-mode. And unlike an earlier conclusion from anmore » eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Z eff, the complete stabilization could be explained. Furthermore, a thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.« less

Stabilizing effect of resistivity towards ELM-free H-mode discharge in lithium-conditioned NSTX

DOE PAGES

Banerjee, Debabrata; Zhu, Ping; Maingi, Rajesh

2017-05-12

Linear stability analysis of the national spherical torus experiment (NSTX) Li-conditioned ELM-free H-mode equilibria is carried out in the context of the extended magneto-hydrodynamic (MHD) model in NIMROD. Our purpose is to investigate the physical cause behind edge localized mode (ELM) suppression in experiment after the Li-coating of the divertor and the first wall of the NSTX tokamak. Besides ideal MHD modeling, including finite-Larmor radius effect and two-fluid Hall and electron diamagnetic drift contributions, a non-ideal resistivity model is employed, taking into account the increase of Z eff after Li-conditioning in ELM-free H-mode. And unlike an earlier conclusion from anmore » eigenvalue code analysis of these equilibria, NIMROD results find that after reduced recycling from divertor plates, profile modification is necessary but insufficient to explain the mechanism behind complete ELMs suppression in ideal two-fluid MHD. After considering the higher plasma resistivity due to higher Z eff, the complete stabilization could be explained. Furthermore, a thorough analysis of both pre-lithium ELMy and with-lithium ELM-free cases using ideal and non-ideal MHD models is presented, after accurately including a vacuum-like cold halo region in NIMROD to investigate ELMs.« 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.

Magnetohydrodynamics with Embedded Particle-in-Cell Simulation of Mercury's Magnetosphere

NASA Astrophysics Data System (ADS)

Chen, Y.; Toth, G.; Jia, X.; Gombosi, T. I.; Markidis, S.

2015-12-01

Mercury's magnetosphere is much more dynamic than other planetary magnetospheres because of Mercury's weak intrinsic magnetic field and its proximity to the Sun. Magnetic reconnection and Kelvin-Helmholtz phenomena occur in Mercury's magnetopause and magnetotail at higher frequencies than in other planetary magnetosphere. For instance, chains of flux transfer events (FTEs) on the magnetopause, have been frequentlyobserved by the the MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) spacecraft (Slavin et al., 2012). Because ion Larmor radius is comparable to typical spatial scales in Mercury's magnetosphere, finite Larmor radius effects need to be accounted for. In addition, it is important to take in account non-ideal dissipation mechanisms to accurately describe magnetic reconnection. A kinetic approach allows us to model these phenomena accurately. However, kinetic global simulations, even for small-size magnetospheres like Mercury's, are currently unfeasible because of the high computational cost. In this work, we carry out global simulations of Mercury's magnetosphere with the recently developed MHD-EPIC model, which is a two-way coupling of the extended magnetohydrodynamic (XMHD) code BATS-R-US with the implicit Particle-in-Cell (PIC) model iPIC3D. The PIC model can cover the regions where kinetic effects are most important, such as reconnection sites. The BATS-R-US code, on the other hand, can efficiently handle the rest of the computational domain where the MHD or Hall MHD description is sufficient. We will present our preliminary results and comparison with MESSENGER observations.

Lower hybrid current drive in experiments for transport barriers at high βN of JET (Joint European Torus)

NASA Astrophysics Data System (ADS)

Cesario, R. C.; Castaldo, C.; Fonseca, A.; De Angelis, R.; Parail, V.; Smeulders, P.; Beurskens, M.; Brix, M.; Calabrò, G.; De Vries, P.; Mailloux, J.; Pericoli, V.; Ravera, G.; Zagorski, R.

2007-09-01

LHCD has been used in JET experiments aimed at producing internal transport barriers (ITBs) in highly triangular plasmas (δ≈0.4) at high βN (up to 3) for steady-state application. The LHCD is a potentially valuable tool for (i) modifying the target q-profile, which can help avoid deleterious MHD modes and favour the formation of ITBs, and (ii) contributing to the non-inductive current drive required to prolong such plasma regimes. The q-profile evolution has been simulated during the current ramp-up phase for such a discharge (B0 = 2.3 T, IP = 1.5 MA) where 2 MW of LHCD has been coupled. The JETTO code was used taking measured plasma profiles, and the LHCD profile modeled by the LHstar code. The results are in agreement with MSE measurements and indicate the importance of the elevated electron temperature due to LHCD, as well as the driven current. During main heating with 18 MW of NBI and 3 MW of ICRH the bootstrap current density at the edge also becomes large, consistently with the observed reduction of the local turbulence and of the MHD activity. JETTO modelling suggests that the bootstrap current can reduce the magnetic shear (sh) at large radius, potentially affecting the MHD stability and turbulence behaviour in this region. Keywords: lower hybrid current drive (LHCD), bootstrap current, q (safety factor) and shear (sh) profile evolutions.

Analysis and Modeling of DIII-D Experiments With OMFIT and Neural Networks

NASA Astrophysics Data System (ADS)

Meneghini, O.; Luna, C.; Smith, S. P.; Lao, L. L.; GA Theory Team

2013-10-01

The OMFIT integrated modeling framework is designed to facilitate experimental data analysis and enable integrated simulations. This talk introduces this framework and presents a selection of its applications to the DIII-D experiment. Examples include kinetic equilibrium reconstruction analysis; evaluation of MHD stability in the core and in the edge; and self-consistent predictive steady-state transport modeling. The OMFIT framework also provides the platform for an innovative approach based on neural networks to predict electron and ion energy fluxes. In our study a multi-layer feed-forward back-propagation neural network is built and trained over a database of DIII-D data. It is found that given the same parameters that the highest fidelity models use, the neural network model is able to predict to a large degree the heat transport profiles observed in the DIII-D experiments. Once the network is built, the numerical cost of evaluating the transport coefficients is virtually nonexistent, thus making the neural network model particularly well suited for plasma control and quick exploration of operational scenarios. The implementation of the neural network model and benchmark with experimental results and gyro-kinetic models will be discussed. Work supported in part by the US DOE under DE-FG02-95ER54309.

Overview of MST Research

NASA Astrophysics Data System (ADS)

Chapman, B. E.

2017-10-01

MST progress in advancing the RFP for (1) fusion plasma confinement with ohmic heating and minimal external magnetization, (2) predictive capability in toroidal confinement physics, and (3) basic plasma physics is summarized. Validation of key plasma models is a program priority, which is enhanced by programmable power supplies (PPS) to maximize inductive capability. The existing PPS enables access to very low plasma current, down to Ip =0.02 MA. This greatly expands the Lundquist number range S =104 -108 and allows nonlinear, 3D MHD computation using NIMROD and DEBS with dimensionless parameters that overlap those of MST plasmas. A new, second PPS will allow simultaneous PPS control of the Bp and Bt circuits. The PPS also enables MST tokamak operation, thus far focused on disruptions and RMP suppression of runaway electrons. Gyrokinetic modeling with GENE predicts unstable TEM in improved-confinement RFP plasmas. Measured fluctuations have TEM properties including a density-gradient threshold larger than for tokamak plasmas. Turbulent energization of an electron tail occurs during sawtooth reconnection. Probe measurements hint that drift waves are also excited via the turbulent cascade in standard RFP plasmas. Exploration of basic plasma science frontiers in MST RFP and tokamak plasmas is proposed as part of WiPPL, a basic science user facility. Work supported by USDoE.

Continuum kinetic modeling of the tokamak plasma edge

DOE PAGES

Dorf, M. A.; Dorr, M.; Rognlien, T.; ...

2016-03-10

In this study, the first 4D (axisymmetric) high-order continuum gyrokinetic transport simulations that span the magnetic separatrix of a tokamak are presented. The modeling is performed with the COGENT code, which is distinguished by fourth-order finite-volume discretization combined with mapped multiblock grid technology to handle the strong anisotropy of plasmatransport and the complex X-point divertor geometry with high accuracy. The calculations take into account the effects of fully nonlinear Fokker-Plank collisions, electrostatic potential variations, and anomalous radial transport. Topics discussed include: (a) ion orbit loss and the associated toroidal rotation and (b) edge plasma relaxation in the presence of anomalousmore » radial transport.« less

Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

DOE PAGES

Hager, Robert; Chang, C. S.

2016-04-08

As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore » edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.« less

Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

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

Hager, Robert; Chang, C. S.

As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore » edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.« less

Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

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

Hager, Robert, E-mail: rhager@pppl.gov; Chang, C. S., E-mail: cschang@pppl.gov

As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steepmore » edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.« less

One-dimensional MHD simulations of MTF systems with compact toroid targets and spherical liners

NASA Astrophysics Data System (ADS)

Khalzov, Ivan; Zindler, Ryan; Barsky, Sandra; Delage, Michael; Laberge, Michel

2017-10-01

One-dimensional (1D) MHD code is developed in General Fusion (GF) for coupled plasma-liner simulations in magnetized target fusion (MTF) systems. The main goal of these simulations is to search for optimal parameters of MTF reactor, in which spherical liquid metal liner compresses compact toroid plasma. The code uses Lagrangian description for both liner and plasma. The liner is represented as a set of spherical shells with fixed masses while plasma is discretized as a set of nested tori with circular cross sections and fixed number of particles between them. All physical fields are 1D functions of either spherical (liner) or small toroidal (plasma) radius. Motion of liner and plasma shells is calculated self-consistently based on applied forces and equations of state. Magnetic field is determined by 1D profiles of poloidal and toroidal fluxes - they are advected with shells and diffuse according to local resistivity, this also accounts for flux leakage into the liner. Different plasma transport models are implemented, this allows for comparison with ongoing GF experiments. Fusion power calculation is included into the code. We performed a series of parameter scans in order to establish the underlying dependencies of the MTF system and find the optimal reactor design point.

Simulations of toroidal Alfvén eigenmode excited by fast ions on the Experimental Advanced Superconducting Tokamak

NASA Astrophysics Data System (ADS)

Pei, Youbin; Xiang, Nong; Shen, Wei; Hu, Youjun; Todo, Y.; Zhou, Deng; Huang, Juan

2018-05-01

Kinetic-MagnetoHydroDynamic (MHD) hybrid simulations are carried out to study fast ion driven toroidal Alfvén eigenmodes (TAEs) on the Experimental Advanced Superconducting Tokamak (EAST). The first part of this article presents the linear benchmark between two kinetic-MHD codes, namely MEGA and M3D-K, based on a realistic EAST equilibrium. Parameter scans show that the frequency and the growth rate of the TAE given by the two codes agree with each other. The second part of this article discusses the resonance interaction between the TAE and fast ions simulated by the MEGA code. The results show that the TAE exchanges energy with the co-current passing particles with the parallel velocity |v∥ | ≈VA 0/3 or |v∥ | ≈VA 0/5 , where VA 0 is the Alfvén speed on the magnetic axis. The TAE destabilized by the counter-current passing ions is also analyzed and found to have a much smaller growth rate than the co-current ions driven TAE. One of the reasons for this is found to be that the overlapping region of the TAE spatial location and the counter-current ion orbits is narrow, and thus the wave-particle energy exchange is not efficient.

Measurements of confined alphas and tritons in the MHD quiescent core of TFTR plasmas using the pellet charge exchange diagnostic

NASA Astrophysics Data System (ADS)

Medley, S. S.; Budny, R. V.; Mansfield, D. K.; Redi, M. H.; Roquemore, A. L.; Fisher, R. K.; Duong, H. H.; McChesney, J. M.; Parks, P. B.; Petrov, M. P.; Gorelenkov, N. N.

1996-10-01

The energy distributions and radial density profiles of the fast confined trapped alpha particles in DT experiments on TFTR are being measured in the energy range 0.5 - 3.5 MeV using the pellet charge exchange (PCX) diagnostic. A brief description of the measurement technique which involves active neutral particle analysis using the ablation cloud surrounding an injected impurity pellet as the neutralizer is presented. This paper focuses on alpha and triton measurements in the core of MHD quiescent TFTR discharges where the expected classical slowing-down and pitch angle scattering effects are not complicated by stochastic ripple diffusion and sawtooth activity. In particular, the first measurement of the alpha slowing-down distribution up to the birth energy, obtained using boron pellet injection, is presented. The measurements are compared with predictions using either the TRANSP Monte Carlo code and/or a Fokker - Planck Post-TRANSP processor code, which assumes that the alphas and tritons are well confined and slow down classically. Both the shape of the measured alpha and triton energy distributions and their density ratios are in good agreement with the code calculations. We can conclude that the PCX measurements are consistent with classical thermalization of the fusion-generated alphas and tritons.

A new free and open source tool for space plasma modeling.

NASA Astrophysics Data System (ADS)

Honkonen, I. J.

2014-12-01

I will present a new distributed memory parallel, free and open source computational model for studying space plasma. The model is written in C++ with emphasis on good software development practices and code readability without sacrificing serial or parallel performance. As such the model could be especially useful for education, for learning both (magneto)hydrodynamics (MHD) and computational model development. By using latest features of the C++ standard (2011) it has been possible to develop a very modular program which improves not only the readability of code but also the testability of the model and decreases the effort required to make changes to various parts of the program. Major parts of the model, functionality not directly related to (M)HD, have been outsourced to other freely available libraries which has reduced the development time of the model significantly. I will present an overview of the code architecture as well as details of different parts of the model and will show examples of using the model including preparing input files and plotting results. A multitude of 1-, 2- and 3-dimensional test cases are included in the software distribution and the results of, for example, Kelvin-Helmholtz, bow shock, blast wave and reconnection tests, will be presented.

Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

NASA Astrophysics Data System (ADS)

Cornille, Brian; White, Dan

2017-10-01

We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

Modeling MHD Equilibrium and Dynamics with Non-Axisymmetric Resistive Walls in LTX and HBT-EP

NASA Astrophysics Data System (ADS)

Hansen, C.; Levesque, J.; Boyle, D. P.; Hughes, P.

2017-10-01

In experimental magnetized plasmas, currents in the first wall, vacuum vessel, and other conducting structures can have a strong influence on plasma shape and dynamics. These effects are complicated by the 3D nature of these structures, which dictate available current paths. Results from simulations to study the effect of external currents on plasmas in two different experiments will be presented: 1) The arbitrary geometry, 3D extended MHD code PSI-Tet is applied to study linear and non-linear plasma dynamics in the High Beta Tokamak (HBT-EP) focusing on toroidal asymmetries in the adjustable conducting wall. 2) Equilibrium reconstructions of the Lithium Tokamak eXperiment (LTX) in the presence of non-axisymmetric eddy currents. An axisymmetric model is used to reconstruct the plasma equilibrium, using the PSI-Tri code, along with a set of fixed 3D eddy current distributions in the first wall and vacuum vessel [C. Hansen et al., PoP Apr. 2017]. 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 and PSI-Tri will also be presented. This work supported by US DOE contract DE-SC0016256.

Modeling of fast neutral-beam-generated ion effects on MHD-spectroscopic observations of resistive wall mode stability in DIII-D plasmas [Modeling of fast neutral-beam-generated ion effects on MHD spectroscopic observations of RWM stability in DIII-D plasmas

DOE PAGES

Turco, Francesca; Turnbull, Alan D.; Hanson, Jeremy M.; ...

2015-02-03

Experiments conducted at DIII-D investigate the role of drift kinetic damping and fast neutral beam injection (NBI)-ions in the approach to the no-wall β N limit. Modelling results show that the drift kinetic effects are significant and necessary to reproduce the measured plasma response at the ideal no-wall limit. Fast neutral-beam ions and rotation play important roles and are crucial to quantitatively match the experiment. In this paper, we report on the model validation of a series of plasmas with increasing β N, where the plasma stability is probed by active magnetohydrodynamic (MHD) spectroscopy. The response of the plasma tomore » an externally applied field is used to probe the stable side of the resistive wall mode and obtain an indication of the proximity of the equilibrium to an instability limit. We describe the comparison between the measured plasma response and that calculated by means of the drift kinetic MARS-K code, which includes the toroidal rotation, the electron and ion drift-kinetic resonances, and the presence of fast particles for the modelled plasmas. The inclusion of kinetic effects allows the code to reproduce the experimental results within ~13% for both the amplitude and phase of the plasma response, which is a significant improvement with respect to the undamped MHD-only model. The presence of fast NBI-generated ions is necessary to obtain the low response at the highest β N levels (~90% of the ideal no-wall limit). Finally, the toroidal rotation has an impact on the results, and a sensitivity study shows that a large variation in the predicted response is caused by the details of the rotation profiles at high β N.« less

Linear dispersion relation for the mirror instability in context of the gyrokinetic theory

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

Porazik, Peter; Johnson, Jay R.

2013-10-15

The linear dispersion relation for the mirror instability is discussed in context of the gyrokinetic theory. The objective is to provide a coherent view of different kinetic approaches used to derive the dispersion relation. The method based on gyrocenter phase space transformations is adopted in order to display the origin and ordering of various terms.

Gyrokinetic Statistical Absolute Equilibrium and Turbulence

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

Jian-Zhou Zhu and Gregory W. Hammett

2011-01-10

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, correspondingmore » to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less