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Sample records for nonlinear gyrokinetic particle

  1. Nonlinear gyrokinetic equations

    SciTech Connect

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  2. Gyrokinetic particle simulation model

    SciTech Connect

    Lee, W.W.

    1986-07-01

    A new type of particle simulation model based on the gyrophase-averaged Vlasov and Poisson equations is presented. The reduced system, in which particle gyrations are removed from the equations of motion while the finite Larmor radius effects are still preserved, is most suitable for studying low frequency microinstabilities in magnetized plasmas. It is feasible to simulate an elongated system (L/sub parallel/ >> L/sub perpendicular/) with a three-dimensional grid using the present model without resorting to the usual mode expansion technique, since there is essentially no restriction on the size of ..delta..x/sub parallel/ in a gyrokinetic plasma. The new approach also enables us to further separate the time and spatial scales of the simulation from those associated with global transport through the use of multiple spatial scale expansion. Thus, the model can be a very efficient tool for studying anomalous transport problems related to steady-state drift-wave turbulence in magnetic confinement devices. It can also be applied to other areas of plasma physics.

  3. Influence of the parallel nonlinearity on zonal flows and heat transport in global gyrokinetic particle-in-cell simulations

    SciTech Connect

    Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.

    2009-07-15

    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. Koenies 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.

  4. High frequency gyrokinetic particle simulation

    SciTech Connect

    Kolesnikov, R. A.; Lee, W. W.; Qin, H.; Startsev, E.

    2007-07-15

    The gyrokinetic approach for arbitrary frequency dynamics in magnetized plasmas is explored, using the gyrocenter-gauge kinetic theory. Contrary to low-frequency gyrokinetics, which views each particle as a rigid charged ring, arbitrary frequency response of a particle is described by a quickly changing Kruskal ring. This approach allows the separation of gyrocenter and gyrophase responses and thus allows for, in many situations, larger time steps for the gyrocenter push than for the gyrophase push. The gyrophase response which determines the shape of Kruskal rings can be described by a Fourier series in gyrophase for some problems, thus allowing control over the cyclotron harmonics at which the plasma responds. A computational algorithm for particle-in-cell simulation based on this concept has been developed. An example of the ion Bernstein wave is used to illustrate its numerical properties, and comparison with a direct Lorentz-force approach is presented.

  5. Electromagnetic nonlinear gyrokinetics with polarization drift

    SciTech Connect

    Duthoit, F.-X.; Hahm, T. S.; 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, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.

  6. 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.

  7. Nonlinear gyrokinetic theory for finite-BETA plasmas

    SciTech Connect

    Hahm, T.S.; Lee, W.W.; Brizard, A.

    1988-02-01

    A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.

  8. Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

    SciTech Connect

    Artun, M.; Tang, W.M.

    1994-03-01

    The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.

  9. Nonlinear electromagnetic gyrokinetic simulations of tokamak plasmas

    NASA Astrophysics Data System (ADS)

    Jenko, F.; Dorland, W.

    2001-12-01

    One of the central physics issues currently targeted by nonlinear gyrokinetic simulations is the role of finite-β effects. The latter change the MHD equilibrium, introduce new dynamical space and time scales, alter and enlarge the zoo of electrostatic microinstabilities and saturation mechanisms, and lead to turbulent transport along fluctuating magnetic field lines. It is shown that the electromagnetic effects on primarily electrostatic microinstabilities are generally weakly or moderately stabilizing. However, the saturation of these modes and hence the determination of the transport level in the quasi-stationary turbulent state can be dominated by nonlinear electromagnetic effects and yield surprising results. Despite this, the induced transport is generally electrostatic in nature well below the ideal ballooning limit.

  10. Nonlinear scattering term in the gyrokinetic Vlasov equation

    SciTech Connect

    Wang, Shaojie

    2013-08-15

    Nonlinear scattering term is found from the nonlinear gyrokinetic equation by decoupling the perturbed gyrocenter motion from the unperturbed motion. The gyro-center distribution function is determined by the well-understood unperturbed motion, with the effects of fields perturbation included in the nonlinear scattering term, which explicitly reveals the nonlinear stochastic dissipation on the time scale longer than the wave correlation time.

  11. Gyro-water-bag approach in nonlinear gyrokinetic turbulence

    SciTech Connect

    Besse, Nicolas Bertrand, Pierre

    2009-06-20

    Turbulent transport is a key issue for controlled thermonuclear fusion based on magnetic confinement. The thermal confinement of a magnetized fusion plasma is essentially determined by the turbulent heat conduction across the equilibrium magnetic field. It has long been acknowledged, that the prediction of turbulent transport requires to solve Vlasov-type gyrokinetic equations. Although the kinetic description is more accurate than fluid models (MHD, gyro-fluid), because among other things it takes into account nonlinear resonant wave-particle interaction, kinetic modeling has the drawback of a huge computer resource request. An unifying approach consists in considering water-bag-like weak solutions of kinetic collisionless equations, which allow to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations, while keeping its kinetic behaviour. As a result this exact reduction induces a multi-fluid numerical resolution cost. Therefore finding water-bag-like weak solutions of the gyrokinetic equations leads to the birth of the gyro-water-bag model. This model is suitable for studying linear and nonlinear low-frequency micro-instabilities and the associated anomalous transport in magnetically-confined plasmas. The present paper addresses the derivation of the nonlinear gyro-water-bag model, its quasilinear approximation and their numerical approximations by Runge-Kutta semi-Lagrangian methods and Runge-Kutta discontinuous Galerkin schemes respectively.

  12. Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence

    SciTech Connect

    Hahm, T. S.; Wang, Lu; Madsen, J.

    2008-08-01

    An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E Χ B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes ρi<< ρθ¡ ~ LE ~ Lp << R (here ρi is the thermal ion Larmor radius and ρθ¡ = B/Bθ] ρi), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take κ perpendicular to ρi ~ 1 for generality, and keep the relative fluctuation amplitudes eδφ /Τi ~ δΒ / Β up to the second order. Extending the electrostatic theory in the presence of high E Χ B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation.

  13. 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.

  14. Visual interrogation of gyrokinetic particle simulations

    NASA Astrophysics Data System (ADS)

    Jones, Chad; Ma, Kwan-Liu; Sanderson, Allen; Myers, Lee Roy, Jr.

    2007-07-01

    Gyrokinetic particle simulations are critical to the study of anomalous energy transport associated with plasma microturbulence in magnetic confinement fusion experiments. The simulations are conducted on massively parallel computers and produce large quantities of particles, variables, and time steps, thus presenting a formidable challenge to data analysis tasks. We present two new visualization techniques for scientists to improve their understanding of the time-varying, multivariate particle data. One technique allows scientists to examine correlations in multivariate particle data with tightly coupled views of the data in both physical space and variable space, and to visually identify and track features of interest. The second technique, built into SCIRun, allows scientists to perform range-based queries over a series of time slices and visualize the resulting particles using glyphs. The ability to navigate the multiple dimensions of the particle data, as well as query individual or a collection of particles, enables scientists to not only validate their simulations but also discover new phenomena in their data.

  15. Gyrokinetic particle simulation of neoclassical transport

    SciTech Connect

    Lin, Z.; Tang, W.M.; Lee, W.W.

    1995-02-01

    A time varying weighting ({delta} f) scheme for gyrokinetic particle simulation is applied to a steady state, multi-species simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated in these multispecies simulations that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion-electron plasma. An important physics feature of the present scheme is the introduction of toroidal sheared flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory of Hinton and Wong. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient driven electron particle flux and the bootstrap current while reducing temperature gradient driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, the present work demonstrates a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes.

  16. Gyrokinetic particle simulation of neoclassical transport

    SciTech Connect

    Lin, Z.; Tang, W.M.; Lee, W.W.

    1995-08-01

    A time varying weighting ({delta}{ital f} ) scheme for gyrokinetic particle simulation is applied to a steady-state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion--electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient-driven electron particle flux and the bootstrap current while reducing temperature gradient-driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, in the present work a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes is demonstrated. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

  17. Nonlinear Gyrokinetic Theory With Polarization Drift

    SciTech Connect

    L. Wang and T.S. Hahm

    2010-03-25

    A set of the electrostatic toroidal gyrokinetic Vlasov equation and the Poisson equation, which explicitly includes the polarization drift, is derived systematically by using Lie-transform method. The polarization drift is introduced in the gyrocenter equations of motion, and the corresponding polarization density is derived. Contrary to the wide-spread expectation, the inclusion of the polarization drift in the gyrocenter equations of motion does not affect the expression for the polarization density significantly. This is due to modification of the gyrocenter phase-space volume caused by the electrostatic potential [T. S. Hahm, Phys. Plasmas 3, 4658 (1996)] .

  18. Second order gyrokinetic theory for particle-in-cell codes

    NASA Astrophysics Data System (ADS)

    Tronko, Natalia; Bottino, Alberto; Sonnendrücker, Eric

    2016-08-01

    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 issued 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.

  19. Gyrokinetic particle simulation of beta-induced Alfven eigenmode

    SciTech Connect

    Zhang, H. S.; Lin, Z.; Holod, I.; Xiao, Y.; Wang, X.; Zhang, W. L.

    2010-11-15

    The beta-induced Alfven eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.

  20. Gyrokinetic simulation studies on the energetic-particle-induced geodesic acoustic mode

    NASA Astrophysics Data System (ADS)

    Miki, Kazuhiro; Idomura, Yasuhiro

    2014-10-01

    Understanding of the energetic particles physics is of great interest in the future burning plasmas. Particularly, particle loss in the presence of EGAM may be critical for ITER. We thus need to know how EGAM is excited and interacts with turbulence. We here introduce energetic particles in a full-f gyrokinetic code (GT5D). (i) We find linear dynamics of the EGAM driven by bump-on-tail particle distributions. We examine flat-q, homogeneous, axisymmetric, electrostatic gyrokinetic simulations. Above a certain level of the beam intensity, an oscillatory mode grows with about a half of the standard GAM. The observed frequencies are consistent with the eigenmode analyses derived from the perturbed gyrokinetic equations. The theoretical analyses also indicate a bifurcation of the excited modes depending on q-value. Estimation of the finite-orbit-width effects can provide a size dependency of the EGAM growth rate. (ii) We find linear and nonlinear dynamics of the EGAM driven by slowing-down distributions. We examine the axisymmetric gyrokinetic simulations with DIII-D-like parameters. The observed growth rates and frequencies are consistent with results of other hybrid code. Furthermore, we will focus on nonlinear phase space dynamics, namely chirping mode. This work is supported by HPCI Strategic Program Field No.4: Next-Generation Industrial Innovations, funded by the MEXT, Japan.

  1. Full f gyrokinetic method for particle simulation of tokamak transport

    SciTech Connect

    Heikkinen, J.A. Janhunen, S.J.; Kiviniemi, T.P.; Ogando, F.

    2008-05-10

    A gyrokinetic particle-in-cell approach with direct implicit construction of the coefficient matrix of the Poisson equation from ion polarization and electron parallel nonlinearity is described and applied in global electrostatic toroidal plasma transport simulations. The method is applicable for calculation of the evolution of particle distribution function f including as special cases strong plasma pressure profile evolution by transport and formation of neoclassical flows. This is made feasible by full f formulation and by recording the charge density changes due to the ion polarization drift and electron acceleration along the local magnetic field while particles are advanced. The code has been validated against the linear predictions of the unstable ion temperature gradient mode growth rates and frequencies. Convergence and saturation in both turbulent and neoclassical limit of the ion heat conductivity is obtained with numerical noise well suppressed by a sufficiently large number of simulation particles. A first global full f validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. At high Mach number (M{sub p}{approx}1) of the poloidal flow, the radial electric field is significantly enhanced over the standard neoclassical prediction. The neoclassical radial electric field together with the related GAM oscillations is found to regulate the turbulent heat and particle diffusion levels particularly strongly in a large aspect ratio tokamak at low plasma current.

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

    SciTech Connect

    Chowdhury, J.; Wan, Weigang; Chen, Yang; Parker, Scott E.; Groebner, Richard J.; Holland, C.; Howard, N. T.

    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. 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.

  3. Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

    NASA Astrophysics Data System (ADS)

    Hatch, D. R.; Jenko, F.; Bañón Navarro, A.; Bratanov, V.; Terry, P. W.; Pueschel, M. J.

    2016-07-01

    A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.

  4. Gyrokinetic particle simulation of a field reversed configuration

    NASA Astrophysics Data System (ADS)

    Fulton, D. P.; Lau, C. K.; Holod, I.; Lin, Z.; Dettrick, S.

    2016-01-01

    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 ion gyroradius. In the SOL, the driftwave is unstable on both ion and electron scales.

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

    SciTech Connect

    White, A. E. Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; and others

    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 compare 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.

  6. Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experimenta)

    NASA Astrophysics Data System (ADS)

    White, A. E.; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G.; Mikkelsen, D. R.; Edlund, E. M.; Kung, C.; Holland, C.; Candy, J.; Petty, C. C.; Reinke, M. L.; Theiler, C.

    2015-05-01

    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 compare 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.

  7. Advanced methods in global gyrokinetic full f particle simulation of tokamak transport

    SciTech Connect

    Ogando, F.; Heikkinen, J. A.; Henriksson, S.; Janhunen, S. J.; Kiviniemi, T. P.; Leerink, S.

    2006-11-30

    A new full f nonlinear gyrokinetic simulation code, named ELMFIRE, has been developed for simulating transport phenomena in tokamak plasmas. The code is based on a gyrokinetic particle-in-cell algorithm, which can consider electrons and ions jointly or separately, as well as arbitrary impurities. The implicit treatment of the ion polarization drift and the use of full f methods allow for simulations of strongly perturbed plasmas including wide orbit effects, steep gradients and rapid dynamic changes. This article presents in more detail the algorithms incorporated into ELMFIRE, as well as benchmarking comparisons to both neoclassical theory and other codes.Code ELMFIRE calculates plasma dynamics by following the evolution of a number of sample particles. Because of using an stochastic algorithm its results are influenced by statistical noise. The effect of noise on relevant magnitudes is analyzed.Turbulence spectra of FT-2 plasma has been calculated with ELMFIRE, obtaining results consistent with experimental data.

  8. Nonequilibrium Gyrokinetic Fluctuation Theory and Sampling Noise in Gyrokinetic Particle-in-cell Simulations

    SciTech Connect

    John A. Krommes

    2007-10-09

    The present state of the theory of fluctuations in gyrokinetic GK plasmas and especially its application to sampling noise in GK particle-in-cell PIC simulations is reviewed. Topics addressed include the Δf method, the fluctuation-dissipation theorem for both classical and GK many-body plasmas, the Klimontovich formalism, sampling noise in PIC simulations, statistical closure for partial differential equations, the theoretical foundations of spectral balance in the presence of arbitrary noise sources, and the derivation of Kadomtsev-type equations from the general formalism.

  9. 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).

  10. Nonlinear theory of drift-cyclotron kinetics and the possible breakdown of gyro-kinetics

    SciTech Connect

    Waltz, R. E.; Deng Zhao

    2013-01-15

    A nonlinear theory of drift-cyclotron kinetics (termed cyclo-kinetics here) is formulated to test the breakdown of the gyro-kinetic approximations. Six dimensional cyclo-kinetics can be regarded as an extension of five dimensional gyro-kinetics to include high-frequency cyclotron waves, which can interrupt the low-frequency gyro-averaging in the (sixth velocity grid) gyro-phase angle. Nonlinear cyclo-kinetics has no limit on the amplitude of the perturbations. Formally, there is no gyro-averaging when all cyclotron (gyro-phase angle) harmonics of the perturbed distribution function (delta-f) are retained. Retaining only the (low frequency) zeroth cyclotron harmonic in cyclo-kinetics recovers both linear and nonlinear gyro-kinetics. Simple recipes are given for converting continuum nonlinear delta-f gyro-kinetic transport simulation codes to cyclo-kinetics codes by retaining (at least some) higher cyclotron harmonics.

  11. Effects of Plasma Shaping on Nonlinear Gyrokinetic Turbulence

    SciTech Connect

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

    2008-08-01

    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 (JET) [P.H. Rebut and B.E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on both 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 χ ~ κ-1.5 or κ-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.

  12. Measurement of plasma current dependent changes in impurity transport and comparison with nonlinear gyrokinetic simulation

    SciTech Connect

    Howard, N. T.; Greenwald, M.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Mikkelsen, D. R.; Candy, J.

    2012-05-15

    Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.

  13. Measurement of plasma current dependent changes in impurity transport and comparison with nonlinear gyrokinetic simulationa)

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; White, A. E.; Reinke, M. L.; Ernst, D.; Podpaly, Y.; Candy, J.

    2012-05-01

    Measured impurity transport coefficients are found to demonstrate a strong dependence on plasma current in the core of Alcator C-Mod. These measurements are compared directly with linear and nonlinear gyrokinetic simulation in an attempt to both qualitatively and quantitatively reproduce the measured impurity transport. Discharges constituting a scan of plasma current from 0.6 to 1.2 MA were performed during the 2010 run campaign. The impurity transport from these discharges was determined using a novel set of spectroscopic diagnostics available on Alcator C-Mod. This diagnostic suite allowed for the effective constraint of impurity transport coefficient profiles inside of r/a = 0.6. A decrease in the measured impurity diffusivity and inward convection is found with increased plasma current. Global, nonlinear gyrokinetic simulations were performed using the GYRO code [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] for all discharges in the experimental scan and are found to reproduce the experimental trends, while demonstrating good quantitative agreement with measurement. A more comprehensive quantitative comparison was performed on the 0.8 MA discharge of the current scan which demonstrates that simultaneous agreement between experiment and simulation in both the impurity particle transport and ion heat transport channels is attainable within experimental uncertainties.

  14. Linear and nonlinear verification of gyrokinetic microstability codes

    SciTech Connect

    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 of 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

  15. Linear and nonlinear verification of gyrokinetic microstability codes

    NASA Astrophysics Data System (ADS)

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

    2011-12-01

    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 of 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

  16. Nonlinear Gyrokinetics: A Powerful Tool for the Description of Microturbulence in Magnetized Plasmas

    SciTech Connect

    John E. Krommes

    2010-09-27

    Gyrokinetics is the description of low-frequency dynamics in magnetized plasmas. In magnetic-confinement fusion, it provides the most fundamental basis for numerical simulations of microturbulence; there are astrophysical applications as well. In this tutorial, a sketch of the derivation of the novel dynamical system comprising the nonlinear gyrokinetic (GK) equation (GKE) and the coupled electrostatic GK Poisson equation will be given by using modern Lagrangian and Lie perturbation methods. No background in plasma physics is required in order to appreciate the logical development. The GKE describes the evolution of an ensemble of gyrocenters moving in a weakly inhomogeneous background magnetic field and in the presence of electromagnetic perturbations with wavelength of the order of the ion gyroradius. Gyrocenters move with effective drifts, which may be obtained by an averaging procedure that systematically, order by order, removes gyrophase dependence. To that end, the use of the Lagrangian differential one-form as well as the content and advantages of Lie perturbation theory will be explained. The electromagnetic fields follow via Maxwell's equations from the charge and current density of the particles. Particle and gyrocenter densities differ by an important polarization effect. That is calculated formally by a "pull-back" (a concept from differential geometry) of the gyrocenter distribution to the laboratory coordinate system. A natural truncation then leads to the closed GK dynamical system. Important properties such as GK energy conservation and fluctuation noise will be mentioned briefly, as will the possibility (and diffculties) of deriving nonlinear gyro fluid equations suitable for rapid numerical solution -- although it is probably best to directly simulate the GKE. By the end of the tutorial, students should appreciate the GKE as an extremely powerful tool and will be prepared for later lectures describing its applications to physical problems.

  17. Measurements of core electron temperature and density fluctuations in DIII-D and comparison to nonlinear gyrokinetic simulations

    SciTech Connect

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

    2008-05-15

    For the first time, profiles (0.3<{rho}<0.9) of electron temperature and density fluctuations in a tokamak have been measured simultaneously and the results compared to nonlinear gyrokinetic simulations. Electron temperature and density fluctuations measured in neutral beam-heated, sawtooth-free low confinement mode (L-mode) plasmas in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are found to be similar in frequency and normalized amplitude, with amplitude increasing with radius. The measured radial profile of two fluctuation fields allows for a new and rigorous comparison with gyrokinetic results. Nonlinear gyrokinetic flux-tube simulations predict that electron temperature and density fluctuations have similar normalized amplitudes in L-mode. At {rho}=0.5, simulation results match experimental heat diffusivities and density fluctuation amplitude, but overestimate electron temperature fluctuation amplitude and particle diffusivity. In contrast, simulations at {rho}=0.75 do not match either the experimentally derived transport properties or the measured fluctuation levels.

  18. Particle pinch and collisionality in gyrokinetic simulations of tokamak plasma turbulence

    SciTech Connect

    Angioni, C.; Candy, J.; Waltz, R. E.; Fable, E.; Maslov, M.; Weisen, H.; Peeters, A. G.

    2009-06-15

    The generic problem of how, in a turbulent plasma, the experimentally relevant conditions of a particle flux very close to the null are achieved, despite the presence of strong heat fluxes, is addressed. Nonlinear gyrokinetic simulations of plasma turbulence in tokamaks reveal a complex dependence of the particle flux as a function of the turbulent spatial scale and of the velocity space as collisionality is increased. At experimental values of collisionality, the particle flux is found close to the null, in agreement with the experiment, due to the balance between inward and outward contributions at small and large scales, respectively. These simulations provide full theoretical support to the prediction of a peaked density profile in a future nuclear fusion reactor.

  19. Energetically consistent collisional gyrokinetics

    SciTech Connect

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

    2015-10-01

    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.

  20. Energetically consistent collisional gyrokinetics

    SciTech Connect

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

    2015-10-15

    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.

  1. Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

    NASA Astrophysics Data System (ADS)

    Hager, Robert; Chang, C. S.

    2016-04-01

    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 steep 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.

  2. Gyrokinetic neoclassical study of the bootstrap current in the tokamak edge pedestal with fully non-linear Coulomb collisions

    DOE PAGESBeta

    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

  3. Gyrokinetic particle simulations of kinetic ballooning mode in tokamak pedestal

    NASA Astrophysics Data System (ADS)

    Holod, Ihor

    2014-10-01

    The pedestal height and width in tokamak H-mode operation are widely believed to be constrained by mesoscale peeling-ballooning modes and microscopic kinetic ballooning modes (KBM). However, direct evidences of the KBM turbulence in pedestal are very limited. The role of the drift-Alfvenic microturbulence during the pedestal recovery period is not clear. Here we use gyrokinetic toroidal code (GTC) to study the edge instability of a DIII-D discharge #131997 using realistic geometry and plasma profiles and focusing on the pedestal region with steep pressure gradient. First, electrostatic simulations find a reactive trapped electron mode with an unusual eigenmode structure, which peaks at the poloidal angle θ = +/- π /2. The electron collisions decrease the growth rate by about one-half. Next, the plasma pressure is scanned in GTC electromagnetic simulations to identify the boundary for the KBM onset. At the finite electron beta an electromagnetic instability is found with KBM characteristics. The linear growth rate increases with βe and the mode propagation is in the ion diamagnetic direction. Nonlinear simulations of the KBM turbulence will also be presented. Work supported by DOE Grant DE-SC0010416, and in collaborations with GTC team.

  4. Gyrokinetic particle simulation of microturbulence for general magnetic geometry and experimental profiles

    SciTech Connect

    Xiao, Yong; Holod, Ihor; Wang, Zhixuan; Lin, Zhihong; Zhang, Taige

    2015-02-15

    Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.

  5. Gyrokinetic simulations of mesoscale energetic particle-driven Alfvenic turbulent transport embedded in microturbulence

    SciTech Connect

    Bass, E. M.; Waltz, R. E.

    2010-11-15

    Energetic particle (EP) transport from local high-n toroidal Alfven eigenmodes (TAEs) and energetic particle modes (EPMs) is simulated with a gyrokinetic code. Linear and nonlinear simulations have identified a parameter range where the longwave TAE and EPM are unstable alongside the well-known ion-temperature-gradient (ITG) and trapped-electron-mode (TEM) instabilities. A new eigenvalue solver in GYRO facilitates this mode identification. States of nonlinearly saturated local TAE/EPM turbulent intensity are identified, showing a 'soft' transport threshold for enhanced energetic particle transport against the TAE/EPM drive from the EP pressure gradient. The very long-wavelength (mesoscale) TAE/EPM transport is saturated partially by nonlinear interaction with microturbulent ITG/TEM-driven zonal flows. Fixed-gradient-length, nonlinearly saturated states are accessible over a relatively narrow range of EP pressure gradient. Within this range, and in the local limit employed, TAE/EPM-driven transport more closely resembles drift-wave microturbulent transport than 'stiff' ideal MHD transport with a clamped critical total pressure gradient. At a higher, critical EP pressure gradient, fixed-gradient nonlinear saturation fails: EP transport increases without limit and background transport decreases. Presumably saturation is then obtained by relaxation of the EP pressure gradient to near this critical EP pressure gradient. If the background plasma gradients driving the ITG/TEM turbulence and zonal flows are weakened, the critical gradient collapses to the TAE/EPM linear stability threshold. Even at the critical EP pressure gradient there is no evidence that TAE/EPM instability significantly increases transport in the background plasma channels.

  6. Relevance of the parallel nonlinearity in gyrokinetic simulations of tokamak plasmas

    SciTech Connect

    Candy, J.; Waltz, R. E.; Parker, S. E.; Chen, Y.

    2006-07-15

    The influence of the parallel nonlinearity on transport in gyrokinetic simulations is assessed for values of {rho}{sub *} which are typical of current experiments. Here, {rho}{sub *}={rho}{sub s}/a is the ratio of gyroradius, {rho}{sub s}, to plasma minor radius, a. The conclusion, derived from simulations with both GYRO [J. Candy and R. E. Waltz, J. Comput. Phys., 186, 585 (2003)] and GEM [Y. Chen and S. E. Parker J. Comput. Phys., 189, 463 (2003)] is that no measurable effect of the parallel nonlinearity is apparent for {rho}{sub *}<0.012. This result is consistent with scaling arguments, which suggest that the parallel nonlinearity should be O({rho}{sub *}) smaller than the ExB nonlinearity. Indeed, for the plasma parameters under consideration, the magnitude of the parallel nonlinearity is a factor of 8{rho}{sub *} smaller (for 0.000 75<{rho}{sub *}<0.012) than the other retained terms in the nonlinear gyrokinetic equation.

  7. Gyrokinetic study of the role of β on electron particle transport in tokamaks

    NASA Astrophysics Data System (ADS)

    Hein, T.; Angioni, C.; Fable, E.; Candy, J.

    2010-10-01

    Electromagnetic effects on the radial transport of electrons in the core of tokamak plasmas are studied by means of linear and nonlinear gyrokinetic simulations with the code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and by an analytical derivation. The impact of a finite β, that is, a finite ratio of the plasma pressure to the magnetic pressure, is considered on the fluctuations of the magnetic field through Ampére's law, as well as on the geometrical modification of the vertical drift produced by the Shafranov shift in the magnetic equilibrium, which, for realistic descriptions, has to be included in both electrostatic and electromagnetic modeling. The condition of turbulent particle flux at the null, which allows the determination of stationary logarithmic density gradients when neoclassical transport and particle sources are negligible, is investigated for increasing values of β, in regimes of ion temperature gradient and trapped electron mode turbulence. The loss of adiabaticity of passing electrons produced by fluctuations in the magnetic vector potential produces an outward convection. When the magnetic equilibrium geometry is kept fixed, this induces a strong reduction of the stationary logarithmic density gradient with increasing β. This effect is partly compensated by the geometrical effect on the vertical drift. This compensation effect, however, is significantly weaker in nonlinear simulations as compared to quasilinear calculations. A detailed comparison between quasilinear and nonlinear results reveals that the predicted value of the logarithmic density gradient is highly sensitive on the assumptions on the wave number spectrum applied in the quasilinear model. The qualitative consistency of the theoretical predictions with the experimental results obtained so far on the dependence of density peaking on β is discussed by considering the additional impact, with increasing β, of a particle source delivered by neutral beam

  8. Gyrokinetic study of the role of {beta} on electron particle transport in tokamaks

    SciTech Connect

    Hein, T.; Angioni, C.; Fable, E.; Candy, J.

    2010-10-15

    Electromagnetic effects on the radial transport of electrons in the core of tokamak plasmas are studied by means of linear and nonlinear gyrokinetic simulations with the code GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and by an analytical derivation. The impact of a finite {beta}, that is, a finite ratio of the plasma pressure to the magnetic pressure, is considered on the fluctuations of the magnetic field through Ampere's law, as well as on the geometrical modification of the vertical drift produced by the Shafranov shift in the magnetic equilibrium, which, for realistic descriptions, has to be included in both electrostatic and electromagnetic modeling. The condition of turbulent particle flux at the null, which allows the determination of stationary logarithmic density gradients when neoclassical transport and particle sources are negligible, is investigated for increasing values of {beta}, in regimes of ion temperature gradient and trapped electron mode turbulence. The loss of adiabaticity of passing electrons produced by fluctuations in the magnetic vector potential produces an outward convection. When the magnetic equilibrium geometry is kept fixed, this induces a strong reduction of the stationary logarithmic density gradient with increasing {beta}. This effect is partly compensated by the geometrical effect on the vertical drift. This compensation effect, however, is significantly weaker in nonlinear simulations as compared to quasilinear calculations. A detailed comparison between quasilinear and nonlinear results reveals that the predicted value of the logarithmic density gradient is highly sensitive on the assumptions on the wave number spectrum applied in the quasilinear model. The qualitative consistency of the theoretical predictions with the experimental results obtained so far on the dependence of density peaking on {beta} is discussed by considering the additional impact, with increasing {beta}, of a particle source delivered

  9. Gyrokinetics Simulation of Energetic Particle Turbulence and Transport

    SciTech Connect

    Diamond, Patrick H.

    2011-09-21

    Progress in research during this year elucidated the physics of precession resonance and its interaction with radial scattering to form phase space density granulations. Momentum theorems for drift wave-zonal flow systems involving precession resonance were derived. These are directly generalizable to energetic particle modes. A novel nonlinear, subcritical growth mechanism was identified, which has now been verified by simulation. These results strengthen the foundation of our understanding of transport in burning plasmas

  10. Energetically consistent collisional gyrokinetics

    DOE PAGESBeta

    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.

  11. Global gyrokinetic particle-in-cell simulations of internal kink instabilities

    SciTech Connect

    Mishchenko, Alexey; Zocco, Alessandro

    2012-12-15

    Internal kink instabilities have been studied in straight tokamak geometry employing an electromagnetic gyrokinetic particle-in-cell (PIC) code. The ideal-MHD internal kink mode and the collisionless m=1 tearing mode have been successfully simulated with the PIC code. Diamagnetic effects on the internal kink modes have also been investigated.

  12. Nonlinear gyrokinetic theory and its application to computation of the gyrocenter motion in ripple field

    NASA Astrophysics Data System (ADS)

    Zhu, Siqiang; Xu, Yingfeng; Wang, Shaojie

    2016-06-01

    The nonlinear gyrokinetic equation with full electromagnetic potential perturbations is derived by using the two-step transform procedure. The second-order transformed Hamiltonian can be simplified as /1 2 δ A∥ 2 , instead of /1 2 δ A 2 in the long-wave-length limit. A numerical code based on the I-transform method is improved to compute the gyrocenter orbit in the TFTR tokamak with a ripple field, and the numerical results indicate that the collisionless stochastic diffusion criterion agrees well with the theoretical prediction.

  13. Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations

    NASA Astrophysics Data System (ADS)

    Bottino, A.; Sonnendrücker, E.

    2015-10-01

    > The particle-in-cell (PIC) algorithm is the most popular method for the discretisation of the general 6D Vlasov-Maxwell problem and it is widely used also for the simulation of the 5D gyrokinetic equations. The method consists of coupling a particle-based algorithm for the Vlasov equation with a grid-based method for the computation of the self-consistent electromagnetic fields. In this review we derive a Monte Carlo PIC finite-element model starting from a gyrokinetic discrete Lagrangian. The variations of the Lagrangian are used to obtain the time-continuous equations of motion for the particles and the finite-element approximation of the field equations. The Noether theorem for the semi-discretised system implies a certain number of conservation properties for the final set of equations. Moreover, the PIC method can be interpreted as a probabilistic Monte Carlo like method, consisting of calculating integrals of the continuous distribution function using a finite set of discrete markers. The nonlinear interactions along with numerical errors introduce random effects after some time. Therefore, the same tools for error analysis and error reduction used in Monte Carlo numerical methods can be applied to PIC simulations.

  14. Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-β Plasmas

    SciTech Connect

    Lin, Zhihong

    2014-03-13

    Supported by this award, the PI and his research group at the University of California, Irvine (UCI) have carried out computational and theoretical studies of instability, turbulence, and transport in laboratory and space plasmas. Several massively parallel, gyrokinetic particle simulation codes have been developed to study electromagnetic turbulence in space and laboratory plasmas. In space plasma projects, the simulation codes have been successfully applied to study the spectral cascade and plasma heating in kinetic Alfven wave turbulence, the linear and nonlinear properties of compressible modes including mirror instability and drift compressional mode, and the stability of the current sheet instabilities with finite guide field in the context of collisionless magnetic reconnection. The research results have been published in 25 journal papers and presented at many national and international conferences. Reprints of publications, source codes, and other research-related information are also available to general public on the PI’s webpage (http://phoenix.ps.uci.edu/zlin/). Two PhD theses in space plasma physics are highlighted in this report.

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

    SciTech Connect

    Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; 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

    2008-09-18

    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 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 flow characteristics qualitatively like those observed in experiments.

  16. Nonlinear Gyrokinetic Turbulence Simulations of the NSTX Spherical Torus

    NASA Astrophysics Data System (ADS)

    Peterson, J. Luc; Hammett, G. W.; Mikkelsen, D.; Kaye, S.; Mazzucato, E.; Bell, R.; Leblanc, B.; Yuh, H.; Smith, D.; Candy, J.; Waltz, R. E.; Belli, E. A.; Staebler, G. M.; Kinsey, J.

    2010-11-01

    The National Spherical Torus Experiment provides a unique environment for the study of electron turbulence and transport. We present nonlinear GYROootnotetextJ. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003). simulations of microturbulence in NSTX discharges and make comparisons between numerically simulated and experimentally measured levels of electron-scale turbulence. In particular we examine the effects of magnetic shear, ExB shearing and collisionality on turbulence driven by the Electron Temperature Gradient (ETG) mode, while paying attention to the roles of electromagnetic fluctuations, kinetic ions and realistic experimental NSTX parameters. We also investigate the interplay between electron turbulence and transport using the TGYROootnotetextJ. Candy et al., Phys. Plasmas 16, 060704 (2009). simulation suite. This work is supported by the SciDAC Center for the Study of Plasma Microturbulence, DOE Contract DE-AC02-09CH11466, and used the resources of the National Center for Computational Sciences at ORNL, under DOE Contract DE-AC05-00OR22725.

  17. 3D hybrid simulations with gyrokinetic particle ions and fluid electrons

    SciTech Connect

    Belova, E.V.; Park, W.; Fu, G.Y.; Strauss, H.R.; Sugiyama, L.E.

    1998-12-31

    The previous hybrid MHD/particle model (MH3D-K code) represented energetic ions as gyrokinetic (or drift-kinetic) particles coupled to MHD equations using the pressure or current coupling scheme. A small energetic to bulk ion density ratio was assumed, n{sub h}/n{sub b} {much_lt} 1, allowing the neglect of the energetic ion perpendicular inertia in the momentum equation and the use of MHD Ohm`s law E = {minus}v{sub b} {times} B. A generalization of this model in which all ions are treated as gyrokinetic/drift-kinetic particles and fluid description is used for the electron dynamics is considered in this paper.

  18. Profile stiffness measurements in the Helically Symmetric experiment and comparison to nonlinear gyrokinetic calculations

    SciTech Connect

    Weir, G. M.; Faber, B. J.; Likin, K. M.; Talmadge, J. N.; Anderson, D. T.; Anderson, F. S. B.

    2015-05-15

    Stiffness measurements are presented in the quasi-helically symmetric experiment (HSX), in which the neoclassical transport is comparable to that in a tokamak and turbulent transport dominates throughout the plasma. Electron cyclotron emission is used to measure the local electron temperature response to modulated electron cyclotron resonant heating. The amplitude and phase of the heat wave through the steep electron temperature gradient (ETG) region of the plasma are used to determine a transient electron thermal diffusivity that is close to the steady-state diffusivity. The low stiffness in the region between 0.2 ≤ r/a ≤ 0.4 agrees with the scaling of the steady-state heat flux with temperature gradient in this region. These experimental results are compared to gyrokinetic calculations in a flux-tube geometry using the gyrokinetic electromagnetic numerical experiment code with two kinetic species. Linear simulations show that the ETG mode may be experimentally relevant within r/a ≤ 0.2, while the Trapped Electron Mode (TEM) is the dominant long-wavelength microturbulence instability across most of the plasma. The TEM is primarily driven by the density gradient. Non-linear calculations of the saturated heat flux driven by the TEM and ETG bracket the experimental heat flux.

  19. Verification of electromagnetic fluid-kinetic hybrid electron model in global gyrokinetic particle simulation

    SciTech Connect

    Holod, I.; Lin, Z.

    2013-03-15

    The fluid-kinetic hybrid electron model is verified in global gyrokinetic particle simulation of linear electromagnetic drift-Alfvenic instabilities in tokamak. In particular, we have recovered the {beta}-stabilization of the ion temperature gradient mode, transition to collisionless trapped electron mode, and the onset of kinetic ballooning mode as {beta}{sub e} (ratio of electron kinetic pressure to magnetic pressure) increases.

  20. Quantitative comparison of experimental impurity transport with nonlinear gyrokinetic simulation in an Alcator C-Mod L-mode plasma

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; Greenwald, M.; Mikkelsen, D. R.; Reinke, M. L.; White, A. E.; Ernst, D.; Podpaly, Y.; Candy, J.

    2012-06-01

    Nonlinear gyrokinetic simulations of impurity transport are compared to experimental impurity transport for the first time. The GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) was used to perform global, nonlinear gyrokinetic simulations of impurity transport for a standard Alcator C-Mod, L-mode discharge. The laser blow-off technique was combined with soft x-ray measurements of a single charge state of calcium to provide time-evolving profiles of this non-intrinsic, non-recycling impurity over a radial range of 0.0 ⩽ r/a ⩽ 0.6. Experimental transport coefficient profiles and their uncertainties were extracted from the measurements using the impurity transport code STRAHL and rigorous Monte Carlo error analysis. To best assess the agreement of gyrokinetic simulations with the experimental profiles, the sensitivity of the GYRO predicted impurity transport to a wide range of turbulence-relevant plasma parameters was investigated. A direct comparison of nonlinear gyrokinetic simulation and experiment is presented with an in depth discussion of error sources and a new data analysis methodology.

  1. Feasibility study for a correlation electron cyclotron emission turbulence diagnostic based on nonlinear gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    White, A. E.; Howard, N. T.; Mikkelsen, D. R.; Greenwald, M.; Candy, J.; Waltz, R. E.

    2011-11-01

    This paper describes the use of nonlinear gyrokinetic simulations to assess the feasibility of a new correlation electron cyclotron emission (CECE) diagnostic that has been proposed for the Alcator C-Mod tokamak (Marmar et al 2009 Nucl. Fusion 49 104014). This work is based on a series of simulations performed with the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545). The simulations are used to predict ranges of fluctuation level, peak poloidal wavenumber and radial correlation length of electron temperature fluctuations in the core of the plasma. The impact of antenna pattern and poloidal viewing location on measurable turbulence characteristics is addressed using synthetic diagnostics. An upper limit on the CECE sample volume size is determined. The modeling results show that a CECE diagnostic capable of measuring transport-relevant, long-wavelength (kθρs < 0.5) electron temperature fluctuations is feasible at Alcator C-Mod.

  2. Center for Gyrokinetic Particle Simulations of Turbulent Transport in Burning Plasmas

    SciTech Connect

    Scott, Parker

    2011-05-02

    This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of

  3. Gyrokinetic particle simulations of reversed shear Alfven eigenmode excited by antenna and fast ions

    SciTech Connect

    Deng Wenjun; Holod, Ihor; Xiao Yong; Lin Zhihong; Wang Xin; Zhang Wenlu

    2010-11-15

    Global gyrokinetic particle simulations of reversed shear Alfven eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfven continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations.

  4. Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection

    NASA Astrophysics Data System (ADS)

    Munoz Sepulveda, Patricio Alejandro; Büchner, Jörg; Kilian, Patrick; Told, Daniel; Jenko, Frank

    2016-07-01

    Fully kinetic Particle-in-Cell (PIC) simulations of (strong) guide-field reconnection can be computationally very demanding, due to the intrinsic stability and accuracy conditions required by this numerical method. One convenient approach to circumvent this issue is using gyrokinetic theory, an approximation of the Vlasov-Maxwell equations for strongly magnetized plasmas that eliminates the fast gyromotion, and thus reduces the computational cost. Although previous works have started to compare the features of reconnection between both approaches, a complete understanding of the differences is far from being complete. This knowledge is essential to discern the limitations of the gyrokinetic simulations of magnetic reconnection when applied to scenarios with moderate guide fields, such as the Solar corona, in contrast to most of the fusion/laboratory plasmas. We extend a previous work by our group, focused in the differences in the macroscopic flows, by analyzing the heating processes and non-thermal features developed by reconnection between both plasma approximations. We relate these processes by identifying some high-frequency cross-streaming instabilities appearing only in the fully kinetic approach. We characterize the effects of these phenonema such as anisotropic electron heating, beam formation and turbulence under different parameter regimes. And finally, we identify the conditions under which these instabilities tends to become negligible in the fully kinetic model, and thus a comparison with gyrokinetic theory becomes more reliable.

  5. Global gyrokinetic models for energetic particle driven Alfvén instabilities in 3D equilibria

    NASA Astrophysics Data System (ADS)

    Spong, Don; Holod, Ihor

    2015-11-01

    The GTC global gyrokinetic PIC model has been adapted to 3D VMEC equilibria and provides a new method for the analysis of Alfvénic instabilities in stellarators, 3D tokamaks, and helical RFP states. The gyrokinetic orderings (k||/k⊥ << 1, ω/Ωci << 1, ρEP/L << 1) are applicable to a range of energetic particle driven instabilities that have been observed in 3D configurations. Applications of this model to stellarators have indicated that a variety of different Alfvén instabilities can be excited, depending on the toroidal mode number, fast ion average energy and fast ion density profile. Both an LHD discharge where bursting n = 1 Alfvén activity in the TAE gap was observed and a W7-X case have been examined. TAE,/EAE/GAE modes have been found in the simulations, depending on the mode family and fast ion profiles used. The dynamical evolution of the instabilities shows the field period coupling between n and n + Nfp expected for a stellarator. The development of gyrofluid reduced models that can capture relevant physics aspects of the gyrokinetic models will also be discussed. Research sponsored by the U.S. Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC and the GSEP SciDAC Center.

  6. Understanding rotation profile structures in ECH-heated plasmas using nonlinear gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    Wang, Weixing; Brian, B.; Ethier, S.; Chen, J.; Startsev, E.; Diamond, P. H.; Lu, Z.

    2015-11-01

    A non-diffusive momentum flux connecting edge momentum sources/sinks and core plasma flow is required to establish the off-axis peaked ion rotation profile typically observed in ECH-heated DIII-D plasmas without explicit external momentum input. The understanding of the formation of such profile structures provides an outstanding opportunity to test the physics of turbulence driving intrinsic rotation, and validate first-principles-based gyrokinetic simulation models. Nonlinear, global gyrokinetic simulations of DIII-D ECH plasmas indicate a substantial ITG fluctuation-induced residual stress generated around the region of peaked toroidal rotation, along with a diffusive momentum flux. The residual stress profile shows an anti-gradient, dipole structure, which is critical for accounting for the formation of the peaked rotation profile. It is showed that both turbulence intensity gradient and zonal flow ExB shear contribute to the generation of k// asymmetry needed for residual stress generation. By balancing the simulated residual stress and the momentum diffusion, a rotation profile is calculated. In general, the radial structure of core rotation profile is largely determined by the residual stress profile, while the amplitude of core rotation depends on the edge toroidal rotation velocity, which is determined by edge physics and used as a boundary condition in our model. The calculated core rotation profile is consistent with the experimental measurements. Also discussed is the modification of turbulence-generated Reynolds stress on poloidal rotation in those plasmas. Work supported by U.S. DOE Contract DE-AC02-09-CH11466.

  7. The non-linear evolution of the tearing mode in electromagnetic turbulence using gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    Hornsby, W. A.; Migliano, P.; Buchholz, R.; Grosshauser, S.; Weikl, A.; Zarzoso, D.; Casson, F. J.; Poli, E.; Peeters, A. G.

    2016-01-01

    The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable {{Δ }\\prime}>0 current profile, is considered. The turbulence is able to seed the magnetic island and bypass the linear growth phase by generating structures that are approximately an ion gyro-radius in width. The non-linear evolution of the island width and its rotation frequency, after this seeding phase, is found to be modified and is dependent on the value of the plasma beta and equilibrium pressure gradients. At low values of beta the island evolves largely independent of the turbulence, while at higher values the interaction has a dramatic effect on island growth, causing the island to grow exponentially at the growth rate of its linear phase, even though the island is larger than linear theory validity. The turbulence forces the island to rotate in the ion-diamagnetic direction as opposed to the electron diamagnetic direction in which it rotates when no turbulence is present. In addition, it is found that the mode rotation slows as the island grows in size.

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

    SciTech Connect

    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 for 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.

  9. Gyrokinetic particle simulation of fast-electron driven beta-induced Aflvén eigenmode

    NASA Astrophysics Data System (ADS)

    Cheng, Junyi; Zhang, Wenlu; Lin, Zhihong; Holod, Ihor; Li, Ding; Chen, Yang; Cao, Jintao

    2016-05-01

    The fast-electron driven beta-induced Alfvén eigenmode (e-BAE) in toroidal plasmas is investigated for the first time using global gyrokinetic particle simulations, where the fast electron is described by the drift kinetic equation. The simulation shows that the e-BAE propagates in the fast electron diamagnetic direction and its polarization is close to an ideal MHD mode. The phase space structure shows that only the fast electron processional resonance is responsible for the e-BAE excitations while fast-ion driven BAE can be excited through all the channels, including transit, bounce, and processional resonance.

  10. Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas

    SciTech Connect

    Ma, Kwan-Liu

    2011-12-21

    In this project, we have developed techniques for visualizing large-scale time-varying multivariate particle and field data produced by the GPS_TTBP team. Our basic approach to particle data visualization is to provide the user with an intuitive interactive interface for exploring the data. We have designed a multivariate filtering interface for scientists to effortlessly isolate those particles of interest for revealing structures in densely packed particles as well as the temporal behaviors of selected particles. With such a visualization system, scientists on the GPS-TTBP project can validate known relationships and temporal trends, and possibly gain new insights in their simulations. We have tested the system using over several millions of particles on a single PC. We will also need to address the scalability of the system to handle billions of particles using a cluster of PCs. To visualize the field data, we choose to use direct volume rendering. Because the data provided by PPPL is on a curvilinear mesh, several processing steps have to be taken. The mesh is curvilinear in nature, following the shape of a deformed torus. Additionally, in order to properly interpolate between the given slices we cannot use simple linear interpolation in Cartesian space but instead have to interpolate along the magnetic field lines given to us by the scientists. With these limitations, building a system that can provide an accurate visualization of the dataset is quite a challenge to overcome. In the end we use a combination of deformation methods such as deformation textures in order to fit a normal torus into their deformed torus, allowing us to store the data in toroidal coordinates in order to take advantage of modern GPUs to perform the interpolation along the field lines for us. The resulting new rendering capability produces visualizations at a quality and detail level previously not available to the scientists at the PPPL. In summary, in this project we have

  11. Gyrokinetic particle simulation of beta-induced Alfven-acoustic eigenmode

    NASA Astrophysics Data System (ADS)

    Zhang, H. S.; Liu, Y. Q.; Lin, Z.; Zhang, W. L.

    2016-04-01

    The beta-induced Alfven-acoustic eigenmode (BAAE) in toroidal plasmas is verified and studied by global gyrokinetic particle simulations. When ion temperature is much lower than electron temperature, the existence of the weakly damped BAAE is verified in the simulations using initial perturbation, antenna excitation, and energetic particle excitation, respectively. When the ion temperature is comparable to the electron temperature, the unstable BAAE can be excited by realistic energetic particle density gradient, even though the stable BAAE (in the absence of energetic particles) is heavily damped by the thermal ions. In the simulations with reversed magnetic shear, BAAE frequency sweeping is observed and poloidal mode structure has a triangle shape with a poloidal direction similar to that observed in tokamak experiments. The triangle shape changes the poloidal direction, and no frequency sweeping is found in the simulations with normal magnetic shear.

  12. Quasisteady and steady states in global gyrokinetic particle-in-cell simulations

    SciTech Connect

    Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Bottino, A.; Angelino, P.

    2009-05-15

    Collisionless delta-f gyrokinetic particle-in-cell simulations suffer from the entropy paradox, in which the entropy grows linearly in time while low-order moments are saturated. As a consequence, these simulations do not reach a steady state and are unsuited to make quantitative predictions. A solution to this issue is the introduction of artificial dissipation. The notion of steady state in gyrokinetic simulations is studied by deriving an evolution equation for the fluctuation entropy and applying it to the global collisionless particle-in-cell code ORB5 [S. Jolliet et al., Comput. Phys. Commun. 177, 409 (2007)]. It is shown that a recently implemented noise-control algorithm [B. F. McMillan et al., Phys. Plasmas 15, 052308 (2008)] based on a W-stat provides the necessary dissipation to reach a steady state. The two interesting situations of decaying and driven turbulence are considered. In addition, it is shown that a separate heating algorithm, not based on a W-stat, does not lead to a statistical steady state.

  13. Center for Gyrokinetic/MHD Hybrid Simulation of Energetic Particle Physics in Toroidal Plasmas (CSEPP). Final report

    SciTech Connect

    Chen, Yang

    2012-03-07

    At Colorado University-Boulder the primary task is to extend our gyrokinetic Particle-in-Cell simulation of tokamak micro-turbulence and transport to the area of energetic particle physics. We have implemented a gyrokinetic ion/massless fluid electron hybrid model in the global {delta} f-PIC code GEM, and benchmarked the code with analytic results on the thermal ion radiative damping rate of Toroidal Alfven Eigenmodes (TAE) and with mode frequency and spatial structure from eigenmode analysis. We also performed nonlinear simulations of both a single-n mode (n is the toroidal mode number) and multiple-n modes, and in the case of single-n, benchmarked the code on the saturation amplitude vs. particle collision rate with analytical theory. Most simulations use the f method for both ions species, but we have explored the full-f method for energetic particles in cases where the burst amplitude of the excited instabilities is large as to cause significant re-distribution or loss of the energetic particles. We used the hybrid model to study the stability of high-n TAEs in ITER. Our simulations show that the most unstable modes in ITER lie in the rage of 10 < n < 20. Thermal ion pressure effect and alpha particles non-perturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about {beta}{sub {alpha}}(0) = 0.7% for the fully shaped ITER equilibrium. We also carried nonlinear simulations of the most unstable n = 15 mode and found that the saturation amplitude for the nominal ITER discharge is too low to cause large redistribution or loss of alpha particles. To include kinetic electron effects

  14. Nonlinear particle simulation of ion cyclotron waves in toroidal geometry

    SciTech Connect

    Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.

    2015-12-10

    Global particle simulation model has been developed in this work to provide a first-principles tool for studying the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation with realistic electron-to-ion mass ratio. Boris push scheme for the ion motion has been developed in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron and ion Bernstein waves in global gyrokinetic toroidal code (GTC). The nonlinear simulation capability is applied to study the parametric decay instability of a pump wave into an ion Bernstein wave side band and a low frequency ion cyclotron quasi mode.

  15. Center for Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasma

    SciTech Connect

    Viktor K. Decyk

    2008-04-24

    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 pointed 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

  16. Gyrokinetic particle-in-cell simulations of Alfvén eigenmodes in presence of continuum effects

    SciTech Connect

    Mishchenko, Alexey Könies, Axel; Hatzky, Roman

    2014-05-15

    First-principle gyrokinetic particle-in-cell simulations of a global Toroidal Alfvén Eigenmode (TAE) are undertaken in the presence of a strong coupling with the continuum. Effects of the bulk plasma temperature on the interplay between the TAE and Kinetic Alfvén Waves (KAWs) are investigated. A global TAE-KAW structure is identified which appears to be more unstable with respect to the fast ions than a simple (fluid-like) TAE mode.

  17. Nonlinear gyrokinetic theory based on a new method and computation of the guiding-center orbit in tokamaks

    SciTech Connect

    Xu, Yingfeng Dai, Zongliang; Wang, Shaojie

    2014-04-15

    The nonlinear gyrokinetic theory in the tokamak configuration based on the two-step transform is developed; in the first step, we transform the magnetic potential perturbation to the Hamiltonian part, and in the second step, we transform away the gyroangle-dependent part of the perturbed Hamiltonian. Then the I-transform method is used to decoupled the perturbation part of the motion from the unperturbed motion. The application of the I-transform method to the computation of the guiding-center orbit and the guiding-center distribution function in tokamaks is presented. It is demonstrated that the I-transform method of the orbit computation which involves integrating only along the unperturbed orbit agrees with the conventional method which integrates along the full orbit. A numerical code based on the I-transform method is developed and two numerical examples are given to verify the new method.

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

    SciTech Connect

    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 SciDAC 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.

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

    SciTech Connect

    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.

    2008-10-15

    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{sub o}{approx}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{sub {theta}}{<=}1.8 cm{sup -1} and k{sub r}{<=}4 cm{sup -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

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

    NASA Astrophysics Data System (ADS)

    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 wo˜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 kθ≤1.8 cm-1 and kr≤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

  1. 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. PMID:19044712

  2. Nonlinear dynamics of beta-induced Alfvén eigenmode driven by energetic particles.

    PubMed

    Wang, X; Briguglio, S; Chen, L; Di Troia, C; Fogaccia, G; Vlad, G; Zonca, F

    2012-10-01

    Nonlinear saturation of a beta-induced Alfvén eigenmode, driven by slowing down energetic particles via transit resonance, is investigated by the nonlinear hybrid magnetohyrodynamic gyrokinetic code. Saturation is characterized by frequency chirping and symmetry breaking between co- and counter-passing particles, which can be understood as the evidence of resonance detuning. The scaling of the saturation amplitude with the growth rate is also demonstrated to be consistent with radial resonance detuning due to the radial nonuniformity and mode structure. PMID:23214643

  3. Geometric Gyrokinetic Theory for Edge Plasma

    SciTech Connect

    Qin, H; Cohen, R H; Nevins, W M; Xu, X Q

    2007-01-18

    It turns out that gyrokinetic theory can be geometrically formulated as special cases of a geometrically generalized Vlasov-Maxwell system. It is proposed that the phase space of the spacetime is a 7-dimensional fiber bundle P over the 4-dimensional spacetime M, and that a Poincare-Cartan-Einstein 1-form {gamma} on the 7-dimensional phase space determines particles worldlines in the phase space. Through Liouville 6-form {Omega} and fiber integral, the 1-form {gamma} also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system. In its most general form, gyrokinetic theory is about a symmetry, called gyro-symmetry, for magnetized plasmas, and the 1-form {gamma} again uniquely defines the gyro-symmetry. The objective is to decouple the gyro-phase dynamics from the rest of particle dynamics by finding the gyro-symmetry in {gamma}. Compared with other methods of deriving the gyrokinetic equations, the advantage of the geometric approach is that it allows any approximation based on mathematical simplification or physical intuition to be made at the 1-form level, and yet the field theories still have the desirable exact conservation properties such as phase space volume conservation and energy-momentum conservation if the 1-form does not depend on the spacetime coordinate explicitly. A set of generalized gyrokinetic equations valid for the edge plasmas is then derived using this geometric method. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. The fact that we adopted the geometric method in the present study does not necessarily imply that the major results reported here can not be achieved using classical methods. What the

  4. Continuum Edge Gyrokinetic Theory and Simulations

    SciTech Connect

    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

    2007-01-09

    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 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.

  5. Generalized Covariant Gyrokinetic Dynamics of Magnetoplasmas

    SciTech Connect

    Cremaschini, C.; Tessarotto, M.; Nicolini, P.; Beklemishev, A.

    2008-12-31

    A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory (Beklemishev et al., 1999-2005). Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out (Tessarotto et al., 2007) which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.

  6. Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges

    NASA Astrophysics Data System (ADS)

    Sung, C.; White, A. E.; Mikkelsen, D. R.; Greenwald, M.; Holland, C.; Howard, N. T.; Churchill, R.; Theiler, C.

    2016-04-01

    Long wavelength turbulent electron temperature fluctuations (kyρs < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (kyρs ≲ 1.7) performed at r/a ˜ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the "Transport Shortfall" [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].

  7. Performance of the UCAN2 Gyrokinetic Particle In Cell (PIC) Code on Two Massively Parallel Mainframes with Intel ``Sandy Bridge'' Processors

    NASA Astrophysics Data System (ADS)

    Leboeuf, Jean-Noel; Decyk, Viktor; Newman, David; Sanchez, Raul

    2013-10-01

    The massively parallel, 2D domain-decomposed, nonlinear, 3D, toroidal, electrostatic, gyrokinetic, Particle in Cell (PIC), Cartesian geometry UCAN2 code, with particle ions and adiabatic electrons, has been ported to two emerging mainframes. These two computers, one at NERSC in the US built by Cray named Edison and the other at the Barcelona Supercomputer Center (BSC) in Spain built by IBM named MareNostrum III (MNIII) just happen to share the same Intel ``Sandy Bridge'' processors. The successful port of UCAN2 to MNIII which came online first has enabled us to be up and running efficiently in record time on Edison. Overall, the performance of UCAN2 on Edison is superior to that on MNIII, particularly at large numbers of processors (>1024) for the same Intel IFORT compiler. This appears to be due to different MPI modules (OpenMPI on MNIII and MPICH2 on Edison) and different interconnection networks (Infiniband on MNIII and Cray's Aries on Edison) on the two mainframes. Details of these ports and comparative benchmarks are presented. Work supported by OFES, USDOE, under contract no. DE-FG02-04ER54741 with the University of Alaska at Fairbanks.

  8. The effect of plasma shaping on turbulent transport and ExB shear quenching in nonlinear gyrokinetic simulations

    SciTech Connect

    Kinsey, J. E.; Waltz, R. E.; Candy, J.

    2007-10-15

    Nonlinear gyrokinetic simulations with kinetic electron dynamics are used to study the effects of plasma shaping on turbulent transport and ExB shear in toroidal geometry including the presence of kinetic electrons using the GYRO code. Over 120 simulations comprised of systematic scans were performed around several reference cases in the local, electrostatic, collisionless limit. Using a parameterized local equilibrium model for shaped geometry, the GYRO simulations show that elongation {kappa} (and its gradient) stabilizes the energy transport from ion temperature gradient (ITG) and trapped electron mode (TEM) instabilities at fixed midplane minor radius. For scans around a reference set of parameters, the GYRO ion energy diffusivity, in gyro-Bohm units, approximately follows a {kappa}{sup -1} scaling which is qualitatively similar to recent experimental energy confinement scalings. Most of the {kappa} scaling is due to the shear in the elongation rather than the local {kappa} itself. The {kappa} scaling for the electrons is found to vary and can be stronger or weaker than {kappa}{sup -1} depending on the wavenumber where the transport peaks. The {kappa} scaling is weaker when the energy diffusivity peaks at low wavenumbers and is stronger when the peak occurs at high wavenumbers. The simulations also demonstrate a nonlinear upshift in the critical temperature gradient as the elongation increases due to an increase in the residual zonal flow amplitude. Triangularity is found to be slightly destabilizing and its effect is strongest for highly elongated plasmas. Finally, we find less ExB shear is needed to quench the transport at high elongation and low aspect ratio. A new linear ExB shear quench rule, valid for shaped tokamak geometry, is presented.

  9. Gyrokinetic simulation of global and local Alfven eigenmodes driven by energetic particles in a DIII-D discharge

    SciTech Connect

    Bass, E. M.; Waltz, R. E.

    2013-01-15

    The unstable spectrum of Alfven eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfven eigenmode (RSAE) at toroidal mode number n=3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfven eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E Multiplication-Sign B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfven eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.

  10. Gyrokinetic simulation of current-driven instabilities

    NASA Astrophysics Data System (ADS)

    McClenaghan, Joseph

    The gyrokinetic toroidal code(GTC) capability has been extended for simulating current-driven instabilities in magnetized plasmas such as kink and resistive tearing modes with kinetic effects. This new gyrokinetic capability enables first-principles, integrated simulations of macroscopic magnetohydrodynamic(MHD) modes, which limit the performance of burning plasmas and threaten the integrity of fusion devices. The excitation and evolution of macroscopic MHD modes often depend on the kinetic effects at microscopic scales and the nonlinear coupling of multiple physical processes. GTC simulation in the fluid limit of the internal kink modes in cylindrical geometry has been verified by benchmarking with an MHD eigenvalue code. The global simulation domain covers the magnetic axis which is necessary for simulating the macroscopic MHD modes. Gyrokinetic simulations of the internal 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. This new GTC capability for current-driven instability has now been extended to simulate fishbone instabilities excited by energetic particles and resistive tearing modes. GTC has also been applied to study the internal kink modes in astrophysical jets that are formed around supermassive black holes. Linear simulations find that the internal kink modes in astrophysical jets are unstable with a broad eigenmode. Nonlinear saturation amplitude of these kink modes is observed to be small, suggesting that the jets can remain collimated even in the presence of the internal kink modes. Generation of a mean parallel electric field by the nonlinear dynamics of internal kink modes and the potential implication of this field on particle acceleration in jets has been examined.

  11. Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence

    SciTech Connect

    Tatsuno, T.; Dorland, W.; Plunk, G. G.; Schekochihin, A. A.; Barnes, M.

    2009-07-03

    Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

  12. Comment on 'Nonlinear gyrokinetic theory with polarization drift' [Phys. Plasmas 17, 082304 (2010)

    SciTech Connect

    Leerink, S.; Parra, F. I.; Heikkinen, J. A.

    2010-12-15

    In this comment, we show that by using the discrete particle distribution function the changes of the phase-space volume of gyrocenter coordinates due to the fluctuating ExB velocity do not explicitly appear in the Poisson equation and the [Sosenko et al., Phys. Scr. 64, 264 (2001)] result is recovered. It is demonstrated that there is no contradiction between the work presented by Sosenko et al. and the work presented by [Wang et al., Phys. Plasmas 17, 082304 (2010)].

  13. LIGKA: A linear gyrokinetic code for the description of background kinetic and fast particle effects on the MHD stability in tokamaks

    SciTech Connect

    Lauber, Ph. Guenter, S.; Koenies, A.; Pinches, S.D.

    2007-09-10

    In a plasma with a population of super-thermal particles generated by heating or fusion processes, kinetic effects can lead to the additional destabilisation of MHD modes or even to additional energetic particle modes. In order to describe these modes, a new linear gyrokinetic MHD code has been developed and tested, LIGKA (linear gyrokinetic shear Alfven physics) [Ph. Lauber, Linear gyrokinetic description of fast particle effects on the MHD stability in tokamaks, Ph.D. Thesis, TU Muenchen, 2003; Ph. Lauber, S. Guenter, S.D. Pinches, Phys. Plasmas 12 (2005) 122501], based on a gyrokinetic model [H. Qin, Gyrokinetic theory and computational methods for electromagnetic perturbations in tokamaks, Ph.D. Thesis, Princeton University, 1998]. A finite Larmor radius expansion together with the construction of some fluid moments and specification to the shear Alfven regime results in a self-consistent, electromagnetic, non-perturbative model, that allows not only for growing or damped eigenvalues but also for a change in mode-structure of the magnetic perturbation due to the energetic particles and background kinetic effects. Compared to previous implementations [H. Qin, mentioned above], this model is coded in a more general and comprehensive way. LIGKA uses a Fourier decomposition in the poloidal coordinate and a finite element discretisation in the radial direction. Both analytical and numerical equilibria can be treated. Integration over the unperturbed particle orbits is performed with the drift-kinetic HAGIS code [S.D. Pinches, Ph.D. Thesis, The University of Nottingham, 1996; S.D. Pinches et al., CPC 111 (1998) 131] which accurately describes the particles' trajectories. This allows finite-banana-width effects to be implemented in a rigorous way since the linear formulation of the model allows the exchange of the unperturbed orbit integration and the discretisation of the perturbed potentials in the radial direction. Successful benchmarks for toroidal Alfven

  14. Gyrokinetic simulation of internal kink modes

    SciTech Connect

    Naitou, Hiroshi; Tsuda, Kenji; Lee, W.W.; Sydora, R.D.

    1995-05-01

    Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode ({delta}f code). The latter, a recent addition, is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction. The plasma is initially uniformly distributed in a square cross section with perfectly conducting walls. The linear mode structure of an unstable m = 1 (poloidal) and n = 1 (toroidal) kinetic internal kink mode is clearly observed, especially in the {delta}f code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth. This is consistent with the theory in which electron inertia has a dominant role. The nonlinear behavior of the mode is found to be quite similar for both codes. Full reconnection in the Alfven time scale is observed along with the electrostatic potential structures created during the full reconnection phase. The E x B drift due to this electrostatic potential dominates the nonlinear phase of the development after the full reconnection.

  15. Gyrokinetic simulations of ion and impurity transport

    SciTech Connect

    Estrada-Mila, C.; Candy, J.; Waltz, R.E.

    2005-02-01

    A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating the potential for fuel separation in a burning plasma. Quasilinear theory together with linear simulations shows that the symmetry breaking which enhances the tritium confinement arises largely from finite-Larmor-radius effects. To justify the numerical methods used in the paper, a variety of linear benchmarks and nonlinear grid refinement studies are detailed.

  16. Gyrokinetic microtearing turbulence.

    PubMed

    Doerk, H; Jenko, F; Pueschel, M J; Hatch, D R

    2011-04-15

    The nonlinear dynamics of microtearing modes in standard tokamak plasmas are investigated by means of ab initio gyrokinetic simulations. The saturation levels of the magnetic field fluctuations can be understood in the framework of a balance between (small poloidal wave number) linear drive and small-scale dissipation. The resulting heat transport is dominated by the electron magnetic component, and the transport levels are found to be experimentally relevant. Microtearing modes thus constitute another candidate for explaining turbulent transport in such toroidal systems. PMID:21568567

  17. Wavenumber-resolved core turbulence studies in the ASDEX Upgrade tokamak and comparison with non-linear gyrokinetic simulations with the GENE code

    NASA Astrophysics Data System (ADS)

    Happel, Tim; Bañón Navarro, Alejandro; Conway, Garrard; Görler, Tobias; Jenko, Frank; Ryter, Francois; Stroth, Ulrich; ASDEX Upgrade Team

    2014-10-01

    Core plasma turbulence determines transport properties and impacts on the efficiency of a fusion reactor. Gyrokinetic codes are developed to predict dominant instabilities and the turbulence level, which causes the observed particle and heat losses. A careful validation of these codes is mandatory to improve the reliability of predictions. To this end, core turbulence is investigated in ASDEX Upgrade by means of Doppler reflectometry, which provides the perpendicular velocity of turbulent structures and their fluctuation level. H-mode discharges have been performed in which ECRH is used to drive the turbulence from the ITG turbulence regime towards the TEM regime. In general, the turbulence level increases from core towards the edge. With increasing R /LTe , core large scale structures show larger fluctuation amplitudes while their phase velocity is altered with respect to that of small structures. Results are compared with gyrokinetic simulations with the GENE code. Linear results show a transition from ITG towards TEM turbulence close to the radial ECRH deposition location. After matching of heat fluxes to results from power balance analysis, the radial trend in the turbulence level is reproduced. The response to additional heating is opposite to the experimental findings.

  18. Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

    SciTech Connect

    Dorf, M. A.; Cohen, R. H.; Dorr, M.; Rognlien, T.; Hittinger, J.; Compton, J.; Colella, P.; Martin, D.; McCorquodale, P.

    2013-01-15

    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{sub Parallel-To }, {mu}) 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{sub Parallel-To} and {mu} 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. 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.

  19. Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

    DOE PAGESBeta

    Dorf, M. A.; Cohen, R. H.; Dorr, M.; Rognlien, T.; Hittinger, J.; Compton, J.; Colella, P.; Martin, D.; McCorquodale, P.

    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

  20. Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

    SciTech Connect

    Dorf, M. A.; Cohen, R. H.; Dorr, M.; Rognlien, T.; Hittinger, J.; Compton, J.; Colella, P.; Martin, D.; McCorquodale, P.

    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. 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.

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

    NASA Astrophysics Data System (ADS)

    McClenaghan, J.; Lin, Z.; Holod, I.; Deng, W.; Wang, Z.

    2014-12-01

    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.

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

    SciTech Connect

    McClenaghan, J.; Lin, Z.; Holod, I.; Deng, W.; Wang, Z.

    2014-12-15

    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.

  3. A Gyrokinetic Approach to Low Frequency Anisotropy-Driven Instabilities in the Solar Wind

    NASA Astrophysics Data System (ADS)

    Johnson, J.; Porazik, P.

    2014-12-01

    Observational surveys of temperature anisotropy in the solar wind indicate that anisotropy is bounded over a wide range of plasma beta and the anisotropy bounds appear to be predominately controlled by wave-particle interactions associated with mirror and oblique firehose instabilities. We present a reduced kinetic description that exploits gyrosymmetry (a symmetry associated with the gyromotion), providing an efficient, self-consistent approach that can be utilized in global models of the solar wind. We discuss the underlying physics of the mirror and firehose instabilities that allow for a reduced gyrokinetic description, and we verify the approach through comparisons of theory and simulations using gyrokinetic, hybrid, and fully kinetic descriptions. We present simulations showing the nonlinear development and saturation of the mirror instability and explain the amplitude and structure of the nonlinear state in terms of particle trapping. We also consider the nonlinear development of the oblique firehose instability and the associated wave spectra.

  4. Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows

    SciTech Connect

    Muñoz, P. A. Kilian, P.; Büchner, J.; Told, D.; Jenko, F.

    2015-08-15

    In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (b{sub g}). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (β{sub i} = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (b{sub g} ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (b{sub g} ≳ 5). Kinetic PIC simulations using guide fields b{sub g} ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (β{sub i} = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (b{sub g} ≲ 3)

  5. Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows

    NASA Astrophysics Data System (ADS)

    Muñoz, P. A.; Told, D.; Kilian, P.; Büchner, J.; Jenko, F.

    2015-08-01

    In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (bg). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (βi = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (bg ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (bg ≳ 5). Kinetic PIC simulations using guide fields bg ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (βi = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (bg ≲ 3).

  6. Exact momentum conservation laws for the gyrokinetic Vlasov-Poisson equations

    SciTech Connect

    Brizard, Alain J.; Tronko, Natalia

    2011-08-15

    The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas 7, 4816 (2000)]. From the gyrokinetic Noether canonical-momentum equation derived by the Noether method, the gyrokinetic parallel momentum equation and other gyrokinetic Vlasov-moment equations are obtained. In addition, an exact gyrokinetic toroidal angular-momentum conservation law is derived in axisymmetric tokamak geometry, where the transport of parallel-toroidal momentum is related to the radial gyrocenter polarization, which includes contributions from the guiding-center and gyrocenter transformations.

  7. A new hybrid kinetic electron model for full-f gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    Idomura, Y.

    2016-05-01

    A new hybrid kinetic electron model is developed for electrostatic full-f gyrokinetic simulations of the ion temperature gradient driven trapped electron mode (ITG-TEM) turbulence at the ion scale. In the model, a full kinetic electron model is applied to the full-f gyrokinetic equation, the multi-species linear Fokker-Planck collision operator, and an axisymmetric part of the gyrokinetic Poisson equation, while in a non-axisymmetric part of the gyrokinetic Poisson equation, turbulent fluctuations are determined only by kinetic trapped electrons responses. By using this approach, the so-called ωH mode is avoided with keeping important physics such as the ITG-TEM, the neoclassical transport, the ambipolar condition, and particle trapping and detrapping processes. The model enables full-f gyrokinetic simulations of ITG-TEM turbulence with a reasonable computational cost. Comparisons between flux driven ITG turbulence simulations with kinetic and adiabatic electrons are presented. Although the similar ion temperature gradients with nonlinear upshift from linear critical gradients are sustained in quasi-steady states, parallel flows and radial electric fields are qualitatively different with kinetic electrons.

  8. Transport in gyrokinetic tokamaks

    SciTech Connect

    Mynick, H.E.; Parker, S.E.

    1995-01-01

    A comprehensive study of transport in full-volume gyrokinetic (gk) simulations of ion temperature gradient driven turbulence in core tokamak plasmas is presented. Though this ``gyrokinetic tokamak`` is much simpler than experimental tokamaks, such simplicity is an asset, because a dependable nonlinear transport theory for such systems should be more attainable. Toward this end, we pursue two related lines of inquiry. (1) We study the scalings of gk tokamaks with respect to important system parameters. In contrast to real machines, the scalings of larger gk systems (a/{rho}{sub s} {approx_gt} 64) with minor radius, with current, and with a/{rho}{sub s} are roughly consistent with the approximate theoretical expectations for electrostatic turbulent transport which exist as yet. Smaller systems manifest quite different scalings, which aids in interpreting differing mass-scaling results in other work. (2) With the goal of developing a first-principles theory of gk transport, we use the gk data to infer the underlying transport physics. The data indicate that, of the many modes k present in the simulation, only a modest number (N{sub k} {approximately} 10) of k dominate the transport, and for each, only a handful (N{sub p} {approximately} 5) of couplings to other modes p appear to be significant, implying that the essential transport physics may be described by a far simpler system than would have been expected on the basis of earlier nonlinear theory alone. Part of this analysis is the inference of the coupling coefficients M{sub kpq} governing the nonlinear mode interactions, whose measurement from tokamak simulation data is presented here for the first time.

  9. Gyrokinetic simulation of isotope scaling in tokamak plasmas

    SciTech Connect

    Lee, W.W.; Santoro, R.A.

    1995-07-01

    A three-dimensional global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H{sup +}), deuterium (D{sup +}) and tritium (T{sup +}), we have found that, under otherwise identical conditions, there exists a favorable isotope scaling for the ion thermal diffusivity, i.e., Xi decreases with mass. Such a scaling, which exists both at the saturation of the instability and also at the nonlinear steady state, can be understood from the resulting wavenumber and frequency spectra.

  10. Nonlinear energetic particle transport in the presence of multiple Alfvénic waves in ITER

    NASA Astrophysics Data System (ADS)

    Schneller, M.; Lauber, Ph; Briguglio, S.

    2016-01-01

    This work presents the results of a multi-mode iter study on toroidal Alfvén eigenmodes (TAEs), using the nonlinear hybrid Hagis-Ligka model. It is found that main conclusions from earlier studies of Asdex Upgrade discharges can be transferred to the iter scenario: global, nonlinear effects are crucial for the evolution of the multi-mode scenario. This work focuses on the iter 15 MA baseline scenario with a safety factor at the magnetic axis of q 0  =  0.986. The least damped eigenmodes of the system are identified with the gyrokinetic, non-perturbative Ligka solver, concerning the mode structure, frequency and damping. Taking into account all weakly damped modes that can be identified linearly, nonlinear simulations with Hagis reveal strong multi-mode behaviour: while in some parameter ranges, quasilinear estimates turn out to be reasonable approximations for the nonlinearly relaxed energetic particle (EP) profile, under certain conditions low-n TAE branches can be excited. As a consequence, not only grow amplitudes of all modes to (up to orders of magnitude) higher values compared to the single mode cases but also, strong redistribution is triggered in the outer radial area between \\sqrt{{{{\\hatρ}}\\text{pol}}}=0.6 and 0.85, far above quasilinear estimates.

  11. Nonlinear particle behavior during cross-type optical particle separation

    SciTech Connect

    Kim, Sang Bok; Lee, Kyung Heon; Sung, Hyung Jin; Kim, Sang Soo

    2009-12-28

    The effects of varying the ratio of the optical force to the viscous drag force, termed S, on cross-type optical particle separation were investigated experimentally to test previous theoretical predictions. The experiments were performed for various flow velocities, powers of the laser beam, and radii of the laser beam waist and the particles. The behaviors of the particles during optical separation were examined by measuring the retention distances and analyzing the particle trajectories. For small values of S, the particles move with constant velocity in the flow direction and the retention distance increases linearly with S. However, the particles accelerate and decelerate within the laser beam and the retention distance increases nonlinearly with S when S increases further.

  12. Linearized model collision operators for multiple ion species plasmas and gyrokinetic entropy balance equations

    SciTech Connect

    Sugama, H.; Watanabe, T.-H.; Nunami, M.

    2009-11-15

    Linearized model collision operators for multiple ion species plasmas are presented that conserve particles, momentum, and energy and satisfy adjointness relations and Boltzmann's H-theorem even for collisions between different particle species with unequal temperatures. The model collision operators are also written in the gyrophase-averaged form that can be applied to the gyrokinetic equation. Balance equations for the turbulent entropy density, the energy of electromagnetic fluctuations, the turbulent transport fluxes of particle and heat, and the collisional dissipation are derived from the gyrokinetic equation including the collision term and Maxwell equations. It is shown that, in the steady turbulence, the entropy produced by the turbulent transport fluxes is dissipated in part by collisions in the nonzonal-mode region and in part by those in the zonal-mode region after the nonlinear entropy transfer from nonzonal to zonal modes.

  13. Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. III. Collisionless tearing mode

    NASA Astrophysics Data System (ADS)

    Liu, Dongjian; Bao, Jian; Han, Tao; Wang, Jiaqi; Lin, Zhihong

    2016-02-01

    A finite-mass electron fluid model for low frequency electromagnetic fluctuations, particularly the collisionless tearing mode, has been implemented in the gyrokinetic toroidal code. Using this fluid model, linear properties of the collisionless tearing mode have been verified. Simulations verify that the linear growth rate of the single collisionless tearing mode is proportional to De2, where De is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to De in the parameter regime of fusion plasmas.

  14. Nonlinear electrophoresis of ideally polarizable particles

    NASA Astrophysics Data System (ADS)

    Figliuzzi, Bruno; Chan, Wai Hong Ronald; Buie, Cullen R.

    2013-11-01

    We focus in this presentation on the nonlinear electrophoresis of ideally polarizable particles. At high applied voltages, significant ionic exchanges occur between the EDL which surrounders the particle and the bulk solution. In this situation, the velocity field, the electric potential and the ionic concentration at the immediate vicinity of the particle are described by a complicated set of coupled nonlinear partial differential equations. These equations are classically considered in the limit of a weak applied field, which enables further analytical progress (Khair and Squires, Phys. Fluids, 2010). However, in the general case, the equation governing the electrophoretic motion of the particle must be solved numerically. In this study, we rely on a numerical approach to determine the electric potential, ionic concentration and velocity field in the bulk solution surrounding the particle. The numerical simulations use a pseudo-spectral which was used successfully by Chu and Bazant to determine the electric potential and the ionic concentration around an ideally polarizable metallic sphere (Physical Review E, 2006). Our numerical model also incorporates the steric model developed by Kilic et al. in 2007 to account for crowding effects in the electric double layer.

  15. A Short Introduction to General Gyrokinetic Theory

    SciTech Connect

    H. Qin

    2005-02-14

    Interesting plasmas in the laboratory and space are magnetized. General gyrokinetic theory is about a symmetry, gyro-symmetry, in the Vlasov-Maxwell system for magnetized plasmas. The most general gyrokinetic theory can be geometrically formulated. First, the coordinate-free, geometric Vlasov-Maxwell equations are developed in the 7-D phase space, which is defined as a fiber bundle over the space-time. The Poincar{copyright}-Cartan-Einstein 1-form pullbacked onto the 7-D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinite small generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincar{copyright}-Cartan-Einstein 1-form, which also generates the most relaxed condition under which the gyro-symmetry still exists. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Since the general gyrokinetic system-developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and Liouville volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered. Three examples of applications of the general gyrokinetic theory developed in the areas of plasma equilibrium and plasma waves are

  16. Gyrokinetic simulation of global and local Alfvén eigenmodes driven by energetic particles in a DIII-D discharge

    NASA Astrophysics Data System (ADS)

    Bass, E. M.; Waltz, R. E.

    2013-01-01

    The unstable spectrum of Alfvén eigenmodes (AEs) driven by neutral beam-sourced energetic particles (EPs) in a benchmark DIII-D discharge (142111) is calculated in a fully gyrokinetic model using the GYRO code's massively parallel linear eigenvalue solver. One cycle of the slow (equilibrium scale) frequency sweep of the reverse shear Alfvén eigenmode (RSAE) at toroidal mode number n =3 is mapped. The RSAE second harmonic and an unstable beta-induced Alfvén eigenmode (BAE) are simultaneously tracked alongside the primary RSAE. An observed twist in the eigenmode pattern, caused mostly by shear in the driving EP profile, is shown through artificially varying the E ×B rotational velocity shear to depend generally on shear in the local wave phase velocity. Coupling to the BAE and to the toroidal Alfvén eigenmode limit the RSAE frequency sweeps at the lower and upper end, respectively. While the present fully gyrokinetic model (including thermal ions and electrons) constitutes the best treatment of compressibility physics available, the BAE frequency is overpredicted by about 20% against experiment here and is found to be sensitive to energetic beam ion pressure. The RSAE frequency is more accurately matched except when it is limited by the BAE. Simulations suggest that the experiment is very close to marginal AE stability at points of RSAE-BAE coupling. A recipe for comparing the radial profile of quasilinear transport flux from local modes to that from global modes paves the way for the development of a stiff (critical gradient) local AE transport model based on local mode stability thresholds.

  17. Gyrokinetic particle simulation of neoclassical transport in the pedestal/scrape-off region of a tokamak plasma

    NASA Astrophysics Data System (ADS)

    Ku, S.; Chang, C.-S.; Adams, M.; Cummings, J.; Hinton, F.; Keyes, D.; Klasky, S.; Lee, W.; Lin, Z.; Parker, S.; CPES Team

    2006-09-01

    A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.

  18. Gyrokinetic particle simulation of neoclassical transport in the pedestal/scrape-off region of a tokamak plasma

    SciTech Connect

    Adams, Mark; Chang, C. S.; Cummings, J.; Hinton, F.; Keyes, David E; Klasky, Scott A; Ku, S.; Lee, W. W.; Lin, Z.; Parker, Scott; CPES Team, the

    2006-01-01

    A gyrokinetic neoclassical solution for a diverted tokamak edge plasma has been obtained for the first time using the massively parallel Jaguar XT3 computer at Oak Ridge National Laboratory. The solutions show similar characteristics to the experimental observations: electric potential is positive in the scrape-off layer and negative in the H-mode layer, and the parallel rotation is positive in the scrape-off layer and at the inside boundary of the H-mode layer. However, the solution also makes a new physical discovery that there is a strong ExB convective flow in the scrape-off plasma. A general introduction to the edge simulation problem is also presented.

  19. Free Energy Cascade in Gyrokinetic Turbulence

    SciTech Connect

    Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.

    2011-02-04

    In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.

  20. Nonlinear electrophoresis of ideally polarizable particles

    NASA Astrophysics Data System (ADS)

    Figliuzzi, B.; Chan, W. H. R.; Moran, J. L.; Buie, C. R.

    2014-10-01

    We focus in this paper on the nonlinear electrophoresis of ideally polarizable particles. At high applied voltages, significant ionic exchange occurs between the electric double layer, which surrounds the particle, and the bulk solution. In addition, steric effects due to the finite size of ions drastically modify the electric potential distribution in the electric double layer. In this situation, the velocity field, the electric potential, and the ionic concentration in the immediate vicinity of the particle are described by a complicated set of coupled nonlinear partial differential equations. In the general case, these equations must be solved numerically. In this study, we rely on a numerical approach to determine the electric potential, the ionic concentration, and the velocity field in the bulk solution surrounding the particle. The numerical simulations rely on a pseudo-spectral method which was used successfully by Chu and Bazant [J. Colloid Interface Sci. 315(1), 319-329 (2007)] to determine the electric potential and the ionic concentration around an ideally polarizable metallic sphere. Our numerical simulations also incorporate the steric model developed by Kilic et al. [Phys. Rev. E 75, 021502 (2007)] to account for crowding effects in the electric double layer, advective transport, and for the presence of a body force in the bulk electrolyte. The simulations demonstrate that surface conduction significantly decreases the electrophoretic mobility of polarizable particles at high zeta potential and at high applied electric field. Advective transport in the electric double layer and in the bulk solution is also shown to significantly impact surface conduction.

  1. Particle systems and nonlinear Landau damping

    SciTech Connect

    Villani, Cédric

    2014-03-15

    Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.

  2. Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments

    SciTech Connect

    Wang, W.X.; Lin, Z.; Tang, W.M.; Lee, W.W.; Ethier, S.; Lewandowski, J.L.V.; Rewoldt, G.; Hahm, T.S.; Manickam, J.

    2006-01-01

    A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.

  3. Predictive Gyrokinetic Transport Simulations and Application of Synthetic Diagnostics

    NASA Astrophysics Data System (ADS)

    Candy, J.

    2009-11-01

    In this work we make use of the gyrokinetic transport solver TGYRO [1] to predict kinetic plasma profiles consistent with energy and particle fluxes in the DIII-D tokamak. TGYRO uses direct nonlinear and neoclassical fluxes calculated by the GYRO and NEO codes, respectively, to solve for global, self-consistent temperature and density profiles via Newton iteration. Previous work has shown that gyrokinetic simulation results for DIII-D discharge 128913 match experimental data rather well in the plasma core, but with a discrepancy in both fluxes and fluctuation levels emerging closer to the edge (r/a > 0.8). The present work will expand on previous results by generating model predictions across the entire plasma core, rather than at isolated test radii. We show that TGYRO predicts temperature and density profiles in good agreement with experimental observations which simultaneously yield near-exact (to within experimental uncertainties) agreement with power balance calculations of the particle and energy fluxes for r/a <=0.8. Moreover, we use recently developed synthetic diagnostic algorithms [2] to show that TGYRO also predicts density and electron temperature fluctuation levels in close agreement with experimental measurements across the simulated plasma volume. 8pt [1] J. Candy, C. Holland, R.E. Waltz, M.R. Fahey, and E. Belli, ``Tokamak profile prediction using direct gyrokinetic and neoclassical simulation," Phys. Plasmas 16, 060704 (2009). [2] C. Holland, A.E. White, G.R. McKee, M.W. Shafer, J. Candy, R.E. Waltz, L. Schmitz, and G.R. Tynan, ``Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence," Phys. Plasmas 16, 052301 (2009).

  4. Electromagnetic gyrokinetic simulation of turbulent transport in high ion temperature discharge of Large Helical Device

    NASA Astrophysics Data System (ADS)

    Ishizawa, Akihiro; Watanabe, Tomo-Hiko; Sugama, Hideo; Maeyama, Shinya; Nunami, Masanori; Nakajima, Noriyoshi

    2014-10-01

    Turbulent transport in a high ion temperature discharge of Large Helical Device (LHD) is investigated by means of electromagnetic gyrokinetic simulations including kinetic electrons. A new electromagnetic gyrokinetic simulation code GKV+enables us to examine electron heat and particle fluxes as well as ion heat flux in finite beta heliotron/stellarator plasmas. This problem has not been previously explored because of numerical difficulties associated with complex three-dimensional magnetic structures as well as multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The turbulent fluxes, which are evaluated through a nonlinear simulation carried out in the K-super computer system, will be reported. This research uses computational resources of K at RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Project ID: hp140044).

  5. Gyrokinetic modelling of stationary electron and impurity profiles in tokamaks

    SciTech Connect

    Skyman, A. Tegnered, D. Nordman, H. Strand, P.

    2014-09-15

    Particle transport due to Ion Temperature Gradient (ITG)/Trapped Electron Mode (TEM) turbulence is investigated using the gyrokinetic code GENE. Both a reduced quasilinear treatment and nonlinear simulations are performed for typical tokamak parameters corresponding to ITG dominated turbulence. The gyrokinetic results are compared and contrasted with results from a computationally efficient fluid model. A selfconsistent treatment is used, where the stationary local profiles are calculated corresponding to zero particle flux simultaneously for electrons and trace impurities. The scaling of the stationary profiles with magnetic shear, safety factor, electron-to-ion temperature ratio, collisionality, toroidal sheared rotation, plasma β, triangularity, and elongation is investigated. In addition, the effect of different main ion mass on the zero flux condition is discussed. The electron density gradient can significantly affect the stationary impurity profile scaling. It is therefore expected that a selfconsistent treatment will yield results more comparable to experimental results for parameter scans where the stationary background density profile is sensitive. This is shown to be the case in scans over magnetic shear, collisionality, elongation, and temperature ratio, for which the simultaneous zero flux electron and impurity profiles are calculated. A slight asymmetry between hydrogen, deuterium, and tritium with respect to profile peaking is obtained, in particular, for scans in collisionality and temperature ratio.

  6. Intercode comparison of gyrokinetic global electromagnetic modes

    NASA Astrophysics Data System (ADS)

    Görler, T.; Tronko, N.; Hornsby, W. A.; Bottino, A.; Kleiber, R.; Norscini, C.; Grandgirard, V.; Jenko, F.; Sonnendrücker, E.

    2016-07-01

    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.

  7. 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.

  8. 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.

  9. Gyrokinetic Studies of Turbulence in Steep Gradient Region: Role of Turbulence Spreading and E x B Shear

    SciTech Connect

    T.S. Hahm; Z. Lin; P.H. Diamond; G. Rewoldt; W.X. Wang; S. Ethier; O. Gurcan; W.W. Lee; W.M. Tang

    2004-12-21

    An integrated program of gyrokinetic particle simulation and theory has been developed to investigate several outstanding issues in both turbulence and neoclassical physics. Gyrokinetic particle simulations of toroidal ion temperature gradient (ITG) turbulence spreading using the GTC code and its related dynamical model have been extended to the case with radially increasing ion temperature gradient, to study the inward spreading of edge turbulence toward the core. Due to turbulence spreading from the edge, the turbulence intensity in the core region is significantly enhanced over the value obtained from simulations of the core region only. Even when the core gradient is within the Dimits shift regime (i.e., self-generated zonal flows reduce the transport to a negligible value), a significant level of turbulence and transport is observed in the core due to spreading from the edge. The scaling of the turbulent front propagation speed is closer to the prediction from our nonlinear diffusion model than one based on linear toroidal coupling. A calculation of ion poloidal rotation in the presence of sharp density and toroidal angular rotation frequency gradients from the GTC-Neo particle simulation code shows that the results are significantly different from the conventional neoclassical theory predictions. An energy conserving set of a fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to edge turbulence, is being derived via the phase-space action variational Lie perturbation method. Our generalized ordering takes the ion poloidal gyroradius to be on the order of the radial electric field gradient length.

  10. Free energy balance in gyrokinetic turbulence

    SciTech Connect

    Banon Navarro, A.; Morel, P.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.

    2011-09-15

    Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.

  11. Analysis and gyrokinetic simulation of MHD Alfven wave interactions

    NASA Astrophysics Data System (ADS)

    Nielson, Kevin Derek

    The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the

  12. Gyrokinetic turbulence simulations at high plasma beta

    SciTech Connect

    Pueschel, M. J.; Kammerer, M.; Jenko, F.

    2008-10-15

    Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for {beta} values up to and beyond the kinetic ballooning threshold. The {beta} scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of {beta} values just below the respective ideal limit. The magnetic transport scales like {beta}{sup 2} and is well described by a Rechester-Rosenbluth-type ansatz.

  13. Beyond linear gyrocenter polarization in gyrokinetic theory

    SciTech Connect

    Brizard, Alain J.

    2013-09-15

    The concept of polarization in gyrokinetic theory is clarified and generalized to include contributions from the guiding-center (zeroth-order) polarization as well as the nonlinear (second-order) gyrocenter polarization. The guiding-center polarization, which appears as the antecedent (zeroth-order) of the standard linear (first-order) gyrocenter polarization, is obtained from a modified guiding-center transformation. The nonlinear gyrocenter polarization is derived either variationally from the third-order gyrocenter Hamiltonian or directly by gyrocenter push-forward method.

  14. Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

    NASA Technical Reports Server (NTRS)

    Kandula, Max

    2010-01-01

    The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction

  15. Status of Continuum Edge Gyrokinetic Code Physics Development

    SciTech Connect

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

    2005-05-31

    We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D ({psi}, {theta}, {epsilon}, {mu}) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. 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. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in ({nu}{sub {parallel}},{nu}{sub {perpendicular}}) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt|{sub coll} to/from ({epsilon}, {mu}) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic

  16. Particle flow for nonlinear filters with log-homotopy

    NASA Astrophysics Data System (ADS)

    Daum, Fred; Huang, Jim

    2008-04-01

    We describe a new nonlinear filter that is vastly superior to the classic particle filter. In particular, the computational complexity of the new filter is many orders of magnitude less than the classic particle filter with optimal estimation accuracy for problems with dimension greater than 2 or 3. We consider nonlinear estimation problems with dimensions varying from 1 to 20 that are smooth and fully coupled (i.e. dense not sparse). The new filter implements Bayes' rule using particle flow rather than with a pointwise multiplication of two functions; this avoids one of the fundamental and well known problems in particle filters, namely "particle collapse" as a result of Bayes' rule. We use a log-homotopy to derive the ODE that describes particle flow. This paper was written for normal engineers, who do not have homotopy for breakfast.

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

    SciTech Connect

    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 allows 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.

  18. Discrete particle noise in a nonlinearly saturated plasma

    NASA Astrophysics Data System (ADS)

    Jenkins, Thomas; Lee, W. W.

    2006-04-01

    Understanding discrete particle noise in an equilibrium plasma has been an important topic since the early days of particle-in- cell (PIC) simulation [1]. In this paper, particle noise in a nonlinearly saturated system is investigated. We investigate the usefulness of the fluctuation-dissipation theorem (FDT) in a regime where drift instabilities are nonlinearly saturated. We obtain excellent agreement between the simulation results and our theoretical predictions of the noise properties. It is found that discrete particle noise always enhances the particle and thermal transport in the plasma, in agreement with the second law of thermodynamics. [1] C.K. Birdsall and A.B. Langdon, Plasma Physics via Computer Simulation, McGraw-Hill, New York (1985).

  19. Comparisons of gyrofluid and gyrokinetic simulations

    SciTech Connect

    Parker, S.E.; Dorland, W.; Santoro, R.A.; Beer, M.A.; Liu, Q.P.; Lee, W.W.; Hammett, G.W.

    1994-03-01

    The gyrokinetic and gyrofluid models show the most promise for large scale simulations of tokamak microturbulence. This paper discusses detailed comparisons of these two complementary approaches. Past comparisons with linear theory have been fairly good, therefore the emphasis here is on nonlinear comparisons. Simulations include simple two dimensional slab test cases, turbulent three dimensional slab cases, and toroidal cases, each modeling the nonlinear evolution of the ion temperature gradient instability. There is good agreement in both turbulent and coherent nonlinear slab comparisons in terms of the ion heat flux, both in magnitude and scaling with magnetic shear. However, the nonlinear saturation level for {vert_bar}{Phi}{vert_bar} in the slab comparisons show differences of approximately 40%. Preliminary toroidal comparisons show agreement within 50%, in terms of ion heat flux and saturation level.

  20. Global gyrokinetic ion temperature gradient turbulence simulations of ITER

    NASA Astrophysics Data System (ADS)

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

    2013-07-01

    Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.

  1. Nonlinearly interacting trapped particle solitons in collisionless plasmas

    NASA Astrophysics Data System (ADS)

    Mandal, Debraj; Sharma, Devendra

    2016-02-01

    The formulation of collective waves in collisionless plasmas is complicated by the kinetic effects produced by the resonant particles, capable of responding to the smallest of the amplitude disturbance. The dispersive plasma manifests this response by generating coherent nonlinear structures associated with phase-space vortices, or holes, at very small amplitudes. The nonlinear interaction between solitary electron phase-space holes is studied in the electron acoustic regime of a collisionless plasma using Vlasov simulations. Evolution of the analytic trapped particle solitary solutions is examined, observing them propagate stably, preserve their identity across strong mutual interactions in adiabatic processes, and display close correspondence with observable processes in nature.

  2. Saturation of Gyrokinetic Turbulence through Damped Eigenmodes

    SciTech Connect

    Hatch, D. R.; Terry, P. W.; Jenko, F.; Merz, F.; Nevins, W. M.

    2011-03-18

    In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems.

  3. Nonlinear dynamics of inhomogeneous mismatched charged particle beams

    SciTech Connect

    Nunes, R. P.; Rizzato, F. B.

    2012-08-13

    This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.

  4. Gyrokinetic large eddy simulations

    SciTech Connect

    Morel, P.; Navarro, A. Banon; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.

    2011-07-15

    The large eddy simulation approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the GENE code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient.

  5. Generalized nonlinear Proca equation and its free-particle solutions

    NASA Astrophysics Data System (ADS)

    Nobre, F. D.; Plastino, A. R.

    2016-06-01

    We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ ^{μ }(ěc {x},t), involves an additional field Φ ^{μ }(ěc {x},t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E2 = p2c2 + m2c4 for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.

  6. Gyrokinetic simulations of momentum transport and fluctuation spectra for ICRF-heated L-Mode plasmas

    NASA Astrophysics Data System (ADS)

    Sierchio, J. M.; White, A. E.; Howard, N. T.; Sung, C.; Ennever, P.; Porkolab, M.; Candy, J.

    2014-10-01

    We examine ICRF-heated L-mode plasmas in Alcator C-Mod, with differing momentum transport (hollow vs. peaked radial profiles of intrinsic toroidal rotation) but similar heat and particle transport. Nonlinear gyrokinetic simulations of heat and particle transport with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] have previously been compared with these experiments [White et al., Phys. Plasmas 20, 056106 (2013); Howard et al. PPCF submitted (2014)] as part of an effort to validate the gyrokinetic model for core turbulent transport in C-Mod plasmas. To further test the model for these plasmas, predicted core turbulence characteristics such as fluctuation spectra will be compared with experiment. Using synthetic diagnostics for the CECE, reflectometry, and PCI systems at C-Mod, synthetic spectra and, when applicable, fluctuation amplitudes, are generated. We compare these generated results with fluctuation measurements from the experiment. We also report the momentum transport results from simulations of these plasmas and compare them to experiment. Supported by USDoE award DE-FC02-99ER54512.

  7. Adiabatic nonlinear waves with trapped particles. III. Wave dynamics

    SciTech Connect

    Dodin, I. Y.; Fisch, N. J.

    2012-01-15

    The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schroedinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.

  8. On the Existence of Canonical Gyrokinetic Variables for Chaotic Magnetic Fields

    SciTech Connect

    Nicolini, Piero; Tessarotto, Massimo

    2008-12-31

    The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called gyrokinetic canonical variables. These are defined in such a way that two of them are respectively identified with the gyrophase-angle, describing the fast particle gyration motion around magnetic field lines, and its canonically conjugate momentum. In this paper we intend to discuss the conditions of existence for these variables.

  9. Weakly nonlinear electrophoresis of a highly charged colloidal particle

    NASA Astrophysics Data System (ADS)

    Schnitzer, Ory; Zeyde, Roman; Yavneh, Irad; Yariv, Ehud

    2013-05-01

    At large zeta potentials, surface conduction becomes appreciable in thin-double-layer electrokinetic transport. In the linear weak-field regime, where this effect is quantified by the Dukhin number, it is manifested in non-Smoluchowski electrophoretic mobilities. In this paper we go beyond linear response, employing the recently derived macroscale model of Schnitzer and Yariv ["Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction," Phys. Rev. E 86, 021503 (2012), 10.1103/PhysRevE.86.021503] as the infrastructure for a weakly nonlinear analysis of spherical-particle electrophoresis. A straightforward perturbation in the field strength is frustrated by the failure to satisfy the far-field conditions, representing a non-uniformity of the weak-field approximation at large distances away from the particle, where salt advection becomes comparable to diffusion. This is remedied using inner-outer asymptotic expansions in the spirit of Acrivos and Taylor ["Heat and mass transfer from single spheres in Stokes flow," Phys. Fluids 5, 387 (1962), 10.1063/1.1706630], with the inner region representing the particle neighborhood and the outer region corresponding to distances scaling inversely with the field magnitude. This singular scheme furnishes an asymptotic correction to the electrophoretic velocity, proportional to the applied field cubed, which embodies a host of nonlinear mechanisms unfamiliar from linear electrokinetic theories. These include the effect of induced zeta-potential inhomogeneity, animated by concentration polarization, on electro-osmosis and diffuso-osmosis; bulk advection of salt; nonuniform bulk conductivity; Coulomb body forces acting on bulk volumetric charge; and the nonzero electrostatic force exerted upon the otherwise screened particle-layer system. A numerical solution of the macroscale model validates our weakly nonlinear analysis.

  10. Particle swarm optimization for complex nonlinear optimization problems

    NASA Astrophysics Data System (ADS)

    Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos

    2016-06-01

    This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.

  11. Dielectric Decrement Effects on Nonlinear Electrophoresis of Ideally Polarizable Particles

    NASA Astrophysics Data System (ADS)

    Moran, Jeffrey L.; Chan, Wai Hong Ronald; Buie, Cullen R.; Figliuzzi, Bruno

    2014-11-01

    We present numerical simulations of nonlinear electrophoresis of ideally polarizable particles that specifically include the effects of a spatially non-uniform dielectric permittivity near the particle surface. Models for this dielectric decrement phenomenon have been developed by several authors, including Ben-Yaakov et al. [J. Phys.: Condens. Matter 2009] Hatlo et al. [EPL 2012], and Zhao & Zhai [JFM 2013]. We extend this work to ideally polarizable particles and include the effects of surface conduction and advective transport in the electric double layer. By numerically solving for the coupled velocity field, electric potential, and ionic concentration distributions in the bulk solution surrounding the particle, we demonstrate that the dielectric decrement model predicts ionic saturation around the particle and thus physical implications that resemble those resulting from the steric model developed by Kilic et al. [PRE 2007], albeit with differences that reflect the nonlinearity of the modified Poisson-Boltzmann equation. In addition, we develop a generalized condensed layer model that approximates both the steric and dielectric decrement models in the limits of strong electric fields and negligible surface conduction to obtain more physical insights into these models. We demonstrate that the mobility in both models asymptotically scales as the square root of the electric field at high fields, recovering the result of Bazant et al. [Adv. Colloid Interface Sci. 2009].

  12. Nonlinear Statistical Signal Processing: A Particle Filtering Approach

    SciTech Connect

    Candy, J

    2007-09-19

    A introduction to particle filtering is discussed starting with an overview of Bayesian inference from batch to sequential processors. Once the evolving Bayesian paradigm is established, simulation-based methods using sampling theory and Monte Carlo realizations are discussed. Here the usual limitations of nonlinear approximations and non-gaussian processes prevalent in classical nonlinear processing algorithms (e.g. Kalman filters) are no longer a restriction to perform Bayesian inference. It is shown how the underlying hidden or state variables are easily assimilated into this Bayesian construct. Importance sampling methods are then discussed and shown how they can be extended to sequential solutions implemented using Markovian state-space models as a natural evolution. With this in mind, the idea of a particle filter, which is a discrete representation of a probability distribution, is developed and shown how it can be implemented using sequential importance sampling/resampling methods. Finally, an application is briefly discussed comparing the performance of the particle filter designs with classical nonlinear filter implementations.

  13. Gyrokinetic Simulations of ETG and ITG Turbulence

    SciTech Connect

    Dimits, A; Nevins, W; Shumaker, D; Hammett, G; Dannert, T; Jenko, F; Dorland, W; Leboeuf, J; Rhodes, T; Candy, J; Estrada-Mila, C

    2006-10-03

    Published gyrokinetic continuum-code simulations indicated levels of the electron thermal conductivity {chi}{sub e} due to electron-temperature-gradient (ETG) turbulence large enough to be significant in some tokamaks, while subsequent global particle-in-cell (PIC) simulations gave significantly lower values. We have carried out an investigation of this discrepancy. We have reproduced the key features of the aforementioned PIC simulations using the flux-tube gyrokinetic PIC code, PG3EQ, thereby eliminating global effects and as the cause of the discrepancy. We show that the late-time low-transport state in both of these sets of PIC simulations is a result of discrete particle noise, which is a numerical artifact. Thus, the low value of {chi}{sub e} along with conclusions about anomalous transport drawn from these particular PIC simulations are unjustified. In our attempts to benchmark PIC and continuum codes for ETG turbulence at the plasma parameters used above, both produce very large intermittent transport. We have therefore undertaken benchmarks at an alternate reference point, magnetic shear s=0.1 instead of s=0.796, and have found that PIC and continuum codes reproduce the same transport levels. Scans in the magnetic shear show an abrupt transition to a high-{chi}{sub e} state as the shear is increased above s=0.4. When nonadiabatic ions are used, this abrupt transition is absent, and {chi}{sub e} increases gradually reaching values consistent with transport analyses of DIII-D, JET, and JT60-U discharges. New results on the balances of zonal-flow driving and damping terms in late-time quasi-steady ITG turbulence and on real-geometry gyrokinetic simulations of shaped DIII-D discharges are also reported.

  14. The theory of gyrokinetic turbulence: A multiple-scales approach

    NASA Astrophysics Data System (ADS)

    Plunk, Gabriel Galad

    Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics -- such as turbulence, universality, self-organization and dynamic criticality -- which are found in physical systems that are driven far from thermodynamic equilibrium. One such system is of particular importance, as it is central in the development of fusion energy -- this system is the turbulent plasma found in magnetically confined fusion device. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I present three projects, based on the work of me and my collaborators, which take a tour of different aspects and approaches to the gyrokinetic turbulence problem. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of Magnetically confined fusion devices. The results of this work include (1) the equations of evolution for the mean scale (equilibrium) density, temperature and magnetic field of the plasma, (2) a detailed Poynting's theorem for the energy balance and (3) the entropy balance equations. The second project presents gyrokinetic secondary instability theory as a mechanism to bring about saturation of the basic instabilities that drive gyrokinetic turbulence. Emphasis is put on the ability for this analytic theory to predict basic properties of the nonlinear state, which can be applied to a mixing length phenomenology of transport. The results of this work include (1) an integral equation for the calculation of the growth rate of the fully gyrokinetic secondary instability with finite Larmor radius (FLR) affects included exactly, (2) the demonstration of the robustness of the secondary instability at fine scales (krhoi for ion temperature gradient (ITG) turbulence and krhoe ≪ 1 for electron temperature

  15. Nonlinear EEG Decoding Based on a Particle Filter Model

    PubMed Central

    Hong, Jun

    2014-01-01

    While the world is stepping into the aging society, rehabilitation robots play a more and more important role in terms of both rehabilitation treatment and nursing of the patients with neurological diseases. Benefiting from the abundant contents of movement information, electroencephalography (EEG) has become a promising information source for rehabilitation robots control. Although the multiple linear regression model was used as the decoding model of EEG signals in some researches, it has been considered that it cannot reflect the nonlinear components of EEG signals. In order to overcome this shortcoming, we propose a nonlinear decoding model, the particle filter model. Two- and three-dimensional decoding experiments were performed to test the validity of this model. In decoding accuracy, the results are comparable to those of the multiple linear regression model and previous EEG studies. In addition, the particle filter model uses less training data and more frequency information than the multiple linear regression model, which shows the potential of nonlinear decoding models. Overall, the findings hold promise for the furtherance of EEG-based rehabilitation robots. PMID:24949420

  16. Testing gyrokinetic simulations of electron turbulence

    NASA Astrophysics Data System (ADS)

    Holland, C.; DeBoo, J. C.; Rhodes, T. L.; Schmitz, L.; Hillesheim, J. C.; Wang, G.; White, A. E.; Austin, M. E.; Doyle, E. J.; Peebles, W. A.; Petty, C. C.; Zeng, L.; Candy, J.

    2012-06-01

    An extensive set of tests comparing gyrokinetic predictions of temperature-gradient driven electron turbulence to power balance transport analyses and fluctuation measurements are presented. These tests use data from an L-mode validation study on the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614) in which the local value of a/L_{T_e } =-(a/T_e )(dT_e /dr) is varied by modulated electron cyclotron heating; the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) is used to make the gyrokinetic predictions. Using a variety of novel measures, both local and global nonlinear simulations are shown to predict key characteristics of the electron energy flux Qe and long-wavelength (low-k) Te fluctuations, but systematically underpredict (by roughly a factor of two) the ion energy flux Qi. A new synthetic diagnostic for comparison to intermediate wavelength Doppler backscattering measurements is presented, and used to compare simulation predictions against experiment. In contrast to the agreement observed in the low-k Te fluctuation comparisons, little agreement is found between the predicted and measured intermediate-k density fluctuation responses. The results presented in this paper significantly expand upon those previously reported in DeBoo et al (2010 Phys. Plasmas 17 056105), comparing transport and multiple turbulence predictions from numerically converged local and global simulations for all four experimental heating configurations (instead of only fluxes and low-k Te fluctuations for one condition) to measurements and power balance analyses.

  17. Optical bistability of a nondilute suspension of nonlinear coated particles

    NASA Astrophysics Data System (ADS)

    Gu, Liping; Gao, Lei

    2005-11-01

    The intrinsic optical bistability (OB) of a nondilute suspension of coated spherical particles is investigated. We assume both the core and the shell to be nonlinear with third-order nonlinear susceptibilities χc and χs, respectively, and thus the local field in the nonlinear core is not uniform and cannot be obtained exactly. In this connection, we establish the self-consistent mean field approximation, and obtain the spatial average of the local field squared in the nonlinear core (or the shell) as a function of the external applied field. We show that an optical bistable behavior exists only when the structure parameter (λ) is less than the critical one λc, which is dependent on the magnitude of both χc and χs. Moreover, the bistable curves depend strongly on χc and are weakly dependent on χs. In addition, the threshold intensity decreases with increasing λ, and it can be lowered further by using a nondilute volume fraction. The field-dependent effective dielectric function is also studied, and the hysteretic loops are again found.

  18. Effect of dynamical friction on nonlinear energetic particle modes

    SciTech Connect

    Lilley, M. K.; Breizman, B. N.; Sharapov, S. E.

    2010-09-15

    A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction (drag) and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed.

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

    NASA Astrophysics Data System (ADS)

    Bravenec, R. V.; Chen, Y.; Candy, J.; Wan, W.; Parker, S.

    2013-10-01

    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. 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.

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

    SciTech Connect

    Bravenec, R. V.; Chen, Y.; Wan, W.; Parker, S.; Candy, J.

    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. 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.

  1. Benchmarking of the Gyrokinetic Microstability Codes GYRO, GS2, and GEM

    NASA Astrophysics Data System (ADS)

    Bravenec, Ronald; Chen, Yang; Wan, Weigang; Parker, Scott; Candy, Jeff; Barnes, Michael; Howard, Nathan; Holland, Christopher; Wang, Eric

    2012-10-01

    The physics capabilities of modern gyrokinetic microstability codes are now so extensive that they cannot be verified fully for realistic tokamak plasmas using purely analytic approaches. Instead, verification (demonstrating that the codes correctly solve the gyrokinetic-Maxwell equations) must rely on benchmarking (comparing code results for identical plasmas and physics). Benchmarking exercises for a low-power DIII-D discharge at the mid-radius have been presented recently for the Eulerian codes GYRO and GS2 [R.V. Bravenec, J. Candy, M. Barnes, C. Holland, Phys. Plasmas 18, 122505 (2011)]. This work omitted ExB flow shear, but we include it here. We also present GYRO/GS2 comparisons for a high-power Alcator C-Mod discharge. To add further confidence to the verification exercises, we have recently added the particle-in-cell (PIC) code GEM to the efforts. We find good agreement of linear frequencies between GEM and GYRO/GS2 for the DIII-D plasma. We also present preliminary nonlinear comparisons. This benchmarking includes electromagnetic effects, plasma shaping, kinetic electrons and one impurity. In addition, we compare linear results among the three codes for the steep-gradient edge region of a DIII-D plasma between edge-localized modes.

  2. Collisionless Dissipative Nonlinear Alfvén Waves: Nonlinear Steepening, Particle Trapping, and Compressible Turbulence

    NASA Astrophysics Data System (ADS)

    Medvedev, M. V.

    1998-11-01

    The magnetic field fluctuations frequently observed in the Solar Wind and Interstellar Medium are likely to be nonlinear Alfvén waves, in which the ponderomotive coupling of Alfvénic magnetic energy to ion-acoustic quasi-modes has modified the phase velocity vA and caused wave-front steepening. In the warm, collisionless Solar Wind plasma the resonant particle-wave interactions result in relatively rapid (compared to the particle bounce time) formation of quasi-stationary Alfvénic Rotational Discontinuities, (M.V. Medvedev, P.H. Diamond, V.I. Shevchenko, and V.L. Galinsky, Phys. Rev. Lett. 78), 4934 (1997) and references therein. which have been the subject of intense satellite observations and theoretical investigations, and whose emergence and dynamics has not been previously understood. These discontinuities are shown to be quasi-stationary wave-form remnants of nonlinearly evolved coherent Alfvén waves. In long-time asymptotics, however, the particle distribution function (PDF) is affected by wave magnetic fields. Indeed, the resonant particles are trapped in the quasi-stationary Alfvénic discontinuities by mirroring forces giving rise to the nonlinear Landau damping and, ultimately, to a formation of a plateau on the PDF, so that the linear collisionless damping vanishes. Using Virial theorem for trapped particles, it is analytically demonstrated (M.V. Medvedev, P.H. Diamond, M.N. Rosenbluth, and V.I. Shevchenko, Submitted to Phys. Rev. Lett. (1998).) that their effect on the nonlinear dynamics of such discontinuities is highly non-trivial and forces a significant departure of the theory from the conventional paradigm. Considering the strongly compressible MHD (Alfvénic) Solar Wind turbulence as an ensemble of randomly interacting Alfvénic discontinuities and nonlinear waves, it is also shown (M.V. Medvedev and P.H. Diamond, Phys. Rev. E 56), R2371 (1997). that there exist two different phases of turbulence which are due to the collisionless (Landau

  3. The isotope effect in turbulent transport control by GAMs. Observation and gyrokinetic modeling

    NASA Astrophysics Data System (ADS)

    Gurchenko, A. D.; Gusakov, E. Z.; Niskala, P.; Altukhov, A. B.; Esipov, L. A.; Kiviniemi, T. P.; Korpilo, T.; Kouprienko, D. V.; Lashkul, S. I.; Leerink, S.; Perevalov, A. A.; Irzak, M. A.

    2016-04-01

    A comparative investigation of the isotope effect in multi-scale anomalous transport phenomena is performed both experimentally by highly localized turbulence diagnostics in comparable hydrogen and deuterium FT-2 tokamak discharges and theoretically with the help of global gyrokinetic modeling. Substantial excess of the geodesic acoustic mode (GAM) amplitude, radial wavelength and correlation length in a wide spatial region of deuterium discharge resulting in stronger modulation of drift-wave turbulence level is demonstrated by both approaches. A larger turbulence radial correlation length is found at LFS in D-discharge in experiment and a stronger modulation of gyrokinetic particles and energy fluxes is shown there by the gyrokinetic code. The gyrokinetic modeling demonstrated comparable levels of drift wave density and electric field fluctuations in hydrogen and deuterium discharges. Nevertheless, the mean value of the ion energy and particle anomalous flux provided by modeling shows the systematic isotope effect at all radii.

  4. Intrinsic rotation with gyrokinetic models

    SciTech Connect

    Parra, Felix I.; Barnes, Michael; Catto, Peter J.; Calvo, Ivan

    2012-05-15

    The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed.

  5. Implementation of 2D domain decomposition in the UCAN gyrokinetic PIC code for non-diffusive transport studies in tokamaks

    NASA Astrophysics Data System (ADS)

    Leboeuf, Jean-Noel; Decyk, Viktor; Newman, David; Sanchez, Raul

    2012-03-01

    The massively parallel, nonlinear, 3D, toroidal, electrostatic, gyrokinetic, PIC, Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in DIII-D-like tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii per minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the 2D domain decomposed PLIB2 library of field and particle management routines developed for UCLA's UPIC framework of conventional PIC codes. The gyro-averaging in gyrokinetic codes has necessitated the use of replicated arrays for efficient charge accumulation and particle push. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain results within roundoff. Production calculations at large system sizes have been performed with UCAN2 on 131072 processors of the Cray XE6 at NERSC.

  6. Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.

    PubMed

    Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A; Wuite, Gijs J L; Roos, Wouter H; Barsegov, Valeri

    2016-01-01

    The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264

  7. Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

    PubMed Central

    Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri

    2016-01-01

    The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264

  8. Saturation of gyrokinetic turbulence through damped eigenmodes.

    PubMed

    Hatch, D R; Terry, P W; Jenko, F; Merz, F; Nevins, W M

    2011-03-18

    In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems. PMID:21469869

  9. Simulations of energetic particles interacting with nonlinear anisotropic dynamical turbulence

    NASA Astrophysics Data System (ADS)

    Heusen, M.; Shalchi, A.

    2016-09-01

    We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of δ B / B0 = 0.75.

  10. Discoveries from the exploration of gyrokinetic momentum transport

    SciTech Connect

    Staebler, G.M.; Waltz, R. E.; Kinsey, J. E.

    2011-05-15

    The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.

  11. Discoveries from the exploration of gyrokinetic momentum transporta)

    NASA Astrophysics Data System (ADS)

    Staebler, G. M.; Waltz, R. E.; Kinsey, J. E.

    2011-05-01

    The momentum transport due to gyroradius scale turbulence in tokamak plasmas is very complex. In general, some type of breaking of the parity of the gyrokinetic equation under simultaneous reflection of the poloidal angle and the sign of the parallel velocity phase space coordinate (poloidal parity) is always involved. There are three distinct types of poloidal parity breaking effects. In this paper, all three types of poloidal parity breaking are explored using the quasi-linear trapped gyro-Landau fluid [G. M. Staebler et al., Phys. Plasmas 12, 102508 (2005)] transport code. Selected results are verified with full nonlinear turbulence simulations using the gyro [J. Candy et al., J. Comput. Phys. 186, 545 (2003)] gyrokinetic code. The observable properties like an energy pinch driven by a parallel velocity shear and a dependence of momentum transport on the direction of the ion grad-B drift relative to the X-point location in single null divertor geometry have been discovered.

  12. The energetic coupling of scales in gyrokinetic plasma turbulence

    SciTech Connect

    Teaca, Bogdan; Jenko, Frank

    2014-07-15

    In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into a series of scale structures, while accounting separately for contributions made by modes possessing special symmetries (e.g., the zonal flow modes). The interaction of these scales is analyzed using the energy transfer functions, including a forward and backward decomposition, scale fluxes, and locality functions. The comparison between the ITG and ETG cases shows that ETG turbulence has a more pronounced classical turbulent behavior, exhibiting a stronger energy cascade, with implications for gyrokinetic turbulence modeling.

  13. 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.

  14. Wave-particle interaction and the nonlinear saturation of the electron temperature gradient mode

    NASA Astrophysics Data System (ADS)

    Vadlamani, Srinath; Parker, Scott E.; Chen, Yang; Howard, James E.

    2004-11-01

    It has been proposed that the electron temperature gradient (ETG) driven turbulence is responsible for experimentally relevant electron thermal transport in tokamak plasmas. Significant transport levels are possible by the creation of radially elongated vortices or ``streamers" [1,2], which are sustained by the nonlinear saturation of the instability and are not susceptible to shear flow destruction, as is the case with the ion temperature gradient (ITG) mode. We present a dynamical system to explore the dependence of saturation level due to E × B and E_\\| motion, as well as the effect of radial elongation. With this model, we can predict the nonlinear saturation level of the ETG streamers. We compare our theoretical predictions with a 2D shear-less slab gyrokinetic electron code that includes the E_\\| nonlinearity. [1]F. Jenko, W. Dorland, M Kotschenreuther, and B.N. Rogers, Phys. Plasmas 7, 1904 (2000). [2]C. Holland, and P.H. Diamond, Phys. Plasmas 9, 3857 (2002). [3]W. M. Manheimer, Phys. Fluids 14, 579 (1971). [4]R. A. Smith, John A. Krommes, and W. W. Lee, Phys. Fluids 28, 1069 (1985).

  15. The Implementation of Magnetic Islands in Gyrokinetic Toroidal Code

    NASA Astrophysics Data System (ADS)

    Jiang, Peng; Lin, Zhihong; Ihor, Holod; Xiao, Chijie

    2016-02-01

    The implementation of magnetic islands in gyrokinetic simulation has been verified in the gyrokinetic toroidal code (GTC). The ion and electron density profiles become partially flattened inside the islands. The density profile at the low field side is less flattened than that at the high field side due to toroidally trapped particles in the low field side, which do not move along the perturbed magnetic field lines. When the fraction of trapped particles decreases, the density profile at the low field becomes more flattened. supported by National Special Research Program of China for ITER (Nos. 2013GB111000 and 2014GB107004), China Scholarship Council (No. 2011601098), U.S. DOE Grants DE-SC0010416 and DE-FG02-07ER54916

  16. 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.

  17. Gyrokinetic simulations of the tearing instability

    SciTech Connect

    Numata, Ryusuke; Dorland, William; Howes, Gregory G.; Loureiro, Nuno F.; Tatsuno, Tomoya

    2011-11-15

    Linear gyrokinetic simulations covering the collisional-collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta.

  18. Gyrokinetic Simulations of the ITER Pedestal

    NASA Astrophysics Data System (ADS)

    Kotschenreuther, Mike

    2015-11-01

    It has been reported that low collisionality pedestals for JET parameters are strongly stable to Kinetic Ballooning Modes (KBM), and it is, as simulations with GENE show, the drift-tearing modes that produce the pedestal transport. It would seem, then, that gyrokinetic simulations may be a powerful, perhaps, indispensable tool for probing the characteristics of the H-mode pedestal in ITER especially since projected ITER pedestals have the normalized gyroradius ρ* smaller than the range of present experimental investigation; they do lie, however, within the regime of validity of gyrokinetics. Since ExB shear becomes small as ρ* approaches zero, strong drift turbulence will eventually be excited. Finding an answer to the question whether the ITER ρ* is small enough to place it in the high turbulence regime compels serious investigation. We begin with MHD equilibria (including pedestal bootstrap current) constructed using VMEC. Plasma profile shapes, very close to JET experimental profiles, are scaled to values expected on ITER (e.g., a 4 keV pedestal). The equilibrium ExB shear is computed using a neoclassical formula for the radial electric field. As with JET, the ITER pedestal is found to be strongly stable to KBM. Preliminary nonlinear simulations with GENE show that the turbulent drift transport is strong for ITER; the electrostatic transport has a highly unfavorable scaling from JET to ITER, going from being highly sub-dominant to electromagnetic transport on JET, to dominant on ITER. At burning plasma parameters, pedestals in spherical tokamak H-modes may have much stronger velocity shear, and hence more favorable transport; preliminary investigations will be reported. This research supported by U.S. Department of Energy, Office of Fusion Energy Science: Grant No. DE-FG02-04ER-54742.

  19. Status of edge gyrokinetic turbulence simulation in XGC1

    NASA Astrophysics Data System (ADS)

    Ku, Seung-Hoe; Chang, C. S.; Zorin, D.; Greengard, L.; Adams, M.; Cummings, J.; Worley, P.; D'Azevedo, E.; Lee, W.; Parker, S.; Chen, Y.; Lin, Z.

    2007-11-01

    Gyrokinetic simulation of a tokamak edge plasma is one of the highest priority research items for ITER and the magnetic fusion program. Due to the complex physical modeling required in the edge plasma (closed and open magnetic field lines with the magnetic separatrix in between, the importance of neoclassical physics, the material wall boundary, steep pressure gradients, a non-Maxwellian distribution function, and the neutral particle physics), most of the gyrokinetic simulation activities have so far been focused on the core plasmas. The status of the gyrokinetic edge turbulence simulation in the XGC1 particle code in the SciDAC Prototype FSP Center for Plasma Edge Simulation (CPES) will be reported. XGC1 includes the above mentioned edge complexities with full- f/delta-f particle technology on an unstructured mesh. Special physics/math/CS features will be discussed. Our current electrostatic turbulence/neoclassical capabilities will be presented and verified. Plans for incorporating full electromagnetic turbulence will also be discussed.

  20. Nonlinear Delta-f Particle Simulations of Collective Effects in High Intensity Charged Particle Beams

    NASA Astrophysics Data System (ADS)

    Qin, Hong; Davidson, Ronald C.; Startsev, Edward A.

    2004-11-01

    A wide range of collective effects in high intensity charged particle beams have been numerically studied using the nonlinear delta-f particle simulation method implemented in the Beam Equilibrium Stability and Transport (BEST) code. For the electron-ion two-stream instability in high intensity accelerators and storage rings, the secondary electron yield effects are self-consistently studied by coupling the secondary electron yield library CMEE with the instability simulations. Progress has also been made in applying the delta-f particle simulation method to bunched beams, and a three-dimensional equilibrium solver has been implemented. With the help of recently developed parallel diagnostic techniques, we are able to characterize the chaotic particle dynamics under the influences of collective instabilities as well as three-dimensional equilibrium fields. To further extend the application areas of the delta-f particle simulation method, 2D domain decomposition is being developed using the Message Passing Interface, and three-dimensional equilibria with anisotropic temperature in the transverse and longitudinal directions are being investigated. References: [1] R. C. Davidson and H. Qin, An Introduction to the Physics of Intense Charged Particle Beams in High Energy Accelerators, World Scientific (2001). [2] H. Qin, Physics of Plasmas 10, 2078 (2003). [3] H. Qin, E. A. Startsev, and R. C. Davidson, Physical Review Special Topics on Accelerators and Beams 6, 014401 (2003).

  1. Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

    NASA Technical Reports Server (NTRS)

    Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

    2009-01-01

    Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

  2. A generalized gyrokinetic Poisson solver

    SciTech Connect

    Lin, Z.; Lee, W.W.

    1995-03-01

    A generalized gyrokinetic Poisson solver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.

  3. A Numerical Instability in an ADI Algorithm for Gyrokinetics

    SciTech Connect

    E.A. Belli; G.W. Hammett

    2004-12-17

    We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.

  4. On push-forward representations in the standard gyrokinetic model

    SciTech Connect

    Miyato, N. Yagi, M.; Scott, B. D.

    2015-01-15

    Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.

  5. Effects of collisions on conservation laws in gyrokinetic field theory

    SciTech Connect

    Sugama, H.; Nunami, M.; Watanabe, T.-H.

    2015-08-15

    Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.

  6. Tokamak profile prediction using direct gyrokinetic and neoclassical simulation

    SciTech Connect

    Candy, Jeff; Holland, Chris; Waltz, R. E.; Fahey, Mark R; Belli, E

    2009-01-01

    okamak transport modeling scenarios, including ITER ITER Physics Basis Editors, Nucl. Fusion 39, 2137 1999 performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles . Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D J. L. Luxon, Nucl. Fusion 42, 614 2002 plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 2003 code, for turbulent transport, and the NEO E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 2008 code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0 <= r/a <= 0.8.

  7. Tokamak profile prediction using direct gyrokinetic and neoclassical simulation

    SciTech Connect

    Candy, J.; Waltz, R. E.; Belli, E.; Holland, C.; Fahey, M. R.

    2009-06-15

    Tokamak transport modeling scenarios, including ITER [ITER Physics Basis Editors, Nucl. Fusion 39, 2137 (1999)] performance predictions, are based exclusively on reduced models for core thermal and particle transport. The reason for this is simple: computational cost. A typical modeling scenario may require the evaluation of thousands of individual transport fluxes (local transport models calculate the energy and particle fluxes across a specified flux surface given fixed profiles). Despite continuous advances in direct gyrokinetic simulation, the cost of an individual simulation remains so high that direct gyrokinetic transport calculations have been avoided. By developing a steady-state iteration scheme suitable for direct gyrokinetic and neoclassical simulations, we can now compute steady-state temperature profiles for DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] plasmas given known plasma sources. The new code, TGYRO, encapsulates the GYRO[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] code, for turbulent transport, and the NEO[E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 50, 095010 (2008)] code, for kinetic neoclassical transport. Results for DIII-D L-mode discharge 128913 are given, with computational and experimental results consistent in the region 0{<=}r/a{<=}0.8.

  8. Effects of collisions on conservation laws in gyrokinetic field theory

    NASA Astrophysics Data System (ADS)

    Sugama, H.; Watanabe, T.-H.; Nunami, M.

    2015-08-01

    Effects of collisions on conservation laws for toroidal plasmas are investigated based on the gyrokinetic field theory. Associating the collisional system with a corresponding collisionless system at a given time such that the two systems have the same distribution functions and electromagnetic fields instantaneously, it is shown how the collisionless conservation laws derived from Noether's theorem are modified by the collision term. Effects of the external source term added into the gyrokinetic equation can be formulated similarly with the collisional effects. Particle, energy, and toroidal momentum balance equations including collisional and turbulent transport fluxes are systematically derived using a novel gyrokinetic collision operator, by which the collisional change rates of energy and canonical toroidal angular momentum per unit volume in the gyrocenter space can be given in the conservative forms. The ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work are shown to include classical, neoclassical, and turbulent transport fluxes which agree with those derived from conventional recursive formulations.

  9. Gyrokinetic study of ASDEX Upgrade inter-ELM pedestal profile evolution

    NASA Astrophysics Data System (ADS)

    Hatch, D. R.; Told, D.; Jenko, F.; Doerk, H.; Dunne, M. G.; Wolfrum, E.; Viezzer, E.; The ASDEX Upgrade Team; Pueschel, M. J.

    2015-06-01

    The gyrokinetic GENE code is used to study the inter-ELM H-mode pedestal profile evolution for an ASDEX Upgrade discharge. Density gradient driven trapped electron modes are the dominant pedestal instability during the early density-buildup phase. Nonlinear simulations produce particle transport levels consistent with experimental expectations. Later inter-ELM phases appear to be simultaneously constrained by electron temperature gradient (ETG) and kinetic ballooning mode (KBM) turbulence. The electron temperature gradient achieves a critical value early in the ELM cycle, concurrent with the appearance of both microtearing modes and ETG modes. Nonlinear ETG simulations demonstrate that the profiles lie at a nonlinear critical gradient. The nominal profiles are stable to KBM, but moderate increases in β are sufficient to surpass the KBM threshold. Certain aspects of the dynamics support the premise of KBM-constrained pedestal evolution; the density and temperature profiles separately undergo large changes, but in a manner that keeps the pressure profile constant and near the KBM limit.

  10. Petascale Parallelization of the Gyrokinetic Toroidal Code

    SciTech Connect

    Ethier, Stephane; Adams, Mark; Carter, Jonathan; Oliker, Leonid

    2010-05-01

    The Gyrokinetic Toroidal Code (GTC) is a global, three-dimensional particle-in-cell application developed to study microturbulence in tokamak fusion devices. The global capability of GTC is unique, allowing researchers to systematically analyze important dynamics such as turbulence spreading. In this work we examine a new radial domain decomposition approach to allow scalability onto the latest generation of petascale systems. Extensive performance evaluation is conducted on three high performance computing systems: the IBM BG/P, the Cray XT4, and an Intel Xeon Cluster. Overall results show that the radial decomposition approach dramatically increases scalability, while reducing the memory footprint - allowing for fusion device simulations at an unprecedented scale. After a decade where high-end computing (HEC) was dominated by the rapid pace of improvements to processor frequencies, the performance of next-generation supercomputers is increasingly differentiated by varying interconnect designs and levels of integration. Understanding the tradeoffs of these system designs is a key step towards making effective petascale computing a reality. In this work, we examine a new parallelization scheme for the Gyrokinetic Toroidal Code (GTC) [?] micro-turbulence fusion application. Extensive scalability results and analysis are presented on three HEC systems: the IBM BlueGene/P (BG/P) at Argonne National Laboratory, the Cray XT4 at Lawrence Berkeley National Laboratory, and an Intel Xeon cluster at Lawrence Livermore National Laboratory. Overall results indicate that the new radial decomposition approach successfully attains unprecedented scalability to 131,072 BG/P cores by overcoming the memory limitations of the previous approach. The new version is well suited to utilize emerging petascale resources to access new regimes of physical phenomena.

  11. Applications of large eddy simulation methods to gyrokinetic turbulence

    SciTech Connect

    Bañón Navarro, A. Happel, T.; Teaca, B. [Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB; Max-Planck für Sonnensystemforschung, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau; Max-Planck Jenko, F. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching; Max-Planck Hammett, G. W. [Max-Planck Collaboration: ASDEX Upgrade Team

    2014-03-15

    The large eddy simulation (LES) approach—solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model—is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.

  12. GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations

    SciTech Connect

    Grandgirard, V.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Besse, N.; Bertrand, P.

    2006-11-30

    This work addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the GYSELA code. The particularity of GYSELA code is to use a fixed grid with a Semi-Lagrangian (SL) scheme and this for the entire distribution function. The 4D non-linear drift-kinetic version of the code already showns the interest of such a SL method which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been upgrated to run 5D simulations of toroidal ITG turbulence. Linear benchmarks and non-linear first results prove that semi-lagrangian codes can be a credible alternative for gyrokinetic simulations.

  13. A multi-species collisional operator for full-F gyrokinetics

    SciTech Connect

    Estève, D.; Garbet, X.; Sarazin, Y.; Grandgirard, V.; Cartier-Michaud, T.; Dif-Pradalier, G.; Ghendrih, P.; Latu, G.; Norscini, C.

    2015-12-15

    A linearized multi-species collision operator has been developed for an efficient implementation in gyrokinetic codes. This operator satisfies the main expected properties: particle, momentum, and energy conservation, and existence of an H-theorem. A gyrokinetic version is then calculated, which involves derivatives with respect to the gyrocenter position, parallel velocity, and magnetic momentum. An isotropic version in the velocity space can be constructed for the specific problem of trace impurities colliding with a main species. A simpler version that involves derivatives with parallel velocity only has been developed. This reduced version has been implemented in the GYSELA gyrokinetic code, and is shown to comply with particle, momentum, and energy conservation laws. Moreover, the interspecies relaxation rates for momentum and energy agree very well with the theoretical values.

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

    SciTech Connect

    Deng, Zhao; 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 tested 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

  15. Plasma Simulation Using Gyrokinetic-Gyrofluid Hybrid Models

    SciTech Connect

    Scott Parker

    2009-04-09

    We are developing kinetic ion models for the simulation of extended MHD phenomena. The model they have developed uses full Lorentz force ions, and either drift-kinetic or gyro-kinetic electrons. Quasi-neutrality is assumed and the displacement current is neglected. They are also studying alpha particle driven Toroidal Alfven Eigenmodes (TAE) in the GEM gyrokinetic code [Chen 07]. The basic kinetic ion MHD model was recently reported in an invited talk given by Dan Barnes at the 2007 American Physical Society - Division of Plasma Physics (APS-DPP) and it has been published [Jones 04, Barnes 08]. The model uses an Ohm's law that includes the Hall term, pressure term and the electron inertia [Jones 04]. These results focused on the ion physics and assumed an isothermal electron closure. It is found in conventional gyrokinetic turbulence simulations that the timestep cannot be made much greater than the ion cyclotron period. However, the kinetic ion MHD model has the compressional mode, which further limits the timestep. They have developed an implicit scheme to avoid this timestep constraint. They have also added drift kinetic electrons. This model has been benchmarked linearly. Waves investigated where shear and compressional Alfven, whisterl, ion acoustic, and drift waves, including the kinetic damping rates. This work is ongoing and was first reported at the 2008 Sherwood Fusion Theory Conference [Chen 08] and they are working on a publication. They have also formulated an integrated gyrokinetic electron model, which is of interest for studying electron gradient instabilities and weak guide-field magnetic reconnection.

  16. Porting the 3D Gyrokinetic Particle-in-cell Code GTC to the CRAY/NEC SX-6 Vector Architecture: Perspectives and Challenges

    SciTech Connect

    S. Ethier; Z. Lin

    2003-09-15

    Several years of optimization on the super-scalar architecture has made it more difficult to port the current version of the 3D particle-in-cell code GTC to the CRAY/NEC SX-6 vector architecture. This paper explains the initial work that has been done to port this code to the SX-6 computer and to optimize the most time consuming parts. Early performance results are shown and compared to the same test done on the IBM SP Power 3 and Power 4 machines.

  17. Gyrokinetic Calculations of Microinstabilities and Transport During RF H-Modes on Alcator C-Mod

    SciTech Connect

    M.H. Redi; C. Fiore; P. Bonoli; C. Bourdelle; R. Budny; W.D. Dorland; D. Ernst; G. Hammett; D. Mikkelsen; J. Rice; S. Wukitch

    2002-06-18

    Physics understanding for the experimental improvement of particle and energy confinement is being advanced through massively parallel calculations of microturbulence for simulated plasma conditions. The ultimate goal, an experimentally validated, global, non-local, fully nonlinear calculation of plasma microturbulence is still not within reach, but extraordinary progress has been achieved in understanding microturbulence, driving forces and the plasma response in recent years. In this paper we discuss gyrokinetic simulations of plasma turbulence being carried out to examine a reproducible, H-mode, RF heated experiment on the Alcator CMOD tokamak3, which exhibits an internal transport barrier (ITB). This off axis RF case represents the early phase of a very interesting dual frequency RF experiment, which shows density control with central RF heating later in the discharge. The ITB exhibits steep, spontaneous density peaking: a reduction in particle transport occurring without a central particle source. Since the central temperature is maintained while the central density is increasing, this also suggests a thermal transport barrier exists. TRANSP analysis shows that ceff drops inside the ITB. Sawtooth heat pulse analysis also shows a localized thermal transport barrier. For this ICRF EDA H-mode, the minority resonance is at r/a * 0.5 on the high field side. There is a normal shear profile, with q monotonic.

  18. Experimentally Relevant Benchmarks for Gyrokinetic Codes

    NASA Astrophysics Data System (ADS)

    Bravenec, Ronald

    2010-11-01

    Although benchmarking of gyrokinetic codes has been performed in the past, e.g., The Numerical Tokamak, The Cyclone Project, The Plasma Microturbulence Project, and various informal activities, these efforts have typically employed simple plasma models. For example, the Cyclone ``base case'' assumed shifted-circle flux surfaces, no magnetic transport, adiabatic electrons, no collisions nor impurities, ρi << a (ρi the ion gyroradius and a the minor radius), and no ExB flow shear. This work presents comparisons of linear frequencies and nonlinear fluxes from GYRO and GS2 with none of the above approximations except ρi << a and no ExB flow shear. The comparisons are performed at two radii of a DIII-D plasma, one in the confinement region (r/a = 0.5) and the other closer to the edge (r/a = 0.7). Many of the plasma parameters differ by a factor of two between these two locations. Good agreement between GYRO and GS2 is found when neglecting collisions. However, differences are found when including e-i collisions (Lorentz model). The sources of the discrepancy are unknown as of yet. Nevertheless, two collisionless benchmarks have been formulated with considerably different plasma parameters. Acknowledgements to J. Candy, E. Belli, and M. Barnes.

  19. Electromagnetic Gyrokinetic Simulations

    SciTech Connect

    Wan, W

    2003-11-19

    A new electromagnetic kinetic electron {delta} particle simulation model has been demonstrated to work well at large values of plasma {beta} times the ion-to-electron mass ratio. The simulation is three-dimensional using toroidal flux-tube geometry and includes electron-ion collisions. The model shows accurate shear Alfven wave damping and microtearing physics. Zonal flows with kinetic electrons are found to be turbulent with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. This is in contrast with adiabatic electron cases where the zonal flows are near stationary, even though the linear behavior of the zonal flow is not significantly affected by kinetic electrons. zonal fields are found to be very weak, consistent with theoretical predictions for {beta} below the kinetic ballooning limit. Detailed spectral analysis of the turbulence data is presented in the various limits.

  20. On intrinsic nonlinear particle motion in compact synchrotrons

    NASA Astrophysics Data System (ADS)

    Hwang, Kyung Ryun

    Due to the low energy and small curvature characteristics of compact synchrotrons, there can be unexpected features that were not present or negligible in high energy accelerators. Nonlinear kinetics, fringe field effect, and space charge effect are those features which become important for low energy and small curvature accelerators. Nonlinear kinematics can limit the dynamics aperture for compact machine even if it consists of all linear elements. The contribution of the nonlinear kinematics on nonlinear optics parameters are first derived. As the dipole bending radius become smaller, the dipole fringe field effect become stronger. Calculation of the Lie map generator and corresponding mapping equation of dipole fringe field is presented. It is found that the higher order nonlinear potential is inverse proportional to powers of fringe field extent and correction to focusing and low order nonlinear potential is proportional to powers of fringe field extent. The fringe field also found to cause large closed orbit deviation for compact synchrotrons. The 2:1 and 4:1 space charge resonances are known to cause beam loss, emittance growth and halo formation for low energy high intensity beams. By numerical simulations, we observe a higher order 6:2 space charge resonance, which can successfully be understood by the concatenation of 2:1 and 4:1 resonances via canonical perturbation. We also develop an explicit symplectic tracking method for compact electrostatic storage rings and explore the feasibility of electric dipole moment (EDM) measurements.

  1. Nonlinear Gyroviscous Force in a Collisionless Plasma

    SciTech Connect

    Belova, E.V.

    2001-05-23

    Nonlinear gyroviscous forces in a collisionless plasma with temperature variations are calculated from the gyrofluid moments of the gyrokinetic Vlasov equation. The low-frequency gyrokinetic ordering and electrostatic perturbations are assumed, and an additional finite Larmor radius (FLR) expansion is performed. This approach leads naturally to an expression for the gyroviscous force in terms of the gyrocenter distribution function, thus including all resonant effects, and represents a systematic FLR expansion in a general form (no assumption of any closure is made). The expression for the gyroviscous force is also calculated in terms of the particle-fluid moments by making the transformation from the gyrocenter to particle coordinates. The calculated expression represents a modification of the Braginskii gyroviscosity for a collisionless plasma with nonuniform temperature. It is compared with previous calculations based on the traditional fluid approach. As a byproduct of the gyroviscosity calculations, we derive a set of nonlinear reduced gyrofluid (and a corresponding set of particle-fluid) moment equations with FLR corrections, which exhibit a generalized form of the ''gyroviscous cancellation.''

  2. Equilibrium fluctuation energy of gyrokinetic plasma

    SciTech Connect

    Krommes, J.A.; Lee, W.W.; Oberman, C.

    1985-11-01

    The thermal equilibrium electric field fluctuation energy of the gyrokinetic model of magnetized plasma is computed, and found to be smaller than the well-known result (k)/8..pi.. = 1/2T/(1 + (klambda/sub D/)/sup 2/) valid for arbitrarily magnetized plasmas. It is shown that, in a certain sense, the equilibrium electric field energy is minimum in the gyrokinetic regime. 13 refs., 2 figs.

  3. Theoretical and Numerical Properties of a Gyrokinetic Plasma: Issues Related to Transport Time Scale Simulation

    SciTech Connect

    W.W. Lee

    2003-09-17

    Particle simulation has played an important role for the recent investigations on turbulence in magnetically confined plasmas. In this paper, theoretical and numerical properties of a gyrokinetic plasma as well as its relationship with magnetohydrodynamics (MHD) are discussed with the ultimate aim of simulating microturbulence in transport time scale using massively parallel computers.

  4. Adiabatic nonlinear waves with trapped particles. II. Wave dispersion

    SciTech Connect

    Dodin, I. Y.; Fisch, N. J.

    2012-01-15

    A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift {omega}{sub NL} is found analytically as a function of the wave amplitude a. Smooth distributions yield {omega}{sub NL}{proportional_to}{radical}(a), as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic {omega}{sub NL}(a) is generally nonlocal.

  5. Neoclassical equilibrium in gyrokinetic simulations

    SciTech Connect

    Garbet, X.; Dif-Pradalier, G.; Nguyen, C.; Sarazin, Y.; Grandgirard, V.; Ghendrih, Ph.

    2009-06-15

    This paper presents a set of model collision operators, which reproduce the neoclassical equilibrium and comply with the constraints of a full-f global gyrokinetic code. The assessment of these operators is based on an entropy variational principle, which allows one to perform a fast calculation of the neoclassical diffusivity and poloidal velocity. It is shown that the force balance equation is recovered at lowest order in the expansion parameter, the normalized gyroradius, hence allowing one to calculate correctly the radial electric field. Also, the conventional neoclassical transport and the poloidal velocity are reproduced in the plateau and banana regimes. The advantages and drawbacks of the various model operators are discussed in view of the requirements for neoclassical and turbulent transport.

  6. Nonlinear dynamics of toroidal Alfvén eigenmodes driven by energetic particles

    SciTech Connect

    Zhu, J.; Ma, Z. W.; Fu, G. Y.

    2013-07-15

    A kinetic simulation code based on a reduced model is developed to study dynamic evolutions of a single toroidicity-induced shear Alfvén eigenmode driven by energetic particles. For zero background damping, it is found that the wave amplitude in nonlinear phase can either saturate for weak energetic particle drives or slowly increase for strong drives. This slow nonlinear growth in strong drive cases is found to be associated with broadening and overlapping of resonances between the wave and trapped particles. For the near-marginal-stability case with a large background damping, the mode nonlinear evolution exhibits strong upward and downward frequency chirping in multiple branches. A hole/clump formation is observed clearly in the corresponding evolution of energetic particle distribution.

  7. Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas

    SciTech Connect

    Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.

    1996-12-17

    A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, {delta}f = f {minus} f{sub 0}, from an initial analytic distribution f{sub 0}. High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question.

  8. 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.

  9. Particle-Wave Micro-Dynamics in Nonlinear Self-Excited Dust Acoustic Waves

    SciTech Connect

    Tsai, C.-Y.; Teng, L.-W.; Liao, C.-T.; I Lin

    2008-09-07

    The large amplitude dust acoustic wave can be self-excited in a low-pressure dusty plasma. In the wave, the nonlinear wave-particle interaction determines particle motion, which in turn determines the waveform and wave propagation. In this work, the above behaviors are investigated by directly tracking particle motion through video-microscopy. A Lagrangian picture for the wave dynamics is constructed. The wave particle interaction associated with the transition from ordered to disordered particle oscillation, the wave crest trapping and wave heating are demonstrated and discussed.

  10. Significance of Wave-Particle Interaction Analyzer for direct measurement of nonlinear wave-particle interactions

    NASA Astrophysics Data System (ADS)

    Katoh, Y.; Kitahara, M.; Kojima, H.; Omura, Y.; Kasahara, S.; Hirahara, M.; Miyoshi, Y.; Seki, K.; Asamura, K.; Takashima, T.

    2012-12-01

    We study the statistical significance of the Wave Particle Interaction Analyzer (WPIA) for measurement of the energy transfer process between energetic electrons and whistler-mode chorus emissions in the Earth's inner magnetosphere. The WPIA measures a relative phase angle between the wave vector and velocity vector of each particle and computes an inner product W(t), while W(t) is equivalent to the variation of the kinetic energy of energetic electrons interacting with plasma waves. The WPIA measurements will be realized by the Software-type WPIA in the SPRINT-B/ERG satellite mission. In the present study, we evaluate the feasibility of WPIA by applying the WPIA analysis to the simulation results on whistler-mode chorus generation. We compute W(t) of a wave electric field observed at a fixed point assumed in the simulation system and a velocity vector of each energetic electron passing through the assumed point. By integrating W(t) in time, we obtain significant values of W_{int} in the kinetic energy and pitch angle ranges as expected from the evolution of chorus emissions in the simulation result. The statistical significance of the obtained W_{int} is evaluated by calculating the standard deviation σ_W of W_{int}. We show that W_{int} greater than σ_W is obtained in the velocity phase space corresponding to the wave generation and acceleration of relativistic electrons. We conduct another analysis of a distribution of energetic electrons in the wave phase space using the same dataset of the simulation results. We clarify that the deviation of the distribution in the wave phase space is found in the velocity phase space corresponding to the large W_{int} values, which is consistent with formation of nonlinear resonant currents assumed in the generation mechanism of chorus emissions. The present study suggests that the statistical significance of the WPIA can be evaluated by calculating σ_W of W_{int}, and reveals the feasibility of the WPIA, which will be on

  11. Numerical comparison between a gyrofluid and gyrokinetic model investigating collisionless magnetic reconnection

    SciTech Connect

    Zacharias, O.; Kleiber, R.; Borchardt, M.; Comisso, L.; Grasso, D.; Hatzky, R.

    2014-06-15

    The first detailed comparison between gyrokinetic and gyrofluid simulations of collisionless magnetic reconnection has been carried out. Both the linear and nonlinear evolution of the collisionless tearing mode have been analyzed. In the linear regime, we have found a good agreement between the two approaches over the whole spectrum of linearly unstable wave numbers, both in the drift kinetic limit and for finite ion temperature. Nonlinearly, focusing on the small-Δ′ regime, with Δ′ indicating the standard tearing stability parameter, we have compared relevant observables such as the evolution and saturation of the island width, as well as the island oscillation frequency in the saturated phase. The results are basically the same, with small discrepancies only in the value of the saturated island width for moderately high values of Δ′. Therefore, in the regimes investigated here, the gyrofluid approach can describe the collisionless reconnection process as well as the more complete gyrokinetic model.

  12. Spectral Attenuation of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

    NASA Technical Reports Server (NTRS)

    Kandula, Max

    2008-01-01

    Previous studies on the sound attenuation in particle-laden flows under Stokesian drag and conduction-controlled heat transfer have been extended to accommodate the nonlinear drag and heat transfer. It has been shown that for large particle-to-fluid density ratio, the particle Reynolds number bears a cubic relationship with (omega(tau))(sub d) (where omega is the circular frequency and (tau)(sub d) the Stokesian particle relaxation time). This dependence leads to the existence of a peak value in the linear absorption coefficient occurring at a finite value of(omega(tau))(sub d). Comparison of the predictions with the test data for the spectral attenuation of sound with water injection in a perfectly expanded supersonic air jet shows a satisfactory trend of the theory accounting for nonlinear particle relaxation processes.

  13. Spectral Attenuation of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

    NASA Technical Reports Server (NTRS)

    Kandula, M.; Lonegran, M.

    2008-01-01

    Theoretical studies on the dissipation and dispersion of sound in two-phase suspensions have been briefly reviewed. Previous studies on the sound attenuation in particle-laden flows under Stokesian drag and conduction-controlled heat transfer have been extended to accommodate the nonlinear drag and heat transfer. It has been shown that for large particle-to-fluid density ratio, the particle Reynolds number bears a cubic relationship with Omega Tau(sub d) (where Omega is the circular frequency and Tau(sub d) the Stokesian particle relaxation time). This dependence leads to the existence of a peak value in the linear absorption coefficient occurring at a finite value Omega Tau (sub d). Comparison of the predictions with the test data for the spectral attenuation of sound with water injection in a perfectly expanded supersonic air jet shows a satisfactory trend of the theory accounting for nonlinear particle relaxation processes.

  14. Direct identification of predator-prey dynamics in gyrokinetic simulations

    SciTech Connect

    Kobayashi, Sumire Gürcan, Özgür D; Diamond, Patrick H.

    2015-09-15

    The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.

  15. Multi-code benchmark of global gyrokinetic electromagnetic instabilities

    NASA Astrophysics Data System (ADS)

    Goerler, Tobias; Bottino, Alberto; Hornsby, William A.; Kleiber, Ralf; Tronko, Natalia; Grandgirard, Virginie; Norscini, Claudia; Sonnendruecker, Eric

    2015-11-01

    Considering the recent major extensions of global gyrokinetic codes towards a comprehensive and self-consistent treatment of electromagnetic (EM) effects, corresponding verification tests are obvious and necessary steps to be taken. While a number of (semi-)analytic test cases and benchmarks exist in the axisymmetric limit, microinstabilities and particularly EM turbulence are rarely addressed. In order to remedy this problem, a hierarchical linear gyrokinetic benchmark study is presented starting with electrostatic ion temperature gradient microinstabilities with adiabatic electron response and progressing finally to the characterization of fully EM instabilities as a function of β. The inter-code comparison involves contributions from Eulerian Vlasov, Lagrangian PIC, and Semi-Lagrange codes at least in one level of this verification exercise, thus confirming a high degree of reliability for the implementations that has rarely been achieved before in this context. Additionally, possible extensions of this benchmark into the physically more relevant nonlinear turbulence regime will be discussed, e.g., relaxation problems or gradient-driven setups. This work has been carried out within the framework of the EUROfusion Consortium.

  16. Gyrokinetic simulations of microturbulence in DIII-D tokamak pedestal

    NASA Astrophysics Data System (ADS)

    Holod, Ihor; Fulton, Daniel; Taimourzadeh, Sam; Lin, Zhihong; Nazikian, Raffi; Spong, Donald

    2015-11-01

    The characteristics of H-mode pedestal are generally believed to be constrained by current-driven peeling-ballooning modes and pressure-driven instabilities, such as kinetic ballooning mode (KBM). In this work we use global gyrokinetic code (GTC) to identify and study the edge pressure-driven instabilities in the H-mode pedestal using realistic geometry and plasma profiles of DIII-D shot 131997. In our simulations we observe the KBM mode marginally dominant in the steep gradient region (ψN = 0 . 98), in the range of kθ ~ 1 cm-1 which corresponds to the most unstable mode number in the nonlinearly saturated state. For shorter wavelengths the trapped electron mode becomes dominant since its linear growth rate increases with the mode number, while the KBM gets saturated. In the pedestal top region (ψN = 0 . 95) the ITG dominates. Resonant magnetic perturbations (RMP) are widely applied for ELM mitigation. During RMP suppression, the increase of edge turbulence is often observed. To understand this phenomena we use gyrokinetic simulations to address the direct effect of magnetic perturbations on the microturbulence. Simulations with 3D equilibrium reconstructed by VMEC code have been compared with toroidally averaged equilibrium, using identical pressure profiles. Work supported by DOE grant DE-SC0010416 and by General Atomics subcontract.

  17. Direct identification of predator-prey dynamics in gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    Kobayashi, Sumire; Gürcan, Özgür D.; Diamond, Patrick H.

    2015-09-01

    The interaction between spontaneously formed zonal flows and small-scale turbulence in nonlinear gyrokinetic simulations is explored in a shearless closed field line geometry. It is found that when clear limit cycle oscillations prevail, the observed turbulent dynamics can be quantitatively captured by a simple Lotka-Volterra type predator-prey model. Fitting the time traces of full gyrokinetic simulations by such a reduced model allows extraction of the model coefficients. Scanning physical plasma parameters, such as collisionality and density gradient, it was observed that the effective growth rates of turbulence (i.e., the prey) remain roughly constant, in spite of the higher and varying level of primary mode linear growth rates. The effective growth rate that was extracted corresponds roughly to the zonal-flow-modified primary mode growth rate. It was also observed that the effective damping of zonal flows (i.e., the predator) in the parameter range, where clear predator-prey dynamics is observed, (i.e., near marginal stability) agrees with the collisional damping expected in these simulations. This implies that the Kelvin-Helmholtz-like instability may be negligible in this range. The results imply that when the tertiary instability plays a role, the dynamics becomes more complex than a simple Lotka-Volterra predator prey.

  18. Validation of the gyrokinetic model in ITG and TEM dominated L-mode plasmas

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; White, A. E.; Reinke, M. L.; Greenwald, M.; Holland, C.; Candy, J.; Walk, J. R.

    2013-12-01

    A rigorous validation of the gyrokinetic model was performed in both ion temperature gradient (ITG) and trapped electron mode (TEM) dominated Alcator C-Mod plasmas at (normalized midplane minor radius) r/a = 0.5 and 0.8. Analysis focuses on two L-mode discharges operated with 1.2 and 3.5 MW of ion cyclotron resonance heating. In depth investigation into the experimental uncertainties and simulation sensitivities in these discharges allows for a stringent test of the gyrokinetic model implemented by the GYRO code (Candy and Waltz 2003 J. Comput. Phys. 186 545) in both the centre of the stiff gradient region (r/a = 0.5) and the middle of the region often associated with the transport ‘shortfall’(r/a = 0.8). To identify the nature of the plasma turbulence and to ensure a robust evaluation of the model's ability to reproduce experiment, the sensitivity of the simulation results to experimental uncertainty in turbulence drive and suppression terms were determined at both radial locations. When significant TEM activity is present, nonlinear gyrokinetic simulations are found to reproduce both electron and ion experimental heat fluxes within their diagnosed uncertainties. In contrast, in the absence of TEM, electron heat fluxes are robustly under predicted by low-k, gyrokinetic simulation.

  19. Hybrid three-dimensional variation and particle filtering for nonlinear systems

    NASA Astrophysics Data System (ADS)

    Leng, Hong-Ze; Song, Jun-Qiang

    2013-03-01

    This work addresses the problem of estimating the states of nonlinear dynamic systems with sparse observations. We present a hybrid three-dimensional variation (3DVar) and particle piltering (PF) method, which combines the advantages of 3DVar and particle-based filters. By minimizing the cost function, this approach will produce a better proposal distribution of the state. Afterwards the stochastic resampling step in standard PF can be avoided through a deterministic scheme. The simulation results show that the performance of the new method is superior to the traditional ensemble Kalman filtering (EnKF) and the standard PF, especially in highly nonlinear systems.

  20. Nonlinear d--ta-f Simulation Studies of Intense Charged Particle Beams with Large Temperature Anisotropy

    SciTech Connect

    Edward A. Startsev; Ronald C. Davidson; Hong Qin

    2002-05-07

    In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.

  1. Basic principles approach for studying nonlinear Alfven wave-alpha particle dynamics

    SciTech Connect

    Berk, H.L.; Breizman, B.N.; Pekker, M.

    1994-01-01

    An analytical model and a numerical procedure are presented which give a kinetic nonlinear description of the Alfven-wave instabilities driven by the source of energetic particles in a plasma. The steady-state and bursting nonlinear scenarios predicted by the analytical theory are verified in the test numerical simulation of the bump-on-tail instability. A mathematical similarity between the bump-on-tail problem for plasma waves and the Alfven wave problem gives a guideline for the interpretation of the bursts in the wave energy and fast particle losses observed in the tokamak experiments with neutral beam injection.

  2. Bounce-Averaged Gyrokinetic Simulation of Current-Collection Feedback in a Laboratory Magnetosphere

    NASA Astrophysics Data System (ADS)

    Roberts, T. M.; Garnier, D.; Kesner, J.; Mauel, M. E.

    2014-10-01

    A self-consistent, nonlinear simulation of interchange dynamics including the bounce-averaged gyro-kinetics of trapped electrons was previously used to understand frequency sweeping and the turbulent cascades observed in dipole-confined plasmas. Through adjustment of the particle and heat sources this code reproduces dynamics that resemble the turbulence measured experimentally, both in spectral power-law trends and in the onset of a steepened density profile. Time stepping is performed in an explicit leap-frog manner and a flux-corrected transport algorithm is implemented. In this presentation, we discuss the physics and numerical methods of the simulations as well as plans for including the effects of a biasing electrode which can collect or inject electrons. By varying this source/sink of electrons at the electrode location based on the potential fluctuations occurring elsewhere, we study the effects of current-collection feedback to compare to recent experiments observed to regulate interchange turbulence. Supported by NSF-DOE Partnership for Plasma Science and DOE Grant DE-FG02-00ER54585 and NSF Award PHY-1201896.

  3. Gyrokinetic Vlasov-Poisson simulation in slab geometry using the conservative IDO scheme

    NASA Astrophysics Data System (ADS)

    Imadera, Kenji; Kishimoto, Yasuaki; Li, Jiquan; Saito, Daisuke; Utsumi, Takayuki

    2008-11-01

    We have introduced the IDO-CF (Conservative Form of Interpolated Differential Operator) scheme [1], which is one of the multi-moment schemes and has been applied to various CFD problems, in solving a Vlasov-Poisson system. The IDO scheme is found to be efficient in capturing a sharp domain interface like shock propagation, and in introducing dissipations like particle collision and also external source/sink terms. Furthermore, the IDO-CF scheme has exact mass conservation properties, so that we can apply it to the problems that need long time scale simulations. We first apply the scheme in studying the nonlinear Landau damping and two-stream instability. We have investigated the conservation property of the total mass, energy and entropy, and found that the IDO-CF scheme allows stable simulation over many bounce periods keeping higher accuracy than other multi-moment schemes. We have also developed a gyrokinetic full-f Vlasov code with the IDO-CF scheme in studying the slab ITG driven turbulence. [1] Y.Imai et al., J. Comput. Phys. 227, 2263(2008).

  4. Gyrokinetic study of edge blobs and divertor heat-load footprint

    NASA Astrophysics Data System (ADS)

    Chang, C.-S.; Ku, S.-H.; Churchill, M.; Zweben, S.

    2014-10-01

    In an attempt to better understand the complicated physics of the inter-related ``intermittent plasma objects (blobs)'' and divertor heat-load footprint, the full-function gyrokinetic PIC code XGC1 has been used in realistic diverted geometry. Neoclassical and turbulence physics are simulated together self-consistently in the presence of Monte Carlo neutral particles. Blobs are modeled here as electrostatic nonlinear turbulence phenomenon. It is found that the ``blobs'' are generated, together with the ``holes,'' around the steep density gradient region. XGC1 reasserts the previous findings that blobs move out convectively into the scrape-off layer, while the holes move inward toward plasma core. The measured radial width of the divertor heat load, mapped to the outer midplane, is found to be much less than the median radial size of the intermittent plasma objects, but is rather closer to the width of neoclassical orbit excursion from pedestal to divertor, yielding approximately the 1/Ip-type scaling found from our previous pure neoclassical simulation or a heuristic neoclassical argument by Goldston. However, it also shows some spreading by the intermittent turbulence. In ITER plasma edge, where the ion banana width at separatrix becomes negligibly small compared to the meso-scale blob size, blobs may saturate the 1/Ip scaling.

  5. Gyrokinetic δ f simulation of collisionless and semi-collisional tearing mode instabilities

    NASA Astrophysics Data System (ADS)

    Wan, Weigang; Chen, Yang; Parker, Scott

    2004-11-01

    The evolution of collisionless and semi-collisional tearing mode instabilities is studied using a three-dimensional particle-in-cell simulation model that utilizes the δ f-method with the split-weight scheme to enhance the time step, and a novel algorithm(Y. Chen and S.E. Parker, J. Comput. Phys. 198), 463 (2003) to accurately solve the Ampere's equation for experimentally relevant β values, βfracm_im_e≫ 1. We use the model of drift-kinetic electrons and gyrokinetic ions. Linear simulation results are benchmarked with eigenmode analysis for the case of fixed ions. In small box simulations the ions response can be neglected but for large box simulations the ions response is important because the width of perturbed current is larger than ρ_i.The nonlinear dynamics of magnetic islands will be studied and the results will be compared with previous theoretical studiesfootnote J.F. Drake and Y. C. Lee, Phys. Rev. Lett. 39, 453 (1977) on the saturation level and the electron bounce frequency. A collision operator is included in the electron drift kinetic equation to study the simulation in the semi-collisional regime. The algebraical growth stage has been observed and compared quantitatively with theory. Our progress on three-dimensional simulations of tearing mode instabilities will be reported.

  6. Complex statistics and diffusion in nonlinear disordered particle chains

    SciTech Connect

    Antonopoulos, Ch. G.; Bountis, T.; Skokos, Ch.; Drossos, L.

    2014-06-15

    We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion, in both cases, in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as 10{sup 9}, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times.

  7. Dynamic procedure for filtered gyrokinetic simulations

    SciTech Connect

    Morel, P.; Banon Navarro, A.; Albrecht-Marc, M.; Carati, D.; Merz, F.; Goerler, T.; Jenko, F.

    2012-01-15

    Large eddy simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the gene code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved direct numerical simulations. Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in ion temperature gradient driven turbulence. Moreover, the degree of anisotropy of the problem, which can vary with parameters, can be adapted dynamically by the method that shows gyrokinetic large eddy simulation to be a serious candidate to reduce numerical cost of gyrokinetic solvers.

  8. A computational and theoretical investigation of nonlinear wave-particle interactions in oblique whistlers

    NASA Astrophysics Data System (ADS)

    Nunn, David; Omura, Yoshiharu

    2015-04-01

    Most previous work on nonlinear wave-particle interactions between energetic electrons and VLF waves in the Earth's magnetosphere has assumed parallel propagation, the underlying mechanism being nonlinear trapping of cyclotron resonant electrons in a parabolic magnetic field inhomogeneity. Here nonlinear wave-particle interaction in oblique whistlers in the Earth's magnetosphere is investigated. The study is nonself-consistent and assumes an arbitrarily chosen wave field. We employ a "continuous wave" wave field with constant frequency and amplitude, and a model for an individual VLF chorus element. We derive the equations of motion and trapping conditions in oblique whistlers. The resonant particle distribution function, resonant current, and nonlinear growth rate are computed as functions of position and time. For all resonances of order n, resonant electrons obey the trapping equation, and provided the wave amplitude is big enough for the prevailing obliquity, nonlinearity manifests itself by a "hole" or "hill" in distribution function, depending on the zero-order distribution function and on position. A key finding is that the n = 1 resonance is relatively unaffected by moderate obliquity up to 25°, but growth rates roll off rapidly at high obliquity. The n = 1 resonance saturates due to the adiabatic effect and here reaches a maximum growth at ~20 pT, 2000 km from the equator. Damping due to the n = 0 resonance is not subject to adiabatic effects and maximizes at some 8000 km from the equator at an obliquity ~55°.

  9. Gyrokinetic Simulations of Enhanced Alpha Transport by De-stabilized Alfvèn Turbulence

    NASA Astrophysics Data System (ADS)

    Bass, E. M.

    2009-11-01

    Alfvèn turbulence, destabilized by fusion-produced α-particles, is expected to greatly enhance transport of these hot fusion products. Previously, the gyrokinetic code GYRO [1] was used to simulate the convective transport of fusion alpha particles by electrostatic (β=0) ITG/TEM turbulence driven at low k (0particles are modeled by a hot Maxwellian (Tα=100,e) superimposed at trace density (0.005< nα/ne<0.025 and a/Lα=4 fixed) on the background plasma. Linear stability studies show two high-frequency modes driven unstable at very long wavelength (0particle mode (EPM), exhibit hybrid ``drift-Alfvèn" frequency scaling with kθρs and nα. At densities below the Alfvèn linear stability threshold (nα/ne<=0.005), ITG/TEM turbulence dominates nonlinear simulations. In this limit, the transported alpha particles are passive tracers and ion and electron transport agrees well with nα=0 results. Just above the alpha-particle density gradient threshold, Alfvènic (TAE/EPM) drive enhances transport in α-particle and background channels. This trend continues as nα and TAE/EPM microturbulence drive increase. The focus is on conditions for obtaining stationary nonlinearly saturated transport avoiding any subcritical limit on the total beta gradient. 8pt [1] J. Candy and R.E. Waltz, Phys. Rev. Lett. 91, 045001 (2003). [2] C. Estrada-Mila, et al., Phys. Plasmas 13, 112303 (2006).

  10. Gyrokinetic investigation of ITG turbulence in helical RFPs

    NASA Astrophysics Data System (ADS)

    Predebon, I.; Xanthopoulos, P.; Terranova, D.

    2014-10-01

    Micro-instabilities in reversed field pinch (RFP) plasmas have been investigated in the last years from several viewpoints and with various numerical tools. So far, axisymmetry of the magnetic equilibrium has always been postulated. Nevertheless, experimental evidence suggests that the physical conditions mostly favoring the onset of electrostatic/electromagnetic turbulence, e.g., the occurrence of large pressure gradients, emerge when magnetic surfaces become helical, during the single helicity states. In this work, we investigate ion-temperature-gradient driven turbulence focusing on the 3D feature, with the aim to describe its distinct properties compared to the axisymmetric geometry. For this study, we will apply the 3D nonlinear gyrokinetic code GENE to RFP equilibria generated by the VMEC code.

  11. Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams

    SciTech Connect

    Nikolas C. Logan and Ronald C. Davidson

    2012-07-18

    This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT⊥ < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.

  12. Summary report of the group on single-particle nonlinear dynamics

    SciTech Connect

    Axinescu, S.; Bartolini, R.; Bazzani, A.

    1996-10-01

    This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects.

  13. Cosmology and low energy particle physics of nonlinear supersymmetric general relativity

    SciTech Connect

    Shima, Kazunari; Tsuda, Motomu

    2009-04-17

    The basic idea and some physical implications of nonlinear supersymmetric general relativity(NLSUSY GR) are discussed, which give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g., the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.

  14. Communication: The origin of many-particle signals in nonlinear optical spectroscopy of non-interacting particles.

    PubMed

    Mukamel, Shaul

    2016-07-28

    Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N. We show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles. PMID:27475341

  15. Communication: The origin of many-particle signals in nonlinear optical spectroscopy of non-interacting particles

    NASA Astrophysics Data System (ADS)

    Mukamel, Shaul

    2016-07-01

    Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N. We show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles.

  16. Gyrokinetic stability theory of electron-positron plasmas

    NASA Astrophysics Data System (ADS)

    Helander, P.; Connor, J. W.

    2016-06-01

    > The linear gyrokinetic stability properties of magnetically confined electron-positron plasmas are investigated in the parameter regime most likely to be relevant for the first laboratory experiments involving such plasmas, where the density is small enough that collisions can be ignored and the Debye length substantially exceeds the gyroradius. Although the plasma beta is very small, electromagnetic effects are retained, but magnetic compressibility can be neglected. The work of a previous publication (Helander, Phys. Rev. Lett., vol. 113, 2014a, 135003) is thus extended to include electromagnetic instabilities, which are of importance in closed-field-line configurations, where such instabilities can occur at arbitrarily low pressure. It is found that gyrokinetic instabilities are completely absent if the magnetic field is homogeneous: any instability must involve magnetic curvature or shear. Furthermore, in dipole magnetic fields, the stability threshold for interchange modes with wavelengths exceeding the Debye radius coincides with that in ideal magnetohydrodynamics. Above this threshold, the quasilinear particle flux is directed inward if the temperature gradient is sufficiently large, leading to spontaneous peaking of the density profile.

  17. Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

    NASA Technical Reports Server (NTRS)

    Tkalcevic, S.

    1982-01-01

    The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

  18. A nonlinear auxetic structural vibration damper with metal rubber particles

    NASA Astrophysics Data System (ADS)

    Ma, Yanhong; Scarpa, Fabrizio; Zhang, Dayi; Zhu, Bin; Chen, Lulu; Hong, Jie

    2013-08-01

    The work describes the mechanical performance of a metal rubber particles (MRP) damper design based on an auxetic (negative Poisson’s ratio) cellular configuration. The auxetic damper configuration is constituted by an anti-tetrachiral honeycomb, where the cylinders are filled with the MRP material. The MRP samples have been subjected to quasi-static loading to measure the stiffness and loss factor from the static hysteresis curve. A parametric experimental analysis has been carried out to investigate the effect of relative density and filling percentage on the static performance of the MRP, and to identify design guidelines for best use of MRP devices. An experimental assessment of the integrated auxetic-MRP damper concept has been provided through static and dynamic force response techniques.

  19. Gyrokinetic simulation of the collisional micro-tearing mode instability

    NASA Astrophysics Data System (ADS)

    Startsev, Edward; Lee, Wei-Li; Wang, Weixing

    2015-11-01

    An application of recently developed perturbative particle simulation scheme for finite- β plasmas in the presence of background inhomogeneities is presented. Originally, using similar scheme, we were able to simulate shear-Alfven waves, finite- β modified drift waves and ion temperature gradient modes using a simple gyrokinetic particle code based on realistic fusion plasma parameters. Recently, we have successfully used the scheme for simulation of linear tearing and drift-tearing modes, in both collisionless semi-collisional regimes in slab geometry with sheared magnetic field. Here, we present further development of this scheme for the simulation of linear semi-collisional micro-tearing mode driven by electron temperature gradient in high-aspect ratio cylindrical cross-section tokamak using the modified turbulence code GTS. Research supported by the U. S. Department of Energy.

  20. Nonlinear gyrofluid model of ITG turbulence

    SciTech Connect

    Dorland, W.; Hammett, G.w.; Hahm, T.S.; Beer, M.A. )

    1994-05-01

    Early results from nonlinear simulations and analysis based on a recently derived nonlinear gyrofluid model [W. Dorland and G. W. Hammett, Phys. Fluids B, 812 (1993)] of electrostatic ion-temperature-gradient driven turbulence are presented. Comparisons with gyrokinetic particle simulations reveal a few important simulation requirements (such as enforcing radial periodicity), and indicate that the gyrofluid description is probably adequate to describe three-dimensional, low-frequency drift-type turbulence. Results from a detailed weak-turbulence analysis of drift wave turbulence are presented which support this conclusion. The importance of keeping the proper adiabatic electron response is also discussed. In particular, perpendicular velocity shear is greatly enhanced when the magnetic shear is weak if the nonphysical radial transport of electrons is disallowed.

  1. Gyrokinetic studies of core turbulence features in ASDEX Upgrade: Can gyrokinetic simulations match the fluctuation measurements?

    NASA Astrophysics Data System (ADS)

    Banon Navarro, Alejandro

    2015-11-01

    Worldwide, gyrokinetic codes are used to predict the dominant micro-instabilities as well as the resulting anomalous transport in fusion experiments. A careful verification and validation of these codes is crucial to develop confidence in the model and improving the predictive capabilities of the numerical simulations. To date, the validation of gyrokinetic simulations versus experiments is mainly done at a macroscopic level, namely, by comparing turbulent heat fluxes. This is usually achieved by varying the profile gradients within the experimental error bars until a match with the experimental heat fluxes is obtained. However, since the turbulent fluxes are caused by plasma fluctuations on microscopic scales, it is also necessary to validate gyrokinetic codes on a microscopic level. We will describe a recent step in this direction by presenting simulation results with the gyrokinetic code GENE for an ASDEX Upgrade discharge. In particular, after flux-matched simulations are achieved, density fluctuations measured by means of Doppler reflectometry are compared with results of gyrokinetic simulations. We will also show that density and temperature fluctuation amplitudes and even the fluctuation spectra can be very sensitive to small changes in the profile gradients. This implies that a match of gyrokinetic simulations with experiment measurements for these quantities can be very difficult to achieve. However, it is observed that cross-phases between different quantities are robust to changes in this parameter, indicating that cross-phases could be a better observable for comparisons with experimental measurements.

  2. Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

    NASA Astrophysics Data System (ADS)

    Huang, Xiaobiao; Safranek, James

    2014-09-01

    Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.

  3. Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulationsa)

    NASA Astrophysics Data System (ADS)

    White, A. E.; Howard, N. T.; Greenwald, M.; Reinke, M. L.; Sung, C.; Baek, S.; Barnes, M.; Candy, J.; Dominguez, A.; Ernst, D.; Gao, C.; Hubbard, A. E.; Hughes, J. W.; Lin, Y.; Mikkelsen, D.; Parra, F.; Porkolab, M.; Rice, J. E.; Walk, J.; Wukitch, S. J.; Team, Alcator C-Mod

    2013-05-01

    Multi-channel transport experiments have been conducted in auxiliary heated (Ion Cyclotron Range of Frequencies) L-mode plasmas at Alcator C-Mod [Marmar and Alcator C-Mod Group, Fusion Sci. Technol. 51(3), 3261 (2007)]. These plasmas provide good diagnostic coverage for measurements of kinetic profiles, impurity transport, and turbulence (electron temperature and density fluctuations). In the experiments, a steady sawtoothing L-mode plasma with 1.2 MW of on-axis RF heating is established and density is scanned by 20%. Measured rotation profiles change from peaked to hollow in shape as density is increased, but electron density and impurity profiles remain peaked. Ion or electron heat fluxes from the two plasmas are the same. The experimental results are compared directly to nonlinear gyrokinetic theory using synthetic diagnostics and the code GYRO [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. We find good agreement with experimental ion heat flux, impurity particle transport, and trends in the fluctuation level ratio (T˜e/Te)/(n ˜e/ne), but underprediction of electron heat flux. We find that changes in momentum transport (rotation profiles changing from peaked to hollow) do not correlate with changes in particle transport, and also do not correlate with changes in linear mode dominance, e.g., Ion Temperature Gradient versus Trapped Electron Mode. The new C-Mod results suggest that the drives for momentum transport differ from drives for heat and particle transport. The experimental results are inconsistent with present quasilinear models, and the strong sensitivity of core rotation to density remains unexplained.

  4. Multi-channel transport experiments at Alcator C-Mod and comparison with gyrokinetic simulations

    SciTech Connect

    White, A. E.; Howard, N. T.; Greenwald, M.; Reinke, M. L.; Sung, C.; Baek, S.; Barnes, M.; Dominguez, A.; Ernst, D.; Gao, C.; Hubbard, A. E.; Hughes, J. W.; Lin, Y.; Parra, F.; Porkolab, M.; Rice, J. E.; Walk, J.; Wukitch, S. J.; Team, Alcator C-Mod; Candy, J.; and others

    2013-05-15

    Multi-channel transport experiments have been conducted in auxiliary heated (Ion Cyclotron Range of Frequencies) L-mode plasmas at Alcator C-Mod [Marmar and Alcator C-Mod Group, Fusion Sci. Technol. 51(3), 3261 (2007)]. These plasmas provide good diagnostic coverage for measurements of kinetic profiles, impurity transport, and turbulence (electron temperature and density fluctuations). In the experiments, a steady sawtoothing L-mode plasma with 1.2 MW of on-axis RF heating is established and density is scanned by 20%. Measured rotation profiles change from peaked to hollow in shape as density is increased, but electron density and impurity profiles remain peaked. Ion or electron heat fluxes from the two plasmas are the same. The experimental results are compared directly to nonlinear gyrokinetic theory using synthetic diagnostics and the code GYRO [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. We find good agreement with experimental ion heat flux, impurity particle transport, and trends in the fluctuation level ratio (T(tilde sign){sub e}/T{sub e})/(ñ{sub e}/n{sub e}), but underprediction of electron heat flux. We find that changes in momentum transport (rotation profiles changing from peaked to hollow) do not correlate with changes in particle transport, and also do not correlate with changes in linear mode dominance, e.g., Ion Temperature Gradient versus Trapped Electron Mode. The new C-Mod results suggest that the drives for momentum transport differ from drives for heat and particle transport. The experimental results are inconsistent with present quasilinear models, and the strong sensitivity of core rotation to density remains unexplained.

  5. On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles

    SciTech Connect

    G. Y. Fu

    2010-06-04

    It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

  6. On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles

    SciTech Connect

    G.Y. Fu

    2010-10-01

    It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

  7. Nonlinear simulations of particle source effects on edge localized mode

    SciTech Connect

    Huang, J.; Tang, C. J.; Chen, S. Y.; Wang, Z. H.

    2015-12-15

    The effects of particle source (PS) with different intensities and located positions on Edge Localized Mode (ELM) are systematically studied with BOUT++ code. The results show the ELM size strongly decreases with increasing the PS intensity once the PS is located in the middle or bottom of the pedestal. The effects of PS on ELM depend on the located position of PS. When it is located at the top of the pedestal, peeling-ballooning (P-B) modes can extract more free energy from the pressure gradient and grow up to be a large filament at the initial crash phase and the broadening of mode spectrum can be suppressed by PS, which leads to more energy loss. When it is located in the middle or bottom of the pedestal, the extraction of free energy by P-B modes can be suppressed, and a small filament is generated. During the turbulence transport phase, the broader mode spectrum suppresses the turbulence transport when PS is located in the middle, while the zonal flow plays an important role in damping the turbulence transport when PS is located at the bottom.

  8. Nonlinear simulations of particle source effects on edge localized mode

    NASA Astrophysics Data System (ADS)

    Huang, J.; Chen, S. Y.; Wang, Z. H.; Tang, C. J.

    2015-12-01

    The effects of particle source (PS) with different intensities and located positions on Edge Localized Mode (ELM) are systematically studied with BOUT++ code. The results show the ELM size strongly decreases with increasing the PS intensity once the PS is located in the middle or bottom of the pedestal. The effects of PS on ELM depend on the located position of PS. When it is located at the top of the pedestal, peeling-ballooning (P-B) modes can extract more free energy from the pressure gradient and grow up to be a large filament at the initial crash phase and the broadening of mode spectrum can be suppressed by PS, which leads to more energy loss. When it is located in the middle or bottom of the pedestal, the extraction of free energy by P-B modes can be suppressed, and a small filament is generated. During the turbulence transport phase, the broader mode spectrum suppresses the turbulence transport when PS is located in the middle, while the zonal flow plays an important role in damping the turbulence transport when PS is located at the bottom.

  9. A modified ensemble Kalman particle filter for non-Gaussian systems with nonlinear measurement functions

    NASA Astrophysics Data System (ADS)

    Shen, Zheqi; Tang, Youmin

    2016-04-01

    The ensemble Kalman particle filter (EnKPF) is a combination of two Bayesian-based algorithms, namely, the ensemble Kalman filter (EnKF) and the sequential importance resampling particle filter(SIR-PF). It was recently introduced to address non-Gaussian features in data assimilation for highly nonlinear systems, by providing a continuous interpolation between the EnKF and SIR-PF analysis schemes. In this paper, we first extend the EnKPF algorithm by modifying the formula for the computation of the covariancematrix, making it suitable for nonlinear measurement functions (we will call this extended algorithm nEnKPF). Further, a general form of the Kalman gain is introduced to the EnKPF to improve the performance of the nEnKPF when the measurement function is highly nonlinear (this improved algorithm is called mEnKPF). The Lorenz '63 model and Lorenz '96 model are used to test the two modified EnKPF algorithms. The experiments show that the mEnKPF and nEnKPF, given an affordable ensemble size, can perform better than the EnKF for the nonlinear systems with nonlinear observations. These results suggest a promising opportunity to develop a non-Gaussian scheme for realistic numerical models.

  10. 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.

  11. Gyrokinetic simulations of electrostatic microinstabilities with bounce-averaged kinetic electrons for shaped tokamak plasmas

    NASA Astrophysics Data System (ADS)

    Qi, Lei; Kwon, Jaemin; Hahm, T. S.; Jo, Gahyung

    2016-06-01

    Nonlinear bounce-averaged kinetic theory [B. H. Fong and T. S. Hahm, Phys. Plasmas 6, 188 (1999)] is used for magnetically trapped electron dynamics for the purpose of achieving efficient gyrokinetic simulations of Trapped Electron Mode (TEM) and Ion Temperature Gradient mode with trapped electrons (ITG-TEM) in shaped tokamak plasmas. The bounce-averaged kinetic equations are explicitly extended to shaped plasma equilibria from the previous ones for concentric circular plasmas, and implemented to a global nonlinear gyrokinetic code, Gyro-Kinetic Plasma Simulation Program (gKPSP) [J. M. Kwon et al., Nucl. Fusion 52, 013004 (2012)]. Verification of gKPSP with the bounce-averaged kinetic trapped electrons in shaped plasmas is successfully carried out for linear properties of the ITG-TEM mode and Rosenbluth-Hinton residual zonal flow [M. N. Rosenbluth and F. L. Hinton, Phys. Rev. Lett. 80, 724 (1998)]. Physics responsible for stabilizing effects of elongation on both ITG mode and TEM is identified using global gKPSP simulations. These can be understood in terms of magnetic flux expansion, leading to the effective temperature gradient R / L T ( 1 - E ') [P. Angelino et al., Phys. Rev. Lett. 102, 195002 (2009)] and poloidal wave length contraction at low field side, resulting in the effective poloidal wave number kθρi/κ.

  12. The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

    NASA Astrophysics Data System (ADS)

    Staebler, G. M.; Candy, J.; Howard, N. T.; Holland, C.

    2016-06-01

    The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

  13. 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.

  14. 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

  15. Gyrokinetic studies of core turbulence features in ASDEX Upgrade H-mode plasmas

    SciTech Connect

    Navarro, A. Bañón Told, D.; Happel, T.; Görler, T.; Abiteboul, J.; Bustos, A.; Doerk, H.; Jenko, F.

    2015-04-15

    Gyrokinetic validation studies are crucial for developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.

  16. Multiscale Nature of the Dissipation Range in Gyrokinetic Simulations of Alfvénic Turbulence.

    PubMed

    Told, D; Jenko, F; TenBarge, J M; Howes, G G; Hammett, G W

    2015-07-10

    Nonlinear energy transfer and dissipation in Alfvén wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at 1 AU, about 30% of the nonlinear energy transfer close to the electron gyroradius scale is mediated by modes in the tail of the MHD cascade. Collisional dissipation occurs across the entire kinetic range k(⊥)ρ(I)≳1. Both mechanisms thus act on multiple coupled scales, which have to be retained for a comprehensive picture of the dissipation range in Alfvénic turbulence. PMID:26207474

  17. Non-perturbative aspects of particle acceleration in non-linear electrodynamics

    NASA Astrophysics Data System (ADS)

    Burton, David A.; Flood, Stephen P.; Wen, Haibao

    2015-04-01

    We undertake an investigation of particle acceleration in the context of non-linear electrodynamics. We deduce the maximum energy that an electron can gain in a non-linear density wave in a magnetised plasma, and we show that an electron can "surf" a sufficiently intense Born-Infeld electromagnetic plane wave and be strongly accelerated by the wave. The first result is valid for a large class of physically reasonable modifications of the linear Maxwell equations, whilst the second result exploits the special mathematical structure of Born-Infeld theory.

  18. Non-perturbative aspects of particle acceleration in non-linear electrodynamics

    SciTech Connect

    Burton, David A.; Flood, Stephen P.; Wen, Haibao

    2015-04-15

    We undertake an investigation of particle acceleration in the context of non-linear electrodynamics. We deduce the maximum energy that an electron can gain in a non-linear density wave in a magnetised plasma, and we show that an electron can “surf” a sufficiently intense Born-Infeld electromagnetic plane wave and be strongly accelerated by the wave. The first result is valid for a large class of physically reasonable modifications of the linear Maxwell equations, whilst the second result exploits the special mathematical structure of Born-Infeld theory.

  19. Verification of nonlinear particle simulation of radio frequency waves in tokamak

    SciTech Connect

    Kuley, A. Lin, Z.; Bao, J.; Wei, X. S.; Xiao, Y.; Zhang, W.; Sun, G. Y.; Fisch, N. J.

    2015-10-15

    Nonlinear simulation model for radio frequency waves in fusion plasmas has been developed and verified using fully kinetic ion and drift kinetic electron. Ion cyclotron motion in the toroidal geometry is implemented using Boris push in the Boozer coordinates. Linear dispersion relation and nonlinear particle trapping are verified for the lower hybrid wave and ion Bernstein wave (IBW). Parametric decay instability is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating, with a heating rate proportional to the pump wave intensity.

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

    DOE PAGESBeta

    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

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

    SciTech Connect

    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 illustrate some of the physics contained in the Hamiltonian form of the gyrokineticequations and some of the numerical challenges in developing an edge gyrokinetic code.

  2. Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed.

    PubMed

    Menzel, Andreas M

    2015-11-01

    Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient. PMID:26651690

  3. Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed

    NASA Astrophysics Data System (ADS)

    Menzel, Andreas M.

    2015-11-01

    Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

  4. Canonical Lie-transform method in Hamiltonian gyrokinetics: a new approach

    SciTech Connect

    Nicolini, Piero; Tessarotto, Massimo

    2005-05-16

    The well-known gyrokinetic problem regards the perturbative expansion related to the dynamics of a charged particle subject to fast gyration motion due to the presence of a strong magnetic field. Although a variety of approaches have been formulated in the past to this well known problem, surprisingly a purely canonical approach based on Lie transform methods is still missing. This paper aims to fill in this gap and provide at the same time new insight in Lie-transform approaches.

  5. Global spectral investigation of plasma turbulence in gyrokinetic simulations

    SciTech Connect

    Henriksson, S. V.; Janhunen, S. J.; Kiviniemi, T. P.; Heikkinen, J. A.

    2006-07-15

    Gyrokinetic global particle-in-cell simulations for a small torus with a large aspect ratio ({epsilon}{sup -1}>{approx}7) indicate a k{sub perpendicular}{sup -{alpha}} spectrum for electrostatic turbulence. When electrons are treated kinetically, the simulation results fit {alpha} that grows from about 1 at the plasma core to about 3 at the plasma edge for the flux surface component of the wave vector perpendicular to the magnetic field, while for adiabatic electrons {alpha}=4 is found for all radii, in agreement with the Hasegawa-Mima model. The relation between spectra and transport is investigated through the formation of an internal transport barrier. The role of flow shear in suppressing turbulence is illustrated by spectral diagnostics. A strong dependence between the presence of small wavenumbers and transport is explicitly observed. The simulated spectra are compared to recent experimental results.

  6. Overview of gyrokinetic studies of finite-β microturbulence

    NASA Astrophysics Data System (ADS)

    Terry, P. W.; Carmody, D.; Doerk, H.; Guttenfelder, W.; Hatch, D. R.; Hegna, C. C.; Ishizawa, A.; Jenko, F.; Nevins, W. M.; Predebon, I.; Pueschel, M. J.; Sarff, J. S.; Whelan, G. G.

    2015-10-01

    Recent results on electromagnetic turbulence from gyrokinetic studies in different magnetic configurations are overviewed, detailing the physics of electromagnetic turbulence and transport, and the effect of equilibrium magnetic field scale lengths. Ion temperature gradient (ITG) turbulence is shown to produce magnetic stochasticity through nonlinear excitation of linearly stable tearing-parity modes. The excitation, which is catalyzed by the zonal flow, produces an electron heat flux proportional to β2 that deviates markedly from quasilinear theory. Above a critical beta known as the non-zonal transition (NZT), the magnetic fluctuations disable zonal flows by allowing electron streaming that shorts zonal potential between flux surfaces. This leads to a regime of very high transport levels. Kinetic ballooning mode (KBM) saturation is described. For tokamaks saturation involves twisted structures arising from magnetic shear; for helical plasmas oppositely inclined convection cells interact by mutual shearing. Microtearing modes are unstable in the magnetic geometry of tokamaks and the reversed field pinch (RFP). In NSTX instability requires finite collisionality, large beta, and is favored by increasing magnetic shear and decreasing safety factor. In the RFP, a new branch of microtearing with finite growth rate at vanishing collisionality is shown from analytic theory to require the electron grad-B/curvature drift resonance. However, gyrokinetic modeling of experimental MST RFP discharges at finite beta reveals turbulence that is electrostatic, has large zonal flows, and a large Dimits shift. Analysis shows that the shorter equilibrium magnetic field scale lengths increase the critical gradients associated with the instability of trapped electron modes, ITG and microtearing, while increasing beta thresholds for KBM instability and the NZT.

  7. Non-linear interactions of plasma waves in the context of solar particle acceleration

    NASA Astrophysics Data System (ADS)

    Gallegos-Cruz, A.; Perez-Peraza, J.

    2001-08-01

    Stochastic particle acceleration in plasmas by means of MHD turbulence in-volves a wide range of alternatives according to, the specific wave mode, the frequency regime of the turbulence, the kind of particles to be accelerated, the assumed plasma model and so on. At present most of the alternatives have been studied with relatively deepness, though some features are not yet com-pletely understood. One of them is the delimitation of the real importance of non-lineal effects of turbulence waves in the process of particle acceleration. In this work we analyse such effects taking into account the temporal evolution of the turbulence. For illustration we exemplify our analysis with the fast MHD mode. Our results show that in some specific stages of the turbulence evolu-tion, non-linear interactions have important effects in the process of particle acceleration.

  8. Nonlinear delta(f) Simulations of Collective Effects in Intense Charged Particle Beams

    SciTech Connect

    Hong Qin

    2003-01-21

    A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.

  9. A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

    DOE PAGESBeta

    Hager, Robert; Yoon, E. S.; Ku, S.; D'Azevedo, E. F.; Worley, P. H.; Chang, C. S.

    2016-04-04

    Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

  10. A fully non-linear multi-species Fokker-Planck-Landau collision operator for simulation 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.

    2016-06-01

    Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker-Planck-Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker-Planck-Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.

  11. Global gyrokinetic simulation of tokamak transport

    SciTech Connect

    Furnish, G.; Horton, W.; Kishimoto, Y.; LeBrun, M.J.; Tajima, T. |

    1998-10-01

    A kinetic simulation code based on the gyrokinetic ion dynamics in global general metric (including a tokamak with circular or noncircular cross-section) has been developed. This gyrokinetic simulation is capable of examining the global and semi-global driftwave structures and their associated transport in a tokamak plasma. The authors investigate the property of the ion temperature gradient (ITG) or {eta}{sub i}({eta}{sub i} {equivalent_to} {partial_derivative}{ell}nT{sub i}/{partial_derivative}{ell}n n{sub i}) driven drift waves in a tokamak plasma. The emergent semi-global drift wave modes give rise to thermal transport characterized by the Bohm scaling.

  12. Chasing hamiltonian structure in gyrokinetic theory

    NASA Astrophysics Data System (ADS)

    Burby, J. W.

    Hamiltonian structure is pursued and uncovered in collisional and collisionless gyrokinetic theory. A new Hamiltonian formulation of collisionless electromagnetic theory is presented that is ideally suited to implementation on modern supercomputers. The method used to uncover this structure is described in detail and applied to a number of examples, where several well-known plasma models are endowed with a Hamiltonian structure for the first time. The first energy- and momentum-conserving formulation of full-F collisional gyrokinetics is presented. In an effort to understand the theoretical underpinnings of this result at a deeper level, a emph{stochastic} Hamiltonian modeling approach is presented and applied to pitch angle scattering. Interestingly, the collision operator produced by the Hamiltonian approach is equal to the Lorentz operator plus higher-order terms, but does not exactly conserve energy. Conversely, the classical Lorentz collision operator is provably not Hamiltonian in the stochastic sense.

  13. Transport of momentum in full f gyrokinetics

    SciTech Connect

    Parra, Felix I.; Catto, Peter J.

    2010-05-15

    Full f electrostatic gyrokinetic formulations employ two gyrokinetic equations, one for ions and the other for electrons, and quasineutrality to obtain the ion and electron distribution functions and the electrostatic potential. We demonstrate with several examples that the long wavelength radial electric field obtained with full f approaches is extremely sensitive to errors in the ion and electron density since small deviations in density give rise to large, nonphysical deviations in the conservation of toroidal angular momentum. For typical tokamak values, a relative error of 10{sup -7} in the ion or electron densities is enough to obtain the incorrect toroidal rotation. Based on the insights gained with the examples considered, three simple tests to check transport of toroidal angular momentum in full f simulations are proposed.

  14. Gyrokinetic Statistical Absolute Equilibrium and Turbulence

    SciTech Connect

    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, corresponding 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.

  15. Parallel magnetic field perturbations in gyrokinetic simulations

    SciTech Connect

    Joiner, N.; Hirose, A.; Dorland, W.

    2010-07-15

    At low beta it is common to neglect parallel magnetic field perturbations on the basis that they are of order beta{sup 2}. This is only true if effects of order beta are canceled by a term in the nablaB drift also of order beta[H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 (1977)]. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)] to investigate whether the compressional magnetic field perturbation B{sub ||} is required for accurate gyrokinetic simulations at low beta for microinstabilities commonly found in tokamaks. The kinetic ballooning mode (KBM) demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient (ETG) driven modes do not typically exhibit this behavior; the effects of B{sub ||} are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with eta{sub e}. The effect of B{sub ||} on the ETG instability is shown to depend on the normalized pressure gradient beta{sup '} at constant beta.

  16. Velocity-space resolution, entropy production, and upwind dissipation in Eulerian gyrokinetic simulations

    SciTech Connect

    Candy, J.; Waltz, R.E.

    2006-03-15

    Equations which describe the evolution of volume-averaged gyrokinetic entropy are derived and added to GYRO [J. Candy and R.E. Waltz, J. Comput. Phys. 186, 545 (2003)], a Eulerian gyrokinetic turbulence simulation code. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor energy flux is significantly changed by a 16-fold increase (from 32 to 512 grid points per cell) in the number of grid points in the two-dimensional velocity space. Third, the measured flux is invariant to an eightfold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure. The issues of density and energy conservation and their relation to negligible second-order effects such as the parallel nonlinearity are also discussed.

  17. A flux-matched gyrokinetic analysis of DIII-D L-mode turbulence

    SciTech Connect

    Görler, T. Told, D.; White, A. E.; Jenko, F.; Holland, C.; Rhodes, T. L.

    2014-12-15

    Previous nonlinear gyrokinetic simulations of specific DIII-D L-mode cases have been found to significantly underpredict the ion heat transport and associated density and temperature fluctuation levels by up to almost one of order of magnitude in the outer-core domain, i.e., roughly in the last third of the minor radius. Since then, this so-called shortfall issue has been subject to various speculations on possible reasons and furthermore motivation for a number of dedicated comparisons for L-mode plasmas in comparable machines. However, only a rather limited number of simulations and gyrokinetic codes has been applied to the original scenario, thus calling for further dedicated investigations in order to broaden the scientific basis. The present work contributes along these lines by employing another well-established gyrokinetic code in a numerically and physically comprehensive manner. Contrary to the previous studies, only a mild underprediction is observed at the outer radial positions which can furthermore be overcome by varying the ion temperature gradient within the error bars associated with the experimental measurement. The significance and reliability of these simulations are demonstrated by benchmarks, numerical convergence tests, and furthermore by extensive validation studies. The latter involve cross-phase and cross-power spectra analyses of various fluctuating quantities and confirm a high degree of realism. The code discrepancies come as a surprise since the involved software packages had been benchmarked repeatedly and very successfully in the past. Further collaborative effort in identifying the underlying difference is hence required.

  18. Extension of Discontinuous Galerkin Algorithms To Preserve the Locality of Parallel Gyrokinetic Dynamics

    NASA Astrophysics Data System (ADS)

    Hammett, G. W.; Hakim, A.

    2012-10-01

    A wide range of physics problems, including gyrokinetics, have an underlying Hamiltonian structure that can be expressed in terms of a Poisson bracket, which leads to two quadratic invariants, such as the energy and enstrophy invariants in 2-D hydrodynamics or Hasegawa-Mima equations. A type of Discontinuous Galerkin (DG) algorithm has been developed in the literature that can preserve both invariants, by coupling the DG algorithm for the advection part of the problem with a continuous Finite Element Method for the elliptic field equations. This algorithm can preserve both invariants if centered fluxes are used, and still preserves energy conservation even if upwind fluxes are used. However, when applied to gyrokinetics, the weak form of the continuous finite-element part of the algorithm causes a coupling along the field line that would require a full 3-D elliptic solver. We show a new type of DG algorithm that allows the potential to be discontinuous along the field line, just as the particle distribution function can be, thus restoring the property that the fields in gyrokinetics can determined by a set of uncoupled 2-D elliptic problems. By accounting for the delta-function electric field as particles cross cell boundaries, energy can still be preserved.

  19. Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas

    SciTech Connect

    Ishizawa, A.; Watanabe, T.-H.; Sugama, H.; Nakajima, N.; Maeyama, S.

    2014-05-15

    A saturation mechanism for microturbulence in a regime of weak zonal flow generation is investigated by means of electromagnetic gyrokinetic simulations. The study identifies a new saturation process of the kinetic ballooning mode (KBM) turbulence originating from the spatial structure of the KBM instabilities in a finite-beta Large Helical Device (LHD) plasma. Specifically, the most unstable KBM in LHD has an inclined mode structure with respect to the mid-plane of a torus, i.e., it has a finite radial wave-number in flux tube coordinates, in contrast to KBMs in tokamaks as well as ion-temperature gradient modes in tokamaks and helical systems. The simulations reveal that the growth of KBMs in LHD is saturated by nonlinear interactions of oppositely inclined convection cells through mutual shearing as well as by the zonal flow. The saturation mechanism is quantitatively investigated by analysis of the nonlinear entropy transfer that shows not only the mutual shearing but also a self-interaction with an elongated mode structure along the magnetic field line.

  20. Particle spectra and efficiency in nonlinear relativistic shock acceleration - survey of scattering models

    NASA Astrophysics Data System (ADS)

    Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M.

    2016-03-01

    We include a general form for the scattering mean free path, λmfp(p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λmfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts, pulsar winds, type Ibc supernovae, and extragalactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λmfp(p) has an important influence on the efficiency of cosmic ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.

  1. Nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

    NASA Astrophysics Data System (ADS)

    Zaleśny, Jarosław; Galant, Grzegorz; Lisak, Mietek; Marczyński, Sławomir; Berczyński, Paweł; Gałkowski, Andrzej; Berczyński, Stefan

    2011-06-01

    A system of two coupled integro-differential equations is derived and solved for the non-linear evolution of two waves excited by the resonant interaction with fast ions just above the linear instability threshold. The effects of a resonant particle source and classical relaxation processes represented by the Krook, diffusion, and dynamical friction collision operators are included in the model, which exhibits different nonlinear evolution regimes, mainly depending on the type of relaxation process that restores the unstable distribution function of fast ions. When the Krook collisions or diffusion dominate, the wave amplitude evolution is characterized by modulation and saturation. However, when the dynamical friction dominates, the wave amplitude is in the explosive regime. In addition, it is found that the finite separation in the phase velocities of the two modes weakens the interaction strength between the modes.

  2. Multispecies density peaking in gyrokinetic turbulence simulations of low collisionality Alcator C-Mod plasmas

    NASA Astrophysics Data System (ADS)

    Mikkelsen, D. R.; Bitter, M.; Delgado-Aparicio, L.; Hill, K. W.; Greenwald, M.; Howard, N. T.; Hughes, J. W.; Rice, J. E.; Reinke, M. L.; Podpaly, Y.; Ma, Y.; Candy, J.; Waltz, R. E.

    2015-06-01

    Peaked density profiles in low-collisionality AUG and JET H-mode plasmas are probably caused by a turbulently driven particle pinch, and Alcator C-Mod experiments confirmed that collisionality is a critical parameter. Density peaking in reactors could produce a number of important effects, some beneficial, such as enhanced fusion power and transport of fuel ions from the edge to the core, while others are undesirable, such as lower beta limits, reduced radiation from the plasma edge, and consequently higher divertor heat loads. Fundamental understanding of the pinch will enable planning to optimize these impacts. We show that density peaking is predicted by nonlinear gyrokinetic turbulence simulations based on measured profile data from low collisionality H-mode plasma in Alcator C-Mod. Multiple ion species are included to determine whether hydrogenic density peaking has an isotope dependence or is influenced by typical levels of low-Z impurities, and whether impurity density peaking depends on the species. We find that the deuterium density profile is slightly more peaked than that of hydrogen, and that experimentally relevant levels of boron have no appreciable effect on hydrogenic density peaking. The ratio of density at r/a = 0.44 to that at r/a = 0.74 is 1.2 for the majority D and minority H ions (and for electrons), and increases with impurity Z: 1.1 for helium, 1.15 for boron, 1.3 for neon, 1.4 for argon, and 1.5 for molybdenum. The ion temperature profile is varied to match better the predicted heat flux with the experimental transport analysis, but the resulting factor of two change in heat transport has only a weak effect on the predicted density peaking.

  3. Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in National Spherical Torus Experiment

    DOE PAGESBeta

    Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.

    2016-05-11

    This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostaticballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes inmore » a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. Lastly, as the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.« less

  4. Quasi-linear gyrokinetic predictions of the Coriolis momentum pinch in National Spherical Torus Experiment

    NASA Astrophysics Data System (ADS)

    Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.

    2016-05-01

    This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.

  5. Multispecies density peaking in gyrokinetic turbulence simulations of low collisionality Alcator C-Mod plasmas

    SciTech Connect

    Mikkelsen, D. R. Bitter, M.; Delgado-Aparicio, L.; Hill, K. W.; Greenwald, M.; Howard, N. T.; Hughes, J. W.; Rice, J. E.; Reinke, M. L.; Podpaly, Y.; Ma, Y.; Candy, J.; Waltz, R. E.

    2015-06-15

    Peaked density profiles in low-collisionality AUG and JET H-mode plasmas are probably caused by a turbulently driven particle pinch, and Alcator C-Mod experiments confirmed that collisionality is a critical parameter. Density peaking in reactors could produce a number of important effects, some beneficial, such as enhanced fusion power and transport of fuel ions from the edge to the core, while others are undesirable, such as lower beta limits, reduced radiation from the plasma edge, and consequently higher divertor heat loads. Fundamental understanding of the pinch will enable planning to optimize these impacts. We show that density peaking is predicted by nonlinear gyrokinetic turbulence simulations based on measured profile data from low collisionality H-mode plasma in Alcator C-Mod. Multiple ion species are included to determine whether hydrogenic density peaking has an isotope dependence or is influenced by typical levels of low-Z impurities, and whether impurity density peaking depends on the species. We find that the deuterium density profile is slightly more peaked than that of hydrogen, and that experimentally relevant levels of boron have no appreciable effect on hydrogenic density peaking. The ratio of density at r/a = 0.44 to that at r/a = 0.74 is 1.2 for the majority D and minority H ions (and for electrons), and increases with impurity Z: 1.1 for helium, 1.15 for boron, 1.3 for neon, 1.4 for argon, and 1.5 for molybdenum. The ion temperature profile is varied to match better the predicted heat flux with the experimental transport analysis, but the resulting factor of two change in heat transport has only a weak effect on the predicted density peaking.

  6. Monte Carlo Simulations of Nonlinear Particle Acceleration in Parallel Trans-relativistic Shocks

    NASA Astrophysics Data System (ADS)

    Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M.

    2013-10-01

    We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoniot value, and fully relativistic shocks, where diffusive shock acceleration is less efficient and the compression ratio remains at the Rankine-Hugoniot value. This transition occurs in the trans-relativistic regime and, for the particular parameters we use, occurs around a shock Lorentz factor γ0 = 1.5. We also find that nonlinear shock smoothing dramatically reduces the acceleration efficiency presumed to occur with large-angle scattering in ultra-relativistic shocks. Our ability to seamlessly treat the transition from ultra-relativistic to trans-relativistic to nonrelativistic shocks may be important for evolving relativistic systems, such as gamma-ray bursts and Type Ibc supernovae. We expect a substantial evolution of shock accelerated spectra during this transition from soft early on to much harder when the blast-wave shock becomes nonrelativistic.

  7. MONTE CARLO SIMULATIONS OF NONLINEAR PARTICLE ACCELERATION IN PARALLEL TRANS-RELATIVISTIC SHOCKS

    SciTech Connect

    Ellison, Donald C.; Warren, Donald C.; Bykov, Andrei M. E-mail: ambykov@yahoo.com

    2013-10-10

    We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and 'smooth' the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoniot value, and fully relativistic shocks, where diffusive shock acceleration is less efficient and the compression ratio remains at the Rankine-Hugoniot value. This transition occurs in the trans-relativistic regime and, for the particular parameters we use, occurs around a shock Lorentz factor γ{sub 0} = 1.5. We also find that nonlinear shock smoothing dramatically reduces the acceleration efficiency presumed to occur with large-angle scattering in ultra-relativistic shocks. Our ability to seamlessly treat the transition from ultra-relativistic to trans-relativistic to nonrelativistic shocks may be important for evolving relativistic systems, such as gamma-ray bursts and Type Ibc supernovae. We expect a substantial evolution of shock accelerated spectra during this transition from soft early on to much harder when the blast-wave shock becomes nonrelativistic.

  8. Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

    SciTech Connect

    Zonca, Fulvio; Chen, Liu

    2014-07-15

    A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, “Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation,” Phys. Plasmas 21, 072121 (2014)].

  9. On the definition of a kinetic equilibrium in global gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

    Angelino, P.; Bottino, A.; Hatzky, R.; Jolliet, S.; Sauter, O.; Tran, T. M.; Villard, L.

    2006-05-01

    Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and E ×B zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric E ×B flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of E ×B flows. In addition, a revised δf scheme is introduced and compared to the standard δf method.

  10. On the definition of a kinetic equilibrium in global gyrokinetic simulations

    SciTech Connect

    Angelino, P.; Bottino, A.; Hatzky, R.; Jolliet, S.; Sauter, O.; Tran, T.M.; Villard, L.

    2006-05-15

    Nonlinear electrostatic global gyrokinetic simulations of collisionless ion temperature gradient (ITG) turbulence and ExB zonal flows in axisymmetric toroidal plasmas are examined for different choices of the initial distribution function. Using a local Maxwellian leads to the generation of axisymmetric ExB flows that can be so strong as to prevent ITG mode growth. A method using a canonical Maxwellian is shown to avoid this spurious generation of ExB flows. In addition, a revised {delta}f scheme is introduced and compared to the standard {delta}f method.

  11. Fully explicit nonlinear optics model in a particle-in-cell framework

    SciTech Connect

    Gordon, D.F. Helle, M.H.; Peñano, J.R.

    2013-10-01

    A numerical technique which incorporates the nonlinear optics of anisotropic crystals into a particle-in-cell framework is described. The model is useful for simulating interactions between crystals, ultra-short laser pulses, intense relativistic electron bunches, plasmas, or any combination thereof. The frequency content of the incident and scattered radiation is limited only by the resolution of the spatial and temporal grid. A numerical stability analysis indicates that the Courant condition is more stringent than in the vacuum case. Numerical experiments are carried out illustrating the electro-optic effect, soliton propagation, and the generation of fields in a crystal by a relativistic electron bunch.

  12. Possible emittance growth induced by nonlinear space charge fields for arbitrary particle distributions

    NASA Astrophysics Data System (ADS)

    Kikuchi, Takashi; Horioka, Kazuhiko

    2016-06-01

    A procedure to obtain a ratio of beam radii at final and initial states in arbitrary particle distributions is proposed, and is applied to the estimation of possible emittance growth for Gaussian and thermal equilibrium distributions. The ratios are estimated for Gaussian and thermal equilibrium distributions as a function of tune depression. The possible emittance growth as a function of tune depression and nonlinear field energy factor is also estimated with and without a constant radius ratio approximation. It is confirmed that the possible emittance growths are almost the same in comparison to the cases with and without the constant radius ratio approximation at each distribution.

  13. Sound Propagation in Gas-Vapor-Droplet Suspensions with Evaporation and Nonlinear Particle Relaxation

    NASA Technical Reports Server (NTRS)

    Kandula, Max

    2012-01-01

    The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration.

  14. Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics.

    PubMed

    Mocz, Philip; Succi, Sauro

    2015-05-01

    We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions. PMID:26066276

  15. Numerical solution of the nonlinear Schrödinger equation using smoothed-particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Mocz, Philip; Succi, Sauro

    2015-05-01

    We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the nonlinear Schrödinger equation in the Madelung formulation. The probability density of the wave function is discretized into moving particles, whose properties are smoothed by a kernel function. The traditional fluid pressure is replaced by a quantum pressure tensor, for which a robust discretization is found. We demonstrate our numerical method on a variety of numerical test problems involving the simple harmonic oscillator, soliton-soliton collision, Bose-Einstein condensates, collapsing singularities, and dark matter halos governed by the Gross-Pitaevskii-Poisson equation. Our method is conservative, applicable to unbounded domains, and is automatically adaptive in its resolution, making it well suited to study problems with collapsing solutions.

  16. Nonlinear wave-particle resonant interaction in the radiation belts: Landau resonance vs. fundamental cyclotron resonance

    NASA Astrophysics Data System (ADS)

    Krasnoselskikh, V.; Artemyev, A.; Agapitov, O. V.; Mourenas, D.

    2013-12-01

    We present selected THEMIS observations of highly-oblique and large amplitude chorus waves at medium latitudes. The major part of observed waves propagates at nearly-electrostatic mode with normal angles close to resonance cone. We use test particle simulations and analytical theory to estimate efficiency of nonlinear particle acceleration by these waves via Landau and fundamental cyclotron resonances. We show that trapping into the Landau resonance corresponds to a decrease of electron equatorial pitch-angles, while trapping into the first cyclotron resonance increases electron equatorial pitch-angles. For 100 keV electrons, the energy gain is larger for the trapping due to Landau resonance. Moreover, trapping into the Landau resonance is accessible for a wider range of initial pitch-angles in comparison with the fundamental resonance.

  17. Applying a fully nonlinear particle filter on a coupled ocean-atmosphere climate model

    NASA Astrophysics Data System (ADS)

    Browne, Philip; van Leeuwen, Peter Jan; Wilson, Simon

    2014-05-01

    It is a widely held assumption that particle filters are not applicable in high-dimensional systems due to filter degeneracy, commonly called the curse of dimensionality. This is only true of naive particle filters, and indeed it has been shown much more advanced methods perform particularly well on systems of dimension up to 216 ≡ 6.5 × 104. In this talk we will present results from using the equivalent weights particle filter in twin experiments with the global climate model HadCM3. These experiments have a number of notable features. Firstly the sheer size of model in use is substantially larger than has been previously achieved. The model has state dimension approximately 4 × 106 and approximately 4 × 104 observations per analysis step. This is 2 orders of magnitude more than has been achieved with a particle filter in the geosciences. Secondly, the use of a fully nonlinear data assimilation technique to initialise a climate model gives us the possibility to find non-Gaussian estimates for the current state of the climate. In doing so we may find that the same model may demonstrate multiple likely scenarios for forecasts on a multi-annular/decadal timescale. The experiments consider to assimilating artificial sea surface temperatures daily for several years. We will discuss how an ensemble based method for assimilation in a coupled system avoids issues faced by variational methods. Practical details of how the experiments were carried out, specifically the use of the EMPIRE data assimilation framework, will be discussed. The results from applying the nonlinear data assimilation method can always be improved through having a better representation of the model error covariance matrix. We will discuss the representation which we have used for this matrix, and in particular, how it was generated from the coupled system.

  18. Segmentation of deformable organs from medical images using particle swarm optimization and nonlinear shape priors

    NASA Astrophysics Data System (ADS)

    Afifi, Ahmed; Nakaguchi, Toshiya; Tsumura, Norimichi

    2010-03-01

    In many medical applications, the automatic segmentation of deformable organs from medical images is indispensable and its accuracy is of a special interest. However, the automatic segmentation of these organs is a challenging task according to its complex shape. Moreover, the medical images usually have noise, clutter, or occlusion and considering the image information only often leads to meager image segmentation. In this paper, we propose a fully automated technique for the segmentation of deformable organs from medical images. In this technique, the segmentation is performed by fitting a nonlinear shape model with pre-segmented images. The kernel principle component analysis (KPCA) is utilized to capture the complex organs deformation and to construct the nonlinear shape model. The presegmentation is carried out by labeling each pixel according to its high level texture features extracted using the overcomplete wavelet packet decomposition. Furthermore, to guarantee an accurate fitting between the nonlinear model and the pre-segmented images, the particle swarm optimization (PSO) algorithm is employed to adapt the model parameters for the novel images. In this paper, we demonstrate the competence of proposed technique by implementing it to the liver segmentation from computed tomography (CT) scans of different patients.

  19. THE LOCAL LIMIT OF GLOBAL GYROKINETIC SIMULATIONS

    SciTech Connect

    CANDY J; WALTZ RE; DORLAND W

    2003-10-01

    OAK-B135 Global gyrokinetic simulations of turbulence include physical effects that are not retained in local flux-tube simulations. nevertheless, in the limit of sufficiently small {rho}* (gyroradius compared to system size) it is expected that a local simulation should agree with a global one (at the local simulation radius) since all effects that are dropped in the local simulations are expected to vanish as {rho}* {yields} 0. In this note, global simulations of a well-established test case are indeed shown to recover the flux-tube limit at each radius.

  20. Gyrokinetic Study of L-H Transition with Profile Evolution

    NASA Astrophysics Data System (ADS)

    Xie, Hua-Sheng; GTC Team

    2015-11-01

    Recent simulations based on gyrokinetic toroidal code (GTC) and theory based on model eigen equation (H. S. Xie and Y. Xiao, arXiv:1503.04440) have found that the eigenstates of mirco-instabilities (trapped electron mode TEM or ion temperature gradient mode ITG) under strong and weak gradients are not the same. Under weak gradient, the most unstable mode is on the ground state, with conventional ballooning mode structure. When the gradient exceed a critical value, the most unstable mode jump to non-ground state. The mode structures of non-ground state are rich and unconventional, and thus can reduced the transport level, which can provide a explanation to the H-mode in the mirco-scale aspect. Nonlinear simulations (H. S. Xie, Y. Xiao and Z. Lin, 9th West Lake International Symposium on Plasma Simulation, May. 18-21, 2015, Hangzhou, China) verified this and have also found a turning point of the gradient. The turbulent transport coefficient would decrease with the gradient increasing when the gradient exceed a critical value. This provide a new route for the L to H transition without invoking shear flow or zonal flow. In the above works, the profiles are fixed. In this work, we will give some preliminary results on self-consistent simulations of L-H transition including the evolution of the radial plasma profiles. Collaboration with GTC team.

  1. Gyrokinetic Simulation of Microturbulent Saturation at Finite β

    NASA Astrophysics Data System (ADS)

    Terry, P. W.; Pueschel, M. J.; Carmody, D.; Whelan, G. G.

    2014-10-01

    Saturation and zonal flow physics for microturbulence is investigated for tokamaks and the RFP using gyrokinetic computation to understand scalings with respect magnetic shear and β. Modeling an MST discharge shows that the critical instability gradient for TEM is higher than the tokamak threshold by the aspect ratio (R / a) . This factor is rooted in the shorter magnetic field scale length of the RFP. Nonlinear simulations show strong zonal flows and a large Dimits shift exceeding the tokamak shift by a factor of order (R / a) . The non zonal transition (NZT), a critical β for which zonal flows are disabled by flutter-induced charge loss is also considered. The critical β occurs when the radial displacement of a magnetic field line over a half connection length is equal to the radial correlation length. These quantities scale with the connection length and magnetic drift scale lengths entering the instability threshold and quasilinear diffusivities, making the RFP critical β for NZT higher than the tokamak value by (R / a) 1 . 5 times tokamak q. These results are consistent with magnetic shear and q dependence in the kinetic ballooning threshold, indicating that β effects will only arise at high β relative to typical RFP operation.

  2. Theory, Verification and Validation of Finite-Beta Gyrokinetics

    NASA Astrophysics Data System (ADS)

    Candy, J.

    2012-10-01

    In this tutorial presentation, both historical challenges and present open issues related to finite-beta gyrokinetic simulation will be discussed, with emphasis on the GYRO code but including material from relevant codes worldwide. There will be focus on numerical issues and solutions (such as the Ampere cancellation problem and its resolution), complicating physical effects (such as magnetic surface destruction and stochastic electron transport) and unresolved issues (for example, the finite-beta runaway observed in multiple codes). Successes related to code benchmarking exercises, and the role of finite-beta effects in experimental validation (for example, when finite-beta effects must be retained and when they may be neglected) will also be discussed. Categorization of finite-beta effects as they relate to different modes (ion temperature gradient, trapped electron, kinetic ballooning, microtearing and toroidal Alfv'en) will be clarified, and recent success in both numerically resolving and explaining electron transport in spherical tokamaks via flutter nonlinearity and associated magnetic stochasticity will be summarized. The material will be organized in roughly chronological order. Also covered will be practical aspects of the topic, including simulation strategies and best practices. This is relevant because the overall difficulty and potential pitfalls of electromagnetic turbulence simulation are far greater than for electrostatic turbulence simulations.

  3. Gyrofluid-Gyrokinetic Hybrid Turbulence Model

    NASA Astrophysics Data System (ADS)

    Dorland, William; Mandell, Noah

    2015-11-01

    Gyrofluid models of tokamak turbulence are efficient compared to gyrokinetic models, in three senses. First, it is typically easier to develop one's intuition from fluid equations than kinetic equations. Second, because gyrofluid equations are only three-dimensional (instead of 5D or 6D), simulations with gyrofluid models require less memory than kinetic simulations and can therefore more easily fit on highly-optimized computing hardware, such as graphics processors. The third advantage is a result of the first two: one can develop and test ideas quickly with gyrofluid models. The disadvantage of gyrofluid models is their potential lack of physics fidelity. In this poster, we present our attempt to take full advantage of gyrofluid models, without sacrificing physics fidelity. Our approach is encapsulated in the Gryf-X code, which is an implementation of hybrid gyrofluid/gyrokinetic equations. The key improvements that we have brought to bear are: an improved understanding of the cascade of free energy simultaneously in k⊥ and v⊥ an improved model of zonal flow physics; and an implementation of the equations on modern heterogeneous computing platforms, both as a standalone simulation tool and as a component of TRINITY (a transport modeling code for tokamaks).

  4. Gyrokinetic Formalism in Plasmas with Flows

    NASA Astrophysics Data System (ADS)

    Chiu, S. C.; Chan, V. S.; Lin-Liu, Y. R.; Chu, M. S.

    1998-11-01

    There is considerable theoretical and experimental evidence that plasma rotations in tokamaks can improve stability and confinement. Understanding the physics of rotating tokamak plasmas is thus of great importance for attaining high performance in reactors. Since present and future tokamaks are likely to have auxiliary heating such as radio frequency (RF) waves or neutral beam injection, it is of interest to understand the interaction of auxiliary heating with plasma rotation, and its consequences to transport and stability. In the past, rotation has not been self-consistently treated in auxiliary heating in that it is either ignored or ambipolarity is not self-consistently maintained. In this work, we describe a gyrokinetic formalism for RF in rotating plasmas which takes ambipolarity and equilibrium into account. A non-canonical guiding center Lagrangian for rotating plasma in a fluctuating field is obtained, and from which the gyrokinetic equation is deduced. Limiting the wave equations to the cyclotron frequency or below, quasilinear equations using an eikonal approximation are derived. Conservation laws for the system shall be discussed.

  5. Comparison of electron temperature fluctuations with gyrokinetic sumulations across the ohmic energy confinement transition in Alcator C-Mod

    NASA Astrophysics Data System (ADS)

    Sung, C.; White, A.; Howard, N.; Mikkelsen, D.; Rice, J.; Reinke, M.; Gao, C.; Ennever, P.; Porkolab, M.; Churchill, R.; Theiler, C.; Hubbard, A.; Greenwald, M.

    2013-10-01

    Long wavelength electron temperature fluctuations (kyρs < 0 . 3) near the edge (r / a ~ 0 . 85) are reduced across the ohmic confinement transition from Linear Ohmic Confinement(LOC) regime to Saturated Ohmic Confinement(SOC) regime in Alcator C-Mod. Linear stability analysis shows that the dominant mode of long wavelength turbulence near the edge is changed from Trapped Electron Mode(TEM) to Ion Temperature Gradient(ITG) mode while the dominant mode is not changed deeper in the core (r / a ~ 0 . 5). This indicates that local turbulence changes near the edge might be responsible for the change of global energy confinement in ohmic plasmas. Further study using nonlinear gyrokinetic simulations is being performed to clarify the relation between the change of local turbulence and global ohmic energy confinement. Through nonlinear gyrokinetic simulation (GYRO), we will investigate the change of fluctuating quantities (T~ , ñ , ϕ~) and their phase relations across ohmic confinement transitions, and relate them to the change of energy transport. A synthetic CECE diagnostic for C-Mod has been developed, and it will be used to validate the gyrokinetic simulations. Research supported by USDoE awards DE-SC0006419, DE-FC02-99ER54512.

  6. Variational symplectic particle-in-cell simulation of nonlinear mode conversion from extraordinary waves to Bernstein waves

    SciTech Connect

    Xiao, Jianyuan; Liu, Jian; Qin, Hong; Yu, Zhi; Xiang, Nong

    2015-09-15

    In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.

  7. Gyrokinetic study of the impact of the electron to ion heating ratio on the turbulent diffusion of highly charged impurities

    NASA Astrophysics Data System (ADS)

    Angioni, C.

    2015-10-01

    A gyrokinetic study based on numerical and analytical calculations is presented, which computes the dependence of the turbulent diffusion of highly charged impurities on the ratio of the electron to the ion heat flux of the plasma. Nonlinear simulations show that the size of the turbulent diffusion of heavy impurities can vary by one order of magnitude with fixed total heat flux and is an extremely sensitive function of the electron to ion heat flux ratio. Numerical linear calculations are found to reproduce the nonlinear results. Thereby, a quasi-linear analytical approach is used to explain the origin of this dependence.

  8. Gyrokinetic study of the impact of the electron to ion heating ratio on the turbulent diffusion of highly charged impurities

    SciTech Connect

    Angioni, C.

    2015-10-15

    A gyrokinetic study based on numerical and analytical calculations is presented, which computes the dependence of the turbulent diffusion of highly charged impurities on the ratio of the electron to the ion heat flux of the plasma. Nonlinear simulations show that the size of the turbulent diffusion of heavy impurities can vary by one order of magnitude with fixed total heat flux and is an extremely sensitive function of the electron to ion heat flux ratio. Numerical linear calculations are found to reproduce the nonlinear results. Thereby, a quasi-linear analytical approach is used to explain the origin of this dependence.

  9. An energy- and charge-conserving, nonlinearly implicit, electromagnetic particle-in-cell algorithm

    NASA Astrophysics Data System (ADS)

    Chen, Guangye; Chacon, Luis; Knoll, Dana; Daughton, William; CoCoMans (LANL) Team

    2013-10-01

    A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension. The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations. An implicit, orbit-averaged central finite difference scheme is applied to both the Darwin field equations and the particle orbit equations to produce a discrete system that remains exactly charge-and energy-conserving. Furthermore, the canonical momentum in any ignorable direction is exactly conserved per particle by appropriate interpolations of the magnetic field. A fluid preconditioner targeting the stiffest electron waves has been developed to accelerate the linear GMRES solver of JFNK. We present 1D numerical experiments (e.g. the Weibel instability, kinetic Alfven wave ion-ion streaming instability, etc.) to demonstrate the accuracy and efficiency of the implicit Darwin PIC algorithm, and the performance of the fluid preconditioner.

  10. Scenarios for the nonlinear evolution of alpha particle induced Alfven wave instability

    SciTech Connect

    Berk, H.L.; Breizman, B.N.; Ye, Huanchun.

    1992-03-01

    Various nonlinear scenarios are given for the evolution of energetic particles that are slowing down in a background plasma and simultaneously causing instability of the background plasma waves. If the background damping is sufficiently weak, a steady-state wave is established as described by Berk and Breizman. For larger background damping rate pulsations develop. Saturation occurs when the wave amplitude rises to where the wave trapping frequency equals the growth rate. The wave then damps due to the small background dissipation present and a relatively long quiet interval exists between bursts while the free energy of the distribution is refilled by classical transport. In this scenario the anomalous energy loss of energetic particles due to diffusion is small compared to the classical collisional energy exchange with the background plasma. However, if at the trapping frequency, the wave amplitude is large enough to cause orbit stochasticity, a phase space explosion'' occurs where the wave amplitudes rise to higher levels which leads to rapid loss of energetic particles.

  11. Scenarios for the nonlinear evolution of alpha particle induced Alfven wave instability

    SciTech Connect

    Berk, H.L.; Breizman, B.N.; Ye, Huanchun

    1992-03-01

    Various nonlinear scenarios are given for the evolution of energetic particles that are slowing down in a background plasma and simultaneously causing instability of the background plasma waves. If the background damping is sufficiently weak, a steady-state wave is established as described by Berk and Breizman. For larger background damping rate pulsations develop. Saturation occurs when the wave amplitude rises to where the wave trapping frequency equals the growth rate. The wave then damps due to the small background dissipation present and a relatively long quiet interval exists between bursts while the free energy of the distribution is refilled by classical transport. In this scenario the anomalous energy loss of energetic particles due to diffusion is small compared to the classical collisional energy exchange with the background plasma. However, if at the trapping frequency, the wave amplitude is large enough to cause orbit stochasticity, a phase space ``explosion`` occurs where the wave amplitudes rise to higher levels which leads to rapid loss of energetic particles.

  12. Nonlinear physics and energetic particle transport features of the beam-plasma instability

    NASA Astrophysics Data System (ADS)

    Carlevaro, Nakia; Falessi, Matteo V.; Montani, Giovanni; Zonca, Fulvio

    2015-10-01

    > In this paper we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analysed.

  13. Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks

    NASA Astrophysics Data System (ADS)

    Fedotov, Sergei; Korabel, Nickolay

    2015-12-01

    We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.

  14. In-situ observations of nonlinear wave particle interaction of electromagnetic ion cyclotron waves

    NASA Astrophysics Data System (ADS)

    Shoji, M.; Miyoshi, Y.; Keika, K.; Katoh, Y.; Angelopoulos, V.; Nakamura, S.; Omura, Y.

    2014-12-01

    Direct measurement method for the electromagnetic wave and space plasma interaction has been suggested by a computer simulation study [Katoh et al., 2013], so-called Wave Particle Interaction Analysis (WPIA). We perform the WPIA for rising tone electromagnetic ion cyclotron (EMIC) waves (so-called EMIC triggered emissions), of which generation mechanism is essentially the same as the chorus emissions. THEMIS observation data (EFI, FGM, and ESA) are used for the WPIA. In the WPIA, we calculate (1) the inner product of the wave electric field and the velocity of the energetic protons: Wint, (2) the inner product of the wave magnetic field and the velocity of the energetic protons: WBint, and (3) the phase angle ζ between the wave magnetic field and the perpendicular velocity of the energetic protons. The values of (1) and (2) indicate the existence of the resonant currents inducing the nonlinear wave growth and the frequency change, respectively. We find the negative Wint and positive WBint at the nonlinear growing phase of the triggered emission as predicted in the theory [e.g. Omura and Nunn, 2011, Shoji and Omura, 2013]. In histogram of (3), we show the existence of the electromagnetic proton holes in the phase space generating the resonant currents. We also perform a hybrid simulation and evaluate WPIA method for EMIC waves. The simulation results show good agreement with the in-situ THEMIS observations.

  15. The Hamiltonian Structure and Euler-Poincare Formulation of the Valsov-Maxwell and Gyrokinetic System

    SciTech Connect

    J. Squire, H. Qin and W.M. Tang

    2012-09-25

    We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________

  16. Gyrokinetic full-torus simulations of ohmic tokamak plasmas in circular limiter configuration

    NASA Astrophysics Data System (ADS)

    Korpilo, T.; Gurchenko, A. D.; Gusakov, E. Z.; Heikkinen, J. A.; Janhunen, S. J.; Kiviniemi, T. P.; Leerink, S.; Niskala, P.; Perevalov, A. A.

    2016-06-01

    The gyrokinetic full 5D particle distribution code ELMFIRE has been extended to simulate circular tokamak plasmas from the magnetic axis to the limiter scrape-off-layer. The predictive power of the code in the full-torus configuration is tested via its ability to reproduce experimental steady-state profiles in FT-2 ohmic L-mode plasmas. The results show that the experimental profile solution is not reproduced numerically due to the difficulty of obtaining global power balance. This is verified by cross-comparison of ELMFIRE code versions, which shows also the impact of boundary conditions and grid resolution on turbulent transport.

  17. A gyrokinetic continuum code based on the numerical Lie transform (NLT) method

    NASA Astrophysics Data System (ADS)

    Ye, Lei; Xu, Yingfeng; Xiao, Xiaotao; Dai, Zongliang; Wang, Shaojie

    2016-07-01

    In this work, we report a novel gyrokinetic simulation method named numerical Lie transform (NLT), which depends on a new physical model derived from the I-transform theory. In this model, the perturbed motion of a particle is decoupled from the unperturbed motion. Due to this property, the unperturbed orbit can be computed in advance and saved as numerical tables for real-time computation. A 4D tensor B-spline interpolation module is developed and applied with the semi-Lagrangian scheme to avoid operator splitting. The NLT code is verified by the Rosenbluth-Hinton test and the linear ITG Cyclone test.

  18. Gyrokinetic simulations of ion temperature gradient modes in the reversed field pinch

    SciTech Connect

    Predebon, I.; Guo, S. C.; Angioni, C.

    2010-01-15

    Linear gyrokinetic calculations are applied to the reversed field pinch configuration to investigate the occurrence of ion temperature gradient instabilities. The analysis shows this type of instability to be only marginally responsible for particle and energy transport. The required gradients could be reached only in correspondence to the temperature slopes arising at the boundary of the helical structure in the quasisingle helicity states. The dependence of the instability threshold on the relevant macroscopic quantities is considered. A discussion on the main differences in the driving mechanisms existing between the reversed field pinch and the tokamak configuration is addressed.

  19. Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence

    NASA Astrophysics Data System (ADS)

    Wang, Eric

    2010-11-01

    One of the fundamental components of a steady state tokamak or stellerator fusion reactor is the structural integrity of nested magnetic surfaces. The consequences of losing this integrity can have very serious implications, ranging from sawtooth crashes to disruptions. In the present work, we use GYRO to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as β is varied from .1% to .7%, as first investigated in [J. Candy, Phys. Plasmas 12, 072307 (2005)]. By integrating the self-consistent magnetic field lines to produce Poincare surface of section plots, we demonstrate destruction of magnetic surfaces for all nonzero values of β. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. We can quantify the stochastic electron heat transport by using test particles to estimate the magnetic diffusion coefficient Dst [A.B. Rechester and M.N. Rosenbluth, PRL 40, 38 (1978)] for hundreds of time slices in each simulation and find the time-history of Dst to be highly correlated with the electron heat transport due to ``magnetic-flutter'' computed in the simulations. The mechanism that couples electromagnetic turbulence to the linearly damped high-n tearing modes that are responsible for reconnection will be discussed.

  20. Benchmarking gyrokinetic simulations in a toroidal flux-tube

    NASA Astrophysics Data System (ADS)

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

    2013-09-01

    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 implementation 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||-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.

  1. Energy conserving continuum algorithms for kinetic & gyrokinetic simulations of plasmas

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

    We present high-order, energy conserving, continuum algorithms for the solution of gyrokinetic equations for use in edge turbulence simulations. The distribution function is evolved with a discontinuous Galerkin scheme, while the fields are evolved with a continuous finite-element method. These algorithms work for a general, possibly non-canonical, Poisson bracket operator and conserve energy exactly. Benchmark simulations with ETG turbulence in 3X/2V are shown, as well as initial applications of the algorithms to turbulence in a simplified SOL geometry. Sheath boundary conditions with recycling and secondary electron emission are implemented, and a Lenard-Bernstein collision operator is included. Extension of these algorithms to full Vlasov-Maxwell equations are presented. It is shown that with a particular choice of numerical fluxes the total (particle+field) energy is conserved. Algorithms are implemented in a flexible and open-source framework, Gkeyll, which also includes fluid models, allowing potential hybrid simulations of various plasma problems. Supported by the Max-Planck/Princeton Center for Plasma Physics, and DOE Contract DE-AC02-09CH11466.

  2. Benchmarking gyrokinetic simulations in a toroidal flux-tube

    SciTech Connect

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

    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 implementation 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.

  3. Gyrokinetic Studies of Microturbulence in the Madison Symmetric Torus

    NASA Astrophysics Data System (ADS)

    Williams, Zachary; Duff, James; Pueschel, M. J.; Terry, Paul

    2015-11-01

    Reversed-field pinches operating with Pulsed Poloidal Current Drive (PPCD) exhibit microturbulence that contributes to heat and particle transport. This work focuses on the analysis of high-frequency fluctuations in a recent 200 kA PPCD discharge in the Madison Symmetric Torus, for which strong experimental evidence of microturbulence exists. Local gyrokinetic simulations were performed at multiple radial positions outside the reversal surface using the Gene code. Linear analysis identifies the dominant instability at all positions to be a density-gradient-driven trapped electron mode. An accurate description of turbulence requires the inclusion of residual tearing mode fluctuations: though reduced in PPCD, large-scale tearing modes introduce non-negligible levels of magnetic perturbations. In simulations, they can be seen to weaken zonal flows and degrade confinement, increasing transport to experimentally observed levels. Importantly, imposed fluctuations appear to be self-consistently reinforced, contrary to the usual island-healing picture in tokamaks. Simulations also include B∥ fluctuations, which provide finite contributions to transport, particularly when artificially zeroing out tearing modes entirely.

  4. A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment

    PubMed Central

    Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

    2016-01-01

    In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405

  5. A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

    PubMed

    Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

    2016-01-01

    In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405

  6. Wave-particle interactions with parallel whistler waves: Nonlinear and time-dependent effects revealed by particle-in-cell simulations

    SciTech Connect

    Camporeale, Enrico; Zimbardo, Gaetano

    2015-09-15

    We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.

  7. Wave-particle interactions with parallel whistler waves: Nonlinear and time-dependent effects revealed by particle-in-cell simulations

    NASA Astrophysics Data System (ADS)

    Camporeale, Enrico; Zimbardo, Gaetano

    2015-09-01

    We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt. By tracking PIC particles and comparing with test-particle simulations, we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular, we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates well before a single bounce period. This calls into question the widely used bounce average performed in most radiation belt diffusion calculations. Furthermore, we discuss how the saturation is related to the fact that the domain in which the particles pitch angle diffuses is bounded, and to the well-known problem of 90° diffusion barrier.

  8. Steady-State Gyrokinetics Transport Code (SSGKT), A Scientific Application Partnership with the Framework Application for Core-Edge Transport Simulations, Final Report

    SciTech Connect

    Fahey, Mark R.; Candy, Jeff

    2013-11-07

    This project initiated the development of TGYRO ? a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale GYRO turbulence simulations into a framework for practical multi-scale simulation of conventional tokamaks as well as future reactors. Using a lightweight master transport code, multiple independent (each massively parallel) gyrokinetic simulations are coordinated. The capability to evolve profiles using the TGLF model was also added to TGYRO and represents a more typical use-case for TGYRO. The goal of the project was to develop a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale gyrokinetic turbulence simulations into a framework for practical multi-scale simulation of a burning plasma core ? the International Thermonuclear Experimental Reactor (ITER) in particular. This multi-scale simulation capability will be used to predict the performance (the fusion energy gain, Q) given the H-mode pedestal temperature and density. At present, projections of this type rely on transport models like GLF23, which are based on rather approximate fits to the results of linear and nonlinear simulations. Our goal is to make these performance projections with precise nonlinear gyrokinetic simulations. The method of approach is to use a lightweight master transport code to coordinate multiple independent (each massively parallel) gyrokinetic simulations using the GYRO code. This project targets the practical multi-scale simulation of a reactor core plasma in order to predict the core temperature and density profiles given the H-mode pedestal temperature and density. A master transport code will provide feedback to O(16) independent gyrokinetic simulations (each massively parallel). A successful feedback scheme offers a novel approach to predictive modeling of an important national and international problem. Success in this area of fusion simulations will allow US scientists to direct the research path of ITER over the next two

  9. Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

    A poloidal tilting symmetry of the local nonlinear δ f gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using up-down asymmetry.

  10. Nonlinear Evolution of a 3D Inertial Alfvén Wave and Its Implication in Particle Acceleration

    NASA Astrophysics Data System (ADS)

    Sharma, Prachi; Yadav, Nitin; Sharma, R. P.

    2016-03-01

    A simulation based on a pseudo-spectral method has been performed in order to study particle acceleration. A model for the acceleration of charged particles by field localization is developed for the low-β plasma. For this purpose, a fractional diffusion approach has been employed. The nonlinear interaction between a 3D inertial Alfvén wave and a slow magnetosonic wave has been examined, and the dynamical equations of these two waves in the presence of ponderomotive nonlinearity have been solved numerically. The nonlinear evolution of the inertial Alfvén wave in the presence of slow magnetosonic wave undergoes a filamentation instability and results in field intensity localization. The results obtained show the localization and power spectrum of inertial Alfvén wave due to nonlinear coupling. The scaling obtained after the first break point of the magnetic power spectrum has been used to calculate the formation of the thermal tail of energetic particles in the solar corona.

  11. In-situ imaging of reacting single-particle zeolites by non-linear optical microscopy

    NASA Astrophysics Data System (ADS)

    Wrzesinski, Paul J.; Slipchenko, Mikhail N.; Zaman, Taslima A.; Rioux, Robert M.; Gord, James R.; Roy, Sukesh

    2015-03-01

    Zeolite catalysis has been exploited by the petrochemical industry since the 1940's for catalytic cracking reactions of long chain hydrocarbons. The selectivity of zeolites strongly depends on a pore size, which is controlled by the chosen structure-directing agent (SDA) and by the SDA decomposition/removal process. Although zeolites are composed of micron-sized crystals, studies of zeolite materials typically focus on bulk (i.e., ensemble) measurements to elucidate structure-function information or to optimize catalysts and/or process parameters. To examine these phenomena on the microscale, non-linear optical microscopy is used to provide real-time imaging of chemical reactions in zeolites at temperatures exceeding 400°C. The template decomposition mechanism is studied, as elucidation of the mechanism is critical to understanding the relationship between the decomposition chemistry and the nanoscale features of the zeolite (topology, Si/Al ratio, added dopants). Forward stimulated Raman scattering (SRS), forward coherent anti-Stokes Raman scattering (CARS) and epi two-photon fluorescence (TPF) modalities are acquired simultaneously providing video-rate structural and chemical information. A high-temperature cell with gas inlet system is used for the study of reactions under various temperatures and gas environments. Examining the decomposition process with single-particle resolution enables access to ensemble-level and spatially-resolved behavior. Parallel experiments on bulk zeolite powders are conducted to enable comparison of ensemble and single-particle behavior during template decomposition. Our multi-technique approach has high potential for gaining insight into the link between nanoscale structure and catalytic activity and selectivity of zeolitic materials.

  12. Benchmarking Nonlinear Turbulence Simulations on Alcator C-Mod

    SciTech Connect

    M.H. Redi; C.L. Fiore; W. Dorland; M.J. Greenwald; G.W. Hammett; K. Hill; D. McCune; D.R. Mikkelsen; G. Rewoldt; J.E. Rice

    2004-06-22

    Linear simulations of plasma microturbulence are used with recent radial profiles of toroidal velocity from similar plasmas to consider nonlinear microturbulence simulations and observed transport analysis on Alcator C-Mod. We focus on internal transport barrier (ITB) formation in fully equilibrated H-mode plasmas with nearly flat velocity profiles. Velocity profile data, transport analysis and linear growth rates are combined to integrate data and simulation, and explore the effects of toroidal velocity on benchmarking simulations. Areas of interest for future nonlinear simulations are identified. A good gyrokinetic benchmark is found in the plasma core, without extensive nonlinear simulations. RF-heated C-Mod H-mode experiments, which exhibit an ITB, have been studied with the massively parallel code GS2 towards validation of gyrokinetic microturbulence models. New, linear, gyrokinetic calculations are reported and discussed in connection with transport analysis near the ITB trigger time of shot No.1001220016.

  13. Nonlinear acceleration of the electron inertia-dominated magnetohydrodynamic modes due to electron parallel compressibility

    SciTech Connect

    Matsumoto, Taro; Naitou, Hiroshi; Tokuda, Shinji; Kishimoto, Yasuaki

    2005-09-15

    The behavior of the collisionless magnetohydrodynamics modes is investigated by the gyrokinetic particle simulation in a cylindrical tokamak plasma in the parameter region where the effects of electron inertia and electron parallel compressibility are competitive for magnetic reconnection. Although the linear growth of the m=1 internal kink-tearing mode is dominated by the electron inertia, it is found that the growth rate can be nonlinearly accelerated due to the electron parallel compressibility proportional to the ion sound Larmor radius {rho}{sub s}. It is also found that, as decreasing the electron skin depth {delta}{sub e}, the maximum growth rate before the internal collapse saturates independently of the microscopic scales such as {delta}{sub e} and {rho}{sub s}. The acceleration of growth rate is also observed in the nonlinear phase of the m=2 double tearing mode.

  14. A nonlinear particle dynamics map of wakefield acceleration in a linear collider

    SciTech Connect

    Tajima, T.; Cheshkov, S.; Horton, W.; Yokoya, K.

    1998-08-01

    The performance of a wakefield accelerator in a high energy collider application is analyzed. In order to carry out this task, it is necessary to construct a strawman design system (no matter how preliminary) and build a code of the systems approach. A nonlinear dynamics map built on a simple theoretical model of the wakefield generated by the laser pulse (or whatever other method) is obtained and they employ this as a base for building a system with multi-stages (and components) as a high energy collider. The crucial figures of merit for such a system other than the final energy include the emittance (that determines the luminosity). The more complex the system is, the more opportunities the system has to degrade the emittance (or entropy of the beam). Thus the map gu ides one to identify where the crucial elements lie that affect the emittance. They find that a strong focusing force of the wakefield coupled with a possible jitter of the axis (or laser aiming) of each stage and a spread in the betatron frequencies arising from different phase space positions for individual particles leads to a phase space mixing. This sensitively controls the emittance degradation. They show that in the case of a uniform plasma the effect of emittance growth is large and may cause serious problems. They discuss possibilities to avoid it and control the situation.

  15. Particle Filter with Novel Nonlinear Error Model for Miniature Gyroscope-Based Measurement While Drilling Navigation

    PubMed Central

    Li, Tao; Yuan, Gannan; Li, Wang

    2016-01-01

    The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the errors of small-angle attitude. However, the simplification of the DCM would introduce errors to the navigation solutions of the MGWD system if the initial alignment cannot provide precise attitude, especially for the low-cost microelectromechanical system (MEMS) sensors operated in harsh multilateral horizontal downhole drilling environments. This paper proposes a novel nonlinear error model (NNEM) by the introduction of the error of DCM, and the NNEM can reduce the propagated errors under large-angle attitude error conditions. The zero velocity and zero position are the reference points and the innovations in the states estimation of particle filter (PF) and Kalman filter (KF). The experimental results illustrate that the performance of PF is better than KF and the PF with NNEM can effectively restrain the errors of system states, especially for the azimuth, velocity, and height in the quasi-stationary condition. PMID:26999130

  16. Particle Filter with Novel Nonlinear Error Model for Miniature Gyroscope-Based Measurement While Drilling Navigation.

    PubMed

    Li, Tao; Yuan, Gannan; Li, Wang

    2016-01-01

    The derivation of a conventional error model for the miniature gyroscope-based measurement while drilling (MGWD) system is based on the assumption that the errors of attitude are small enough so that the direction cosine matrix (DCM) can be approximated or simplified by the errors of small-angle attitude. However, the simplification of the DCM would introduce errors to the navigation solutions of the MGWD system if the initial alignment cannot provide precise attitude, especially for the low-cost microelectromechanical system (MEMS) sensors operated in harsh multilateral horizontal downhole drilling environments. This paper proposes a novel nonlinear error model (NNEM) by the introduction of the error of DCM, and the NNEM can reduce the propagated errors under large-angle attitude error conditions. The zero velocity and zero position are the reference points and the innovations in the states estimation of particle filter (PF) and Kalman filter (KF). The experimental results illustrate that the performance of PF is better than KF and the PF with NNEM can effectively restrain the errors of system states, especially for the azimuth, velocity, and height in the quasi-stationary condition. PMID:26999130

  17. Nonlinear elastic behavior and failure mechanism of polyhedral graphite particles undergoing uniaxial compression

    NASA Astrophysics Data System (ADS)

    Li, B.; Zhang, P.; Fu, Q. Q.; Li, X. F.; Zhao, X.; Song, X. L.

    2014-08-01

    Load-displacement responses and ultimate strength of polyhedral graphite particles (PGPs) undergoing in situ nano-compression at ambient temperature have been studied. The dynamic responses of PGPs to uniaxial loads exhibit a typical nonlinear elastic behavior for graphitic nanomaterials. Based on the analysis of stress-strain relationship, the intrinsic strength is slightly larger than actual ultimate strength, indicating the mechanical properties influenced by the initial defects in PGPs. For a given case, compressive Young's modulus E and third-order elastic modulus D achieve to 12.8 GPa and -13.9 GPa, respectively. Weibull probability analysis confirmed its broad range of structural defects inside PGPs and mechanical properties are sensitive to initial defects. The values of ultimate strength of tested PGPs with diameter of 150-400 nm fall within 2-4.5 GPa, which are in the range between shear elastic modulus C44 of turbo-g (minimum) and C44 of hex-g (maximum) in the literature. The deformation and failure mechanisms are discussed and rationalized in terms of structural factors and elastic moduli of perfect graphite crystals.

  18. Comparison of BES measurements of ion-scale turbulence with direct gyro-kinetic simulations of MAST L-mode plasmas

    NASA Astrophysics Data System (ADS)

    Field, A. R.; Dunai, D.; Ghim, Y.-c.; Hill, P.; McMillan, B.; Roach, C. M.; Saarelma, S.; Schekochihin, A. A.; Zoletnik, S.; the MAST Team

    2014-02-01

    Observations of ion-scale (kyρi ⩽ 1) density turbulence of relative amplitude ≳0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial × 4 poloidal channel) imaging beam emission spectroscopy diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplitude and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be ‘critically balanced’, the simulated turbulence is weak.

  19. Developments in non-linear Kalman Ensemble and Particle Filtering techniques for hydrological data assimilation

    NASA Astrophysics Data System (ADS)

    Khaki, Mehdi; Forootan, Ehsan; Kuhn, Michael; Awange, Joseph; Pattiaratchi, Charitha

    2016-04-01

    Quantifying large-scale (basin/global) water storage changes is essential to understand the Earth's hydrological water cycle. Hydrological models have usually been used to simulate variations in storage compartments resulting from changes in water fluxes (i.e., precipitation, evapotranspiration and runoff) considering physical or conceptual frameworks. Models however represent limited skills in accurately simulating the storage compartments that could be the result of e.g., the uncertainty of forcing parameters, model structure, etc. In this regards, data assimilation provides a great chance to combine observational data with a prior forecast state to improve both the accuracy of model parameters and to improve the estimation of model states at the same time. Various methods exist that can be used to perform data assimilation into hydrological models. The one more frequently used particle-based algorithms suitable for non-linear systems high-dimensional systems is the Ensemble Kalman Filtering (EnKF). Despite efficiency and simplicity (especially in EnKF), this method indicate some drawbacks. To implement EnKF, one should use the sample covariance of observations and model state variables to update a priori estimates of the state variables. The sample covariance can be suboptimal as a result of small ensemble size, model errors, model nonlinearity, and other factors. Small ensemble can also lead to the development of correlations between state components that are at a significant distance from one another where there is no physical relation. To investigate the under-sampling issue raise by EnKF, covariance inflation technique in conjunction with localization was implemented. In this study, a comparison between latest methods used in the data assimilation framework, to overcome the mentioned problem, is performed. For this, in addition to implementing EnKF, we introduce and apply the Local Ensemble Kalman Filter (LEnKF) utilizing covariance localization to remove

  20. Gyrokinetic theory and simulation of turbulent energy exchange

    SciTech Connect

    Waltz, R. E.; Staebler, G. M.

    2008-01-15

    A previous gyrokinetic theory of turbulent heating [F. L. Hinton and R. E. Waltz, Phys. Plasma 13, 102301 (2006)] is simplified and extended to show that the local radial average of terms in the gyrokinetic turbulent heating (which survive in the drift kinetic limit) are actually closer to a turbulent energy exchange between electrons and ions. The integrated flow for the local exchange is simulated with the GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] delta-f gyrokinetic code and found to be small in a well studied DIII-D [M. A. Mahdavi and J. L. Luxon, ''DIII-D Tokamak Special Issue'' Fusion Sci. Technol. 48, 2 (2005)] L-mode discharge.

  1. Magnetohydrodynamics for collisionless plasmas from the gyrokinetic perspective

    NASA Astrophysics Data System (ADS)

    Lee, W. W.

    2016-07-01

    The effort to obtain a set of MagnetoHydroDynamic (MHD) equations for a magnetized collisionless plasma was started nearly 60 years ago by Chew et al. [Proc. R. Soc. London, Ser. A 236(1204), 112-118 (1956)]. Many attempts have been made ever since. Here, we will show the derivation of a set of these equations from the gyrokinetic perspective, which we call it gyrokinetic MHD, and it is different from the conventional ideal MHD. However, this new set of equations still has conservation properties and, in the absence of fluctuations, recovers the usual MHD equilibrium. Furthermore, the resulting equations allow for the plasma pressure balance to be further modified by finite-Larmor-radius effects in regions with steep pressure gradients. The present work is an outgrowth of the paper on "Alfven Waves in Gyrokinetic Plasmas" by Lee and Qin [Phys. Plasmas 10, 3196 (2003)].

  2. The physics of the second-order gyrokinetic magnetohydrodynamic Hamiltonian: μ conservation, Galilean invariance, and ponderomotive potential

    SciTech Connect

    Krommes, J. A.

    2013-12-15

    Some physical interpretations are given of the well-known second-order gyrokinetic Hamiltonian in the magnetohydrodynamic limit. Its relations to the conservation of the true (Galilean-invariant) magnetic moment and fluid nonlinearities are described. Subtleties about its derivation as a cold-ion limit are explained; it is important to take that limit in the frame moving with the E×B velocity. The discussion also provides some geometric understanding of certain well-known Lie generating functions, and it makes contact with general discussions of ponderomotive potentials and the thermodynamics of dielectric media.

  3. Incorrectness of the usual gyrokinetic treatment in cylindrically symmetric systems

    SciTech Connect

    Linsker, R.

    1980-07-01

    It is shown that the usual gyrokinetic theory does not consistently retain all terms of leading order in the expansion parameter epsilon = gyroradius/equilibrium scale length. This is illustrated for cylindrically symmetric systems by comparing the perturbed distribution function calculated by the gyrokinetic method with that obtained by explicitly integrating the Vlasov equation over the unperturbed orbit. The integral equation used in some recent treatments of drift waves in sheared-slab geometry is shown to be incorrect. The correct calculation of the ion density perturbation for a collisionless ..beta.. = 0 plasma with cylindrical symmetry is presented.

  4. Pareto optimal calibration of highly nonlinear reactive transport groundwater models using particle swarm optimization

    NASA Astrophysics Data System (ADS)

    Siade, A. J.; Prommer, H.; Welter, D.

    2014-12-01

    Groundwater management and remediation requires the implementation of numerical models in order to evaluate the potential anthropogenic impacts on aquifer systems. In many situations, the numerical model must, not only be able to simulate groundwater flow and transport, but also geochemical and biological processes. Each process being simulated carries with it a set of parameters that must be identified, along with differing potential sources of model-structure error. Various data types are often collected in the field and then used to calibrate the numerical model; however, these data types can represent very different processes and can subsequently be sensitive to the model parameters in extremely complex ways. Therefore, developing an appropriate weighting strategy to address the contributions of each data type to the overall least-squares objective function is not straightforward. This is further compounded by the presence of potential sources of model-structure errors that manifest themselves differently for each observation data type. Finally, reactive transport models are highly nonlinear, which can lead to convergence failure for algorithms operating on the assumption of local linearity. In this study, we propose a variation of the popular, particle swarm optimization algorithm to address trade-offs associated with the calibration of one data type over another. This method removes the need to specify weights between observation groups and instead, produces a multi-dimensional Pareto front that illustrates the trade-offs between data types. We use the PEST++ run manager, along with the standard PEST input/output structure, to implement parallel programming across multiple desktop computers using TCP/IP communications. This allows for very large swarms of particles without the need of a supercomputing facility. The method was applied to a case study in which modeling was used to gain insight into the mobilization of arsenic at a deepwell injection site

  5. Gyrokinetic turbulence cascade via predator-prey interactions between different scales

    SciTech Connect

    Kobayashi, Sumire Gurcan, Ozgur D.

    2015-05-15

    Gyrokinetic simulations in a closed fieldline geometry are presented to explore the physics of nonlinear transfer in plasma turbulence. As spontaneously formed zonal flows and small-scale turbulence demonstrate “predator-prey” dynamics, a particular cascade spectrum emerges. The electrostatic potential and the density spectra appear to be in good agreement with the simple theoretical prediction based on Charney-Hasegawa-Mima equation | ϕ{sup ~}{sub k} |{sup 2}∼| n{sup ~}{sub k} |{sup 2}∝k{sup −3}/(1+k{sup 2}){sup 2}, with the spectra becoming anisotropic at small scales. The results indicate that the disparate scale interactions, in particular, the refraction and shearing of larger scale eddies by the self-consistent zonal flows, dominate over local interactions, and contrary to the common wisdom, the comprehensive scaling relation is created even within the energy injection region.

  6. Gyrokinetic turbulence cascade via predator-prey interactions between different scales

    NASA Astrophysics Data System (ADS)

    Kobayashi, Sumire; Gurcan, Ozgur D.

    2015-05-01

    Gyrokinetic simulations in a closed fieldline geometry are presented to explore the physics of nonlinear transfer in plasma turbulence. As spontaneously formed zonal flows and small-scale turbulence demonstrate "predator-prey" dynamics, a particular cascade spectrum emerges. The electrostatic potential and the density spectra appear to be in good agreement with the simple theoretical prediction based on Charney-Hasegawa-Mima equation |ϕ˜ k | 2˜|n˜ k | 2∝k-3/(1+k2 ) 2 , with the spectra becoming anisotropic at small scales. The results indicate that the disparate scale interactions, in particular, the refraction and shearing of larger scale eddies by the self-consistent zonal flows, dominate over local interactions, and contrary to the common wisdom, the comprehensive scaling relation is created even within the energy injection region.

  7. Collision-dependent power law scalings in two dimensional gyrokinetic turbulence

    SciTech Connect

    Cerri, S. S. Bañón Navarro, A.; Told, D.; Jenko, F.

    2014-08-15

    Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.

  8. Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator

    SciTech Connect

    Faber, B. J.; Pueschel, M. J.; Terry, P. W.; Proll, J. H. E.; Hegna, C. C.; Weir, G. M.; Likin, K. M.; Talmadge, J. N.

    2015-07-15

    Gyrokinetic simulations of plasma microturbulence in the Helically Symmetric eXperiment are presented. Using plasma profiles relevant to experimental operation, four dominant drift wave regimes are observed in the ion wavenumber range, which are identified as different flavors of density-gradient-driven trapped electron modes. For the most part, the heat transport exhibits properties associated with turbulence driven by these types of modes. Additionally, long-wavelength, radially localized, nonlinearly excited coherent structures near the resonant central flux surface, not predicted by linear simulations, can further enhance flux levels. Integrated heat fluxes are compatible with experimental observations in the corresponding density gradient range. Despite low shearing rates, zonal flows are observed to regulate turbulence but can be overwhelmed at higher density gradients by the long-wavelength coherent structures.

  9. Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics

    SciTech Connect

    W.M. Tang

    2005-01-03

    The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.

  10. 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.

  11. GYROKINETIC PARTICLE SIMULATION OF TURBULENT TRANSPORT IN BURNING PLASMAS

    SciTech Connect

    Horton, Claude Wendell

    2014-06-10

    The SciDAC project at the IFS advanced the state of high performance computing for turbulent structures and turbulent transport. The team project with Prof Zhihong Lin [PI] at Univ California Irvine produced new understanding of the turbulent electron transport. The simulations were performed at the Texas Advanced Computer Center TACC and the NERSC facility by Wendell Horton, Lee Leonard and the IFS Graduate Students working in that group. The research included a Validation of the electron turbulent transport code using the data from a steady state university experiment at the University of Columbia in which detailed probe measurements of the turbulence in steady state were used for wide range of temperature gradients to compare with the simulation data. These results were published in a joint paper with Texas graduate student Dr. Xiangrong Fu using the work in his PhD dissertation. X.R. Fu, W. Horton, Y. Xiao, Z. Lin, A.K. Sen and V. Sokolov, “Validation of electron Temperature gradient turbulence in the Columbia Linear Machine, Phys. Plasmas 19, 032303 (2012).

  12. Gyrokinetic Particle Simulation of Turbulent Transport in Burning Plasmas

    SciTech Connect

    Diamond, P.H.; Lin, Z.; Wang, W.; Horton, W.; Klasky, S.; Decyk, V.; Ma, K.-L.; Chames, J.; Adams, M.

    2011-09-21

    The three-year project GPS-TTBP resulted in over 152 publications and 135 presentations. This summary focuses on the scientific progress made by the project team. A major focus of the project was on the physics intrinsic rotation in tokamaks. Progress included the first ever flux driven study of net intrinsic spin-up, mediated by boundary effects (in collaboration with CPES), detailed studies of the microphysics origins of the Rice scaling, comparative studies of symmetry breaking mechanisms, a pioneering study of intrinsic torque driven by trapped electron modes, and studies of intrinsic rotation generation as a thermodynamic engine. Validation studies were performed with C-Mod, DIII-D and CSDX. This work resulted in very successful completion of the FY2010 Theory Milestone Activity for OFES, and several prominent papers of the 2008 and 2010 IAEA Conferences. A second major focus was on the relation between zonal flow formation and transport non-locality. This culminated in the discovery of the ExB staircase - a conceptually new phenomenon. This also makes useful interdisciplinary contact with the physics of the PV staircase, well-known in oceans and atmospheres. A third topic where progress was made was in the simulation and theory of turbulence spreading. This work, now well cited, is important for understanding the dynamics of non-locality in turbulent transport. Progress was made in studies of conjectured non-diffusive transport in trapped electron turbulence. Pioneering studies of ITB formation, coupling to intrinsic rotation and hysteresis were completed. These results may be especially significant for future ITER operation. All told, the physics per dollar performance of this project was quite good. The intense focus was beneficial and SciDAC resources were essential to its success.

  13. PREFACE: 14th Annual International Astrophysics Conference: Linear and Nonlinear Particle Energization throughout the Heliosphere and Beyond

    NASA Astrophysics Data System (ADS)

    Zank, G. P.

    2015-09-01

    The 14th Annual International Astrophysics Conference was held at the Sheraton Tampa Riverwalk Hotel, Tampa, Florida, USA, during the week of 19-24 April 2015. The meeting drew some 75 participants from all over the world, representing a wide range of interests and expertise in the energization of particles from the perspectives of theory, modelling and simulations, and observations. The theme of the meeting was "Linear and Nonlinear Particle Energization throughout the Heliosphere and Beyond." Energetic particles are ubiquitous to plasma environments, whether collisionless such as the supersonic solar wind, the magnetospheres of planets, the exospheres of nonmagnetized planets and comets, the heliospheric-local interstellar boundary regions, interstellar space and supernova remnant shocks, and stellar wind boundaries. Energetic particles are found too in more collisional regions such as in the solar corona, dense regions of the interstellar medium, accretion flows around stellar objects, to name a few. Particle acceleration occurs wherever plasma boundaries, magnetic and electric fields, and turbulence are present. The meeting addressed the linear and nonlinear physical processes underlying the variety of particle acceleration mechanisms, the role of particle acceleration in shaping different environments, and acceleration processes common to different regions. Both theory and observations were addressed with a view to encouraging crossdisciplinary fertilization of ideas, concepts, and techniques. The meeting addressed all aspects of particle acceleration in regions ranging from the Sun to the interplanetary medium to magnetospheres, exospheres, and comets, the boundaries of the heliosphere, and beyond to supernova remnant shocks, galactic jets, stellar winds, accretion flows, and more. The format of the meeting included 25-minute presentations punctuated by two 40-minute talks, one by Len Fisk that provided an historical overview of particle acceleration in the

  14. Particle filter for state estimation of jump Markov nonlinear system with application to multi-targets tracking

    NASA Astrophysics Data System (ADS)

    Han, Hua; Ding, Yongsheng; Hao, Kuangrong; Hu, Liangjian

    2013-07-01

    In this article, we first introduce the problem of state estimation of jump Markov nonlinear systems (JMNSs). Since the density evolution method for predictor equations satisfies Fokker-Planck-Kolmogorov equation (FPKE) in Bayes estimation, the FPKE in conjunction with Bayes' conditional density update formula can provide optimal estimation for a general continuous-discrete nonlinear filtering problem. It is well known that the analytical solution of the FPKE and Bayes' formula is extremely difficult to obtain except a few special cases. Hence, we try to design a particle filter to achieve Bayes estimation of the JMNSs. In order to test the viability of our algorithm, we apply it to multiple targets tracking in video surveillance. Before starting simulation, we introduce the 'birth' and 'death' description of targets, targets' transitional probability model, and observation probability. The experiment results show good performance of our proposed filter for multiple targets tracking.

  15. On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

    NASA Astrophysics Data System (ADS)

    Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

    2015-04-01

    The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

  16. Non-Linear Transmission Line (NLTL) Microwave Source Lecture Notes the United States Particle Accelerator School

    SciTech Connect

    Russell, Steven J.; Carlsten, Bruce E.

    2012-06-26

    We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.

  17. Unambiguous identification of superparamagnetic iron oxide (SPIO) particles through quantitative susceptibility mapping of the nonlinear response to magnetic fields

    PubMed Central

    Liu, Tian; Spincemaille, Pascal; de Rochefort, Ludovic; Wong, Richard; Prince, Martin; Wang, Yi

    2010-01-01

    Superparamagnetic iron oxide (SPIO) particles generate signal void regions on gradient echo images due to their strong magnetization. In practice, the signal void region might be indistinguishable from that generated by air. However, the response of SPIO to an externally applied magnetic field is non-linear. Magnetization of SPIO saturates at around 1 Tesla while magnetization of water and air increase linearly with field strength. Phantom experiment and mice experiments demonstrated the feasibility of a non-ambiguous identification of superparamagnetic contrast agents. PMID:20688448

  18. An Introduction to Twisted Particle Filters and Parameter Estimation in Non-Linear State-Space Models

    NASA Astrophysics Data System (ADS)

    Ala-Luhtala, Juha; Whiteley, Nick; Heine, Kari; Piche, Robert

    2016-09-01

    Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.

  19. Quasilinear model for energetic particle diffusion in radial and velocity space

    SciTech Connect

    Waltz, R. E.; Staebler, G. M.; Bass, E. M.

    2013-04-15

    A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2 Multiplication-Sign 2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.

  20. Quasilinear model for energetic particle diffusion in radial and velocity space

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Bass, E. M.; Staebler, G. M.

    2013-04-01

    A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2×2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.

  1. Extended gyrokinetic field theory for time-dependent magnetic confinement fields

    SciTech Connect

    Sugama, H.; Watanabe, T.-H.; Nunami, M.

    2014-01-15

    A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.

  2. Grid-based Parallel Data Streaming Implemented for the Gyrokinetic Toroidal Code

    SciTech Connect

    S. Klasky; S. Ethier; Z. Lin; K. Martins; D. McCune; R. Samtaney

    2003-09-15

    We have developed a threaded parallel data streaming approach using Globus to transfer multi-terabyte simulation data from a remote supercomputer to the scientist's home analysis/visualization cluster, as the simulation executes, with negligible overhead. Data transfer experiments show that this concurrent data transfer approach is more favorable compared with writing to local disk and then transferring this data to be post-processed. The present approach is conducive to using the grid to pipeline the simulation with post-processing and visualization. We have applied this method to the Gyrokinetic Toroidal Code (GTC), a 3-dimensional particle-in-cell code used to study microturbulence in magnetic confinement fusion from first principles plasma theory.

  3. The Hamiltonian structure and Euler-Poincare formulation of the Vlasov-Maxwell and gyrokinetic systems

    SciTech Connect

    Squire, J.; Tang, W. M.; Qin, H.; Chandre, C.

    2013-02-15

    We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in H. Cendra et al., [J. Math. Phys. 39, 3138 (1998)]. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.

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

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; White, A. E.; Greenwald, M.; Holland, C.; Candy, J.

    2014-03-01

    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 = (mD/me).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., 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 (kθρs˜O(1.0)) and electron (kθρe˜O(1.0)) scales for experimental plasma conditions both exhibiting strong (high-power) and marginally stable (low-power) low-k (kθρs < 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.

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

    SciTech Connect

    Howard, N. T. White, A. E.; Greenwald, M.; Holland, C.; Candy, J.

    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., 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.

  6. From charge motion in general magnetic fields to the non perturbative gyrokinetic equation

    NASA Astrophysics Data System (ADS)

    Di Troia, C.

    2015-04-01

    The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.

  7. From charge motion in general magnetic fields to the non perturbative gyrokinetic equation

    SciTech Connect

    Di Troia, C.

    2015-04-15

    The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem, even if it has not been solved until now, apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field; the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.

  8. Linear and Nonlinear Study of Fast Particle Excitation of Alfvén Eigemodes

    SciTech Connect

    Berk, H.L.; Chen, Y.; Cheng, C.Z.; Fu, G.Y.; Gorelenkov, N.N; Gorelenkova, M.V.; Nazikian, R.; White, R.B.

    1998-11-01

    Recent new results concerning toroidicity-induced Alfvén eigenmode (TAE) linear stability and nonlinear amplitude saturation and associated fast ion transport are presented for tokamaks, such as the National Spherical Torus Experiment (NSTX) and the International Thermonuclear Experimental Reactor (ITER), using the numerical codes HINST, NOVA-K, and ORBIT.

  9. Consequences of using nonlinear particle trajectories to compute spatial diffusion coefficients. [for charged particles in interplanetary space

    NASA Technical Reports Server (NTRS)

    Goldstein, M. L.

    1976-01-01

    The propagation of charged particles through interstellar and interplanetary space has often been described as a random process in which the particles are scattered by ambient electromagnetic turbulence. In general, this changes both the magnitude and direction of the particles' momentum. Some situations for which scattering in direction (pitch angle) is of primary interest were studied. A perturbed orbit, resonant scattering theory for pitch-angle diffusion in magnetostatic turbulence was slightly generalized and then utilized to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field, Kappa. All divergences inherent in the quasilinear formalism when the power spectrum of the fluctuation field falls off as K to the minus Q power (Q less than 2) were removed. Various methods of computing Kappa were compared and limits on the validity of the theory discussed. For Q less than 1 or 2, the various methods give roughly comparable values of Kappa, but use of perturbed orbits systematically results in a somewhat smaller Kappa than can be obtained from quasilinear theory.

  10. Destabilizing Effect of Dynamical Friction on Fast-Particle-Driven Waves in a Near-Threshold Nonlinear Regime

    NASA Astrophysics Data System (ADS)

    Lilley, M. K.; Breizman, B. N.; Sharapov, S. E.

    2009-05-01

    The nonlinear evolution of waves excited by the resonant interaction with energetic particles, just above the instability threshold, is shown to depend on the type of relaxation process that restores the unstable distribution function. When dynamical friction dominates over diffusion in the phase space region surrounding the wave-particle resonance, an explosive evolution of the wave is found to be the only solution. This is in contrast with the case of dominant diffusion when the wave may exhibit steady-state, amplitude modulation, chaotic and explosive regimes near marginal stability. The experimentally observed differences between Alfvénic instabilities driven by neutral beam injection and those driven by ion-cyclotron resonance heating are interpreted.

  11. Efficient hyperentanglement concentration for N-particle Greenberger-Horne-Zeilinger state assisted by weak cross-Kerr nonlinearity

    NASA Astrophysics Data System (ADS)

    Liu, Huan-Juan; Xia, Yan; Song, Jie

    2016-05-01

    In this scheme, based on the weak cross-Kerr nonlinearity, an hyperconcentration protocol for the arbitrary partially hyperentangled N-particle Greenberger-Horne-Zeilinger (GHZ) state is presented. Considering the N photons initially in the nonmaximally hyperentangled GHZ state in which photons are entangled simultaneously in the polarization and the spatial-mode degrees of freedom, we can obtain the maximally hyperentangled N-particle GHZ state by the projection measurements on the additional photons. Numerical simulation demonstrates that by iterating the entanglement concentration process, we can improve the success probability of the scheme. Furthermore, we discuss the feasibility of the setups of the protocol, concluding that the present protocol is feasible with existing experimental technology. All these advantages make this scheme more efficient and more convenient in quantum communication.

  12. Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit

    NASA Astrophysics Data System (ADS)

    Di Francesco, M.; Rosini, M. D.

    2015-09-01

    We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in ) to the unique Kružkov entropy solution of the conservation law. The initial data are taken in , nonnegative, and with compact support, hence we are able to handle densities with a vacuum. Our result holds for a reasonably general class of velocity maps (including all the relevant examples in the applications, for example in the Lighthill-Whitham-Richards model for traffic flow) with a possible degenerate slope near the vacuum state. The proof of the result is based on discrete estimates and on a discrete version of the one-sided Oleinik-type condition. In particular, we prove that the regularizing effect for nonlinear scalar conservation laws is intrinsic to the discrete model.

  13. Simulating Gyrokinetic/fluid hybrid electromagnetic modes in the total-f gyrokinetic code XGC1

    NASA Astrophysics Data System (ADS)

    Lang, Jianying; Hager, Robert; Ku, Seung-Hoe; Chang, Choong-Seock

    2015-11-01

    XGC1 code has been extended to include the electronmagnetic capability using the hybrid model with gyrokinetic ions and fluid electrons. This feature will enable a more complete description of the MHD/fluid type mode activities including ELMs and low-n tearing modes. Their interaction with the kinetic neoclassical and microturbulence dynamics needs to be simulated together. Evolution of the background profile should also be captured self-consistently. We report recent development and verification of this hybrid model in the limit of small delta-B. The code has been verified for Alfven waves and ITG/KBM transition, and low-n resistive tearing modes. The KBM capability of XGC1 has been verified against the published results from Gyro, GEM, GS2, Gene, and GTC. Detailed verification of resistive tearing modes and kink modes in the toroidal geometry will be also presented. An implicit method is implemented in XGC1 to bypass the Courant condition caused by fast Alfven oscillations. Work supported by US DOE OFES and OASCR.

  14. A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

    NASA Technical Reports Server (NTRS)

    Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

    1995-01-01

    High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

  15. Gyrokinetics for high-frequency modes in tokamaks

    NASA Astrophysics Data System (ADS)

    Wang, Z. T.; Wang, L.; Long, L. X.; Dong, J. Q.; He, Zhixiong; Liu, Y.; Tang, C. J.

    2012-07-01

    Gyrokinetics for high-frequency modes in tokamaks is developed. It is found that the breakdown of the invariants by perturbed electromagnetic fields drives microinstability. The obtained diamagnetic frequency, ω∗, is proportional to only the toroidal mode number rather than transverse mode numbers. Therefore, there is no nonadiabatic drive for axisymmetrical modes in gyrokinetics. Meanwhile, the conventional eikonal Ansatz breaks down for the axisymmetrical modes. The ion drift-cyclotron instability discovered in a mirror machine is found for the first time in the toroidal system. The growth rates are proportional to ρi/Ln, and the slope changes with magnetic curvature. In spherical torus, where magnetic curvature is greater than that of traditional tokamaks, instability poses a potential danger to such devices.

  16. Gyrokinetics for high-frequency modes in tokamaks

    SciTech Connect

    Wang, Z. T.; Long, L. X.; Dong, J. Q.; He, Zhixiong; Wang, L.; Liu, Y.; Tang, C. J.

    2012-07-15

    Gyrokinetics for high-frequency modes in tokamaks is developed. It is found that the breakdown of the invariants by perturbed electromagnetic fields drives microinstability. The obtained diamagnetic frequency, {omega}{sup *}, is proportional to only the toroidal mode number rather than transverse mode numbers. Therefore, there is no nonadiabatic drive for axisymmetrical modes in gyrokinetics. Meanwhile, the conventional eikonal Ansatz breaks down for the axisymmetrical modes. The ion drift-cyclotron instability discovered in a mirror machine is found for the first time in the toroidal system. The growth rates are proportional to {rho}{sub i}/L{sub n}, and the slope changes with magnetic curvature. In spherical torus, where magnetic curvature is greater than that of traditional tokamaks, instability poses a potential danger to such devices.

  17. Global particle-in-cell simulations of Alfvenic modes

    SciTech Connect

    Mishchenko, A.; Koenies, A.; Hatzky, R.

    2008-11-01

    Global linear gyro-kinetic particle-in-cell (PIC) simulations of electromagnetic modes in pinch and tokamak geometries are reported. The Toroidal Alfven Eigenmode and the Kinetic Ballooning Mode have been simulated. All plasma species have been treated kinetically (i.e. no hybrid fluid-kinetic or reduced-kinetic model has been applied). The main intention of the paper is to demonstrate that the global Alfven modes can be treated with the gyro-kinetic PIC method.

  18. Nonlinear Flow Generation By Electrostatic Turbulence In Tokamaks

    SciTech Connect

    Wang, W. X.; Diamond, P. H.; Hahm, T. S.; Ethier, S.; Rewoldt, G.; Tang, W. M.

    2010-07-07

    Global gyrokinetic simulations have revealed an important nonlinear flow generation process due to the residual stress produced by electrostatic turbulence of ion temperature gradient (ITG) modes and trapped electron modes (TEM). In collisionless TEM (CTEM) turbulence, nonlinear residual stress generation by both the fluctuation intensity and the intensity gradient in the presence of broken symmetry in the parallel wave number spectrum is identified for the first time. Concerning the origin of the symmetry breaking, turbulence self-generated low frequency zonal flow shear has been identified to be a key, universal mechanism in various turbulence regimes. Simulations reported here also indicate the existence of other mechanisms beyond E × B shear. The ITG turbulence driven “intrinsic” torque associated with residual stress is shown to increase close to linearly with the ion temperature gradient, in qualitative agreement with experimental observations in various devices. In CTEM dominated regimes, a net toroidal rotation is driven in the cocurrent direction by “intrinsic” torque, consistent with the experimental trend of observed intrinsic rotation. The finding of a “flow pinch” in CTEM turbulence may offer an interesting new insight into the underlying dynamics governing the radial penetration of modulated flows in perturbation experiments. Finally, simulations also reveal highly distinct phase space structures between CTEM and ITG turbulence driven momentum, energy and particle fluxes, elucidating the roles of resonant and non-resonant particles.

  19. Investigation of the nonlinear effects during the sedimentation process of a charged colloidal particle by direct numerical simulation.

    PubMed

    Keller, Florian; Feist, Markus; Nirschl, Hermann; Dörfler, Willy

    2010-04-01

    In this article we study the settling process of a colloidal particle under the influence of a gravitational or centrifugal field in an unbounded electrolyte solution. Since particles in aqueous solutions normally carry a non-zero surface charge, a microscopic electric field develops which alters the sedimentation process compared to an uncharged particle. This process can be mathematically modelled via the Stokes-Poisson-Nernst-Planck system, a system of coupled partial differential equations that have to be solved in an exterior domain. After a dimensional analysis we investigate the influence of the various characteristic dimensionless numbers on the sedimentation velocity. Thereby the linear-response (weak-field) approximation that underpins almost all existing theoretical work on classical electrokinetic phenomena is relaxed, such that no additional assumption on the thickness of the double layer as well as on its displacement is needed. We show that there exists a strong influence of the fluid Reynolds number and the ionic strength on the sedimentation velocity. Further we have developed an asymptotic expansion to describe the limit of small values of the surface potential of a single particle. This expansion incorporates all nonlinear effects and extends the well-known results of Booth (1954) [1] and Ohshima et al. (1984) [2] to higher fluid Reynolds numbers. PMID:20097350

  20. Verification of gyrokinetic microstability codes with an LHD configuration

    SciTech Connect

    Mikkelsen, D. R.; Nunami, M.; Watanabe, T. -H.; Sugama, H.; Tanaka, K.

    2014-11-01

    We extend previous benchmarks of the GS2 and GKV-X codes to verify their algorithms for solving the gyrokinetic Vlasov-Poisson equations for plasma microturbulence. Code benchmarks are the most complete way of verifying the correctness of implementations for the solution of mathematical models for complex physical processes such as those studied here. The linear stability calculations reported here are based on the plasma conditions of an ion-ITB plasma in the LHD configuration. The plasma parameters and the magnetic geometry differ from previous benchmarks involving these codes. We find excellent agreement between the independently written pre-processors that calculate the geometrical coefficients used in the gyrokinetic equations. Grid convergence tests are used to establish the resolution and domain size needed to obtain converged linear stability results. The agreement of the frequencies, growth rates and eigenfunctions in the benchmarks reported here provides additional verification that the algorithms used by the GS2 and GKV-X codes are correctly finding the linear eigenvalues and eigenfunctions of the gyrokinetic Vlasov-Poisson equations.

  1. Verification of gyrokinetic microstability codes with an LHD configuration

    SciTech Connect

    Mikkelsen, D. R.; Nunami, M.; Sugama, H.; Tanaka, K.; Watanabe, T.-H.

    2014-11-15

    We extend previous benchmarks of the GS2 and GKV-X codes to verify their algorithms for solving the gyrokinetic Vlasov-Poisson equations for plasma microturbulence. Code benchmarks are the most complete way of verifying the correctness of implementations for the solution of mathematical models for complex physical processes such as those studied here. The linear stability calculations reported here are based on the plasma conditions of an ion-ITB plasma in the LHD configuration. The plasma parameters and the magnetic geometry differ from previous benchmarks involving these codes. We find excellent agreement between the independently written pre-processors that calculate the geometrical coefficients used in the gyrokinetic equations. Grid convergence tests are used to establish the resolution and domain size needed to obtain converged linear stability results. The agreement of the frequencies, growth rates, and eigenfunctions in the benchmarks reported here provides additional verification that the algorithms used by the GS2 and GKV-X codes are correctly finding the linear eigenvalues and eigenfunctions of the gyrokinetic Vlasov-Poisson equations.

  2. Nonlinear acoustic-gravity waves and dust particle redistribution in earth's atmosphere

    NASA Astrophysics Data System (ADS)

    Izvekova, Yu. N.; Popel, S. I.; Chen, B. B.

    2015-11-01

    A continuously stratified model of nonadiabatic terrestrial atmosphere with taking into account the temperature profile is developed to study a possibility of instability development of acoustic-gravity (AG-) waves. It is shown that the existence of the regions in the atmosphere where the instability conditions are satisfied is due to the cooperation of thermal flow of solar radiation, infrared emission of the atmosphere, water vapor condensation, as well as thermal conductivity. Large-amplitude vortices in Earth's troposphere and ionosphere and their possible structure as well as redistribution of dust particles in the ionosphere as a result of vortical motions are discussed. The following possibilities for the dust particle redistribution are studied: capture and evolution of dust particles in AG-vortices, formation of dust vortices as a result of involving a great number of dust particles into vortex motions, and formation of vertical and horizontal dust flows (streamers and zonal flows). It is shown that excitation of AG-vortices at the ionospheric altitudes as a result of development of AG-wave instability leads to a substantial transportation of dust particles and their mixing. Layers of dust particles with a thickness of about a kilometer, forming at the altitudes less than 120 km, distribute within the region of the existence of AG-vortical structures. As a result, at altitudes of 110-120 km, dust vortices can appear, and transportation of particles up to altitudes of 130 km becomes possible. One of the ways of transportation of dust particles in the ionosphere is dust flows, which are generated by dust vortices as a result of development of parametric instability.

  3. Validation of gyrokinetic modelling of light impurity transport including rotation in ASDEX Upgrade

    NASA Astrophysics Data System (ADS)

    Casson, F. J.; McDermott, R. M.; Angioni, C.; Camenen, Y.; Dux, R.; Fable, E.; Fischer, R.; Geiger, B.; Manas, P.; Menchero, L.; Tardini, G.; the ASDEX Upgrade Team

    2013-06-01

    Upgraded spectroscopic hardware and an improved impurity concentration calculation allow accurate determination of boron density in the ASDEX Upgrade tokamak. A database of boron measurements is compared to quasilinear and nonlinear gyrokinetic simulations including Coriolis and centrifugal rotational effects over a range of H-mode plasma regimes. The peaking of the measured boron profiles shows a strong anti-correlation with the plasma rotation gradient, via a relationship explained and reproduced by the theory. It is demonstrated that the rotodiffusive impurity flux driven by the rotation gradient is required for the modelling to reproduce the hollow boron profiles at higher rotation gradients. The nonlinear simulations validate the quasilinear approach, and, with the addition of perpendicular flow shear, demonstrate that each symmetry breaking mechanism that causes momentum transport also couples to rotodiffusion. At lower rotation gradients, the parallel compressive convection is required to match the most peaked boron profiles. The sensitivities of both datasets to possible errors is investigated, and quantitative agreement is found within the estimated uncertainties. The approach used can be considered a template for mitigating uncertainty in quantitative comparisons between simulation and experiment.

  4. Verification of particle simulation of radio frequency waves in fusion plasmas

    SciTech Connect

    Kuley, Animesh; Lin, Z.; Wang, Z. X.; Wessel, F.

    2013-10-15

    Radio frequency (RF) waves can provide heating, current and flow drive, as well as instability control for steady state operations of fusion experiments. A particle simulation model has been developed in this work to provide a first-principles tool for studying the RF nonlinear interactions with plasmas. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation. This model has been implemented in a global gyrokinetic toroidal code using real electron-to-ion mass ratio. To verify the model, linear simulations of ion plasma oscillation, ion Bernstein wave, and lower hybrid wave are carried out in cylindrical geometry and found to agree well with analytic predictions.

  5. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

    NASA Astrophysics Data System (ADS)

    Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.

    2016-06-01

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles provide scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation - e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others - can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function - driven by ionization, charge exchange and wall loss - is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.

  6. Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

    NASA Technical Reports Server (NTRS)

    Chen, J.; Palmadesso, P. J.

    1986-01-01

    The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

  7. Nonlinear Simulation Studies of Tokamaks and STs

    SciTech Connect

    W. Park; J. Breslau; J. Chen; G.Y. Fu; S.C. Jardin; S. Klasky; J. Menard; A. Pletzer; B.C. Stratton; D. Stutman; H.R. Strauss; L.E. Sugiyama

    2003-07-07

    The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.

  8. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

    SciTech Connect

    Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut

    2015-06-14

    Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

  9. Global nonlinear kernel prediction for large data set with a particle swarm-optimized interval support vector regression.

    PubMed

    Ding, Yongsheng; Cheng, Lijun; Pedrycz, Witold; Hao, Kuangrong

    2015-10-01

    A new global nonlinear predictor with a particle swarm-optimized interval support vector regression (PSO-ISVR) is proposed to address three issues (viz., kernel selection, model optimization, kernel method speed) encountered when applying SVR in the presence of large data sets. The novel prediction model can reduce the SVR computing overhead by dividing input space and adaptively selecting the optimized kernel functions to obtain optimal SVR parameter by PSO. To quantify the quality of the predictor, its generalization performance and execution speed are investigated based on statistical learning theory. In addition, experiments using synthetic data as well as the stock volume weighted average price are reported to demonstrate the effectiveness of the developed models. The experimental results show that the proposed PSO-ISVR predictor can improve the computational efficiency and the overall prediction accuracy compared with the results produced by the SVR and other regression methods. The proposed PSO-ISVR provides an important tool for nonlinear regression analysis of big data. PMID:25974954

  10. Gravitational dynamics of an infinite shuffled lattice: Particle coarse-graining, nonlinear clustering, and the continuum limit.

    PubMed

    Baertschiger, T; Joyce, M; Gabrielli, A; Sylos Labini, F

    2007-07-01

    We study the evolution under their self-gravity of particles evolving from infinite "shuffled lattice" initial conditions. We focus here specifically on the comparison between the evolution of such a system and that of "daughter" coarse-grained particle distributions. These are sparser (i.e., lower density) particle distributions, defined by a simple coarse-graining procedure, which share the same large-scale mass fluctuations. We consider both the case that such coarse-grainings are performed (i) on the initial conditions, and (ii) at a finite time with a specific additional prescription. In numerical simulations we observe that, to a first approximation, these coarse-grainings represent well the evolution of the two-point correlation properties over a significant range of scales. We note, in particular, that the form of the two-point correlation function in the original system, when it is evolving in the asymptotic "self-similar" regime, may be reproduced well in a daughter coarse-grained system in which the dynamics are still dominated by two-body (nearest neighbor) interactions. This provides a simple physical description of the origin of the form of part of the asymptotic nonlinear correlation function. Using analytical results on the early time evolution of these systems, however, we show that small observed differences between the evolved system and its coarse-grainings at the initial time will in fact diverge as the ratio of the coarse-graining scale to the original interparticle distance increases. The second coarse-graining studied, performed at a finite time in a specified manner, circumvents this problem. It also makes it more physically transparent why gravitational dynamics from these initial conditions tends toward a self-similar evolution. We finally discuss the precise definition of a limit in which a continuum (specifically Vlasov-type) description of the observed linear and nonlinear evolution should be applicable. This requires the introduction

  11. On the dynamics of nonlinear, unsteady landslide flow within the smoothed particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Khvostova, O.; Averbukh, E.

    2012-04-01

    In the present study the idea of landslide modeling by particle method is described. Smoothed particle hydrodynamics was invented in 1977 by Leon Lucy and independently by Bob Gingold and Joe Monaghan [1]. It was used for astrophysics phenomena's simulation. Later it was adapted for hydrodynamics, gas dynamics and solid body problems. Landslides can be caused by the influence of different factors. Landslides occur when the angle of inclination of the slope of the slope or if the slope is burdened with loose material. A landslide flow is a thin homogeneous layer of nearly incompressible fluid. It is considered that at the initial moment shifted part of a ground mass is splitting and turning into liquid of several layers which then is streaming down along the slope. The landslide flow motion is described with the Navie-Stocks set of equations: D→u-= - 1\\upsidedownBigTriangle P + μ \\upsidedownBigTriangle →u + g Dt ρ (1) D-ρ = 0, Dt (2) where u is velocity vector, t is time, ρ is a flow density, P is a pressure, μ is a viscosity coefficient, g is gravity. Continuum discretization by finite number of lagrangian particles is the main idea of SPH [2,3]. Particles moves with the flow and arbitrary connectivity is allowed. Therefore, SPH does not need a grid to calculate spatial derivatives. For any field A(r), involved in equation (1), e.g. pressure, density, viscosity etc., we consider an approximation with a finite function: A(r) = ∫ω A (r')W (r- r',h)dr' (3) where A is a desired field, r is a radius-vector, W is an interpolating kernel. The free boundary condition problem is discussed. Finding the particles on a free surface is described. Also the surface tension force defining is shown. Described method is implemented and mathematical modeling of landslide flows motion along slope is simulated. Different types of slopes are considered: with constant and variable steepness, long and wide. Wave-breaking effects near the wall are shown. Findings are analyzed

  12. The Study of Non-Linear Acceleration of Particles during Substorms Using Multi-Scale Simulations

    SciTech Connect

    Ashour-Abdalla, Maha

    2011-01-04

    To understand particle acceleration during magnetospheric substorms we must consider the problem on multple scales ranging from the large scale changes in the entire magnetosphere to the microphysics of wave particle interactions. In this paper we present two examples that demonstrate the complexity of substorm particle acceleration and its multi-scale nature. The first substorm provided us with an excellent example of ion acceleration. On March 1, 2008 four THEMIS spacecraft were in a line extending from 8 R{sub E} to 23 R{sub E} in the magnetotail during a very large substorm during which ions were accelerated to >500 keV. We used a combination of a global magnetohydrodynamic and large scale kinetic simulations to model the ion acceleration and found that the ions gained energy by non-adiabatic trajectories across the substorm electric field in a narrow region extending across the magnetotail between x = -10 R{sub E} and x = -15 R{sub E}. In this strip called the 'wall region' the ions move rapidly in azimuth and gain 100s of keV. In the second example we studied the acceleration of electrons associated with a pair of dipolarization fronts during a substorm on February 15, 2008. During this substorm three THEMIS spacecraft were grouped in the near-Earth magnetotail (x {approx}-10 R{sub E}) and observed electron acceleration of >100 keV accompanied by intense plasma waves. We used the MHD simulations and analytic theory to show that adiabatic motion (betatron and Fermi acceleration) was insufficient to account for the electron acceleration and that kinetic processes associated with the plasma waves were important.

  13. LETTER On the nonlinear response of a particle interacting with fermions in a 1D lattice

    NASA Astrophysics Data System (ADS)

    Zotos, X.

    2010-12-01

    By the Bethe ansatz method we study the energy dispersion of a particle interacting by a local interaction with fermions (or hard core bosons) of equal mass in a one-dimensional lattice. We focus on the period of the Bloch oscillations, which turns out to be related to the Fermi wavevector of the Fermi sea and in particular on how this dispersion emerges as a collective effect in the thermodynamic limit. We also discuss the adiabatic coherent collective response of the system to an applied field.

  14. Analytical Solutions for the Nonlinear Longitudinal Drift Compression (Expansion) of Intense Charged Particle Beams

    SciTech Connect

    Edward A. Startsev; Ronald C. Davidson

    2004-04-09

    To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

  15. Nonlinear Effects of Nanoparticles: Biological Variability From Hormetic Doses, Small Particle Sizes, and Dynamic Adaptive Interactions

    PubMed Central

    Bell, Iris R.; Ives, John A.; Jonas, Wayne B.

    2014-01-01

    Researchers are increasingly focused on the nanoscale level of organization where biological processes take place in living systems. Nanoparticles (NPs, e.g., 1–100 nm diameter) are small forms of natural or manufactured source material whose properties differ markedly from those of the respective bulk forms of the “same” material. Certain NPs have diagnostic and therapeutic uses; some NPs exhibit low-dose toxicity; other NPs show ability to stimulate low-dose adaptive responses (hormesis). Beyond dose, size, shape, and surface charge variations of NPs evoke nonlinear responses in complex adaptive systems. NPs acquire unique size-dependent biological, chemical, thermal, optical, electromagnetic, and atom-like quantum properties. Nanoparticles exhibit high surface adsorptive capacity for other substances, enhanced bioavailability, and ability to cross otherwise impermeable cell membranes including the blood-brain barrier. With super-potent effects, nano-forms can evoke cellular stress responses or therapeutic effects not only at lower doses than their bulk forms, but also for longer periods of time. Interactions of initial effects and compensatory systemic responses can alter the impact of NPs over time. Taken together, the data suggest the need to downshift the dose-response curve of NPs from that for bulk forms in order to identify the necessarily decreased no-observed-adverse-effect-level and hormetic dose range for nanoparticles. PMID:24910581

  16. Comparison of gradient and flux driven gyro-kinetic turbulent transport

    NASA Astrophysics Data System (ADS)

    Rath, F.; Peeters, A. G.; Buchholz, R.; Grosshauser, S. R.; Migliano, P.; Weikl, A.; Strintzi, D.

    2016-05-01

    Flux and gradient driven ion temperature gradient turbulence in tokamak geometry and for Cyclone base case parameters are compared in the local limit using the same underlying gyro-kinetic turbulence model. The gradient driven turbulence described using the flux tube model with periodic boundary conditions has a finite ion heat flux Qi≈10 n0T0ρ*2vth , where n0 (T0) is the background density (temperature), ρ*=ρ/R is the normalized Larmor radius, R is the major radius of the device, and vth is the ion thermal velocity at the nonlinear threshold of the temperature gradient length for turbulence generation. Consequently, the gradient driven local transport model is unable to accurately describe heat fluxes below Qi<10 n0T0ρ*2vt h , since no stationary fully developed turbulent state can be obtained. The turbulence in the flux driven case shows intermittent behaviour and avalanches for Qi<10 n0T0ρ*2vth . Isolated avalanches disappear for Qi>10 n0T0ρ*2vt h , and at higher heat fluxes, the statistics of the turbulence is the same for the flux and gradient driven case. The nonlinear upshift of the temperature gradient length threshold for turbulence generation (known as the Dimits shift) is larger in the case of flux driven turbulence. This higher nonlinear upshift is attributed to the generation of structures in the radial temperature profile, known as staircases [Dif-Pradalier, Phys. Rev. E 82, 025401 (2010)]. Avalanches are initiated at specific locations and have roughly the same radial extent of 50-70 ion Larmor radii. The staircases are obtained at low heating rates, and become unstable and break up at higher heating rates. At the heat fluxes for which staircase formation is observed, no stationary gradient driven simulations can be obtained.

  17. Multi-scale gyrokinetic simulation of tokamak plasmas: enhanced heat loss due to cross-scale coupling of plasma turbulence

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.

    2016-01-01

    The transport of heat in laboratory and astrophysical plasmas is dominated by the complex nonlinear dynamics of plasma turbulence. In magnetically confined plasmas used for fusion energy research, turbulence is responsible for cross-field transport that limits the performance of tokamak reactors. We report a set of novel gyrokinetic simulations that capture ion and electron-scale turbulence simultaneously, revealing the dynamics of cross-scale energy transfer and zonal flow modification that give rise to heat losses. Multi-scale simulations are required to match experimental ion and electron heat fluxes and electron profile stiffness, establishing the applicability of the newly discovered physics to experiment. Importantly, these results provide a likely explanation for the loss of electron heat from tokamak plasmas, the ‘great unsolved problem’ (Bachelor et al (2007 Plasma Sci. Technol. 9 312-87)) in plasma turbulence and the projected dominant loss channel in ITER.

  18. A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

    NASA Astrophysics Data System (ADS)

    Chen, Guangye; Chacón, Luis; CoCoMans Team

    2014-10-01

    For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

  19. Higher Harmonics In Vacuum From Nonlinear QED Effects without Low-Mass Intermediate Particles

    SciTech Connect

    Tito Mendonca, J.; Dias de Deus, J.; Castelo Ferreira, P.

    2006-09-08

    We show that in the presence of a slowly rotating strong transverse magnetic field there is an infinite spectrum of harmonic wave functions A{sub n} due to the first order QED correction (in {alpha}{sup 2}) given by the Euler-Heisenberg Lagrangian. The frequency shifts are integer multiples {+-}{omega}{sub 0}n of the magnetic field angular frequency rotation {omega}{sub 0}=2{pi}{nu}{sub m}, and the several modes n are coupled to the nearest harmonics n{+-}1. This is a new effect due to QED vacuum fluctuations, not exploited before, that can explain, both qualitatively and quantitatively, the recent experimental results of the PVLAS collaboration without the need of a low-mass intermediate particle, hence may dismiss the recent claim of the discovery of the axion.

  20. Nonlinear Evolution of Ion Acoustic Solitary Waves in Earth's Magnetosphere: Fluid and Particle-In-Cell Simulations

    NASA Astrophysics Data System (ADS)

    Kakad, A.; Kakad, B. A.; Omura, Y.

    2014-12-01

    In recent spacecraft observations, coherent electrostatic solitary wave (ESWs) structures are observed in various regions of the Earth's magnetosphere. Over the years, many researchers have attempted to model these observations in terms of electron/ion acoustic solitary waves by using nonlinear fluid theory/simulations. The ESW structures predicted by fluid models can be inadequate due to its inability in handling kinetic effects. To provide clear view on the application of the fluid and kinetic treatments in modeling the ESWs, we perform both fluid and particle-in-cell (PIC) simulations of ion acoustic solitary waves (IASWs) and estimate the quantitative differences in their characteristics like speed, amplitude, and width. It is noted that a long time evolution of Gaussian type perturbations in the equilibrium electron and ion densities generated the nonlinear IASW structures in both fluid and PIC simulations. The IASW structures represent vortices of trapped electrons in PIC simulations. We find that the number of trapped electrons in the wave potential is higher for the large amplitude IASW, which are generated by large-amplitude initial density perturbation (IDP). The present fluid and PIC simulation results are in close agreement for small amplitude IDPs, whereas for large IDPs they show discrepancy in the amplitude, width, and speed of the IASW, which is attributed to negligence of kinetic effects in the former approach. The speed of IASW in the fluid simulations increases with the increase of IASW amplitude, while the reverse tendency is seen in the PIC simulation. The present study suggests that the fluid treatment is appropriate to model the IASW observations when the magnitude of phase velocity of IASW is less than the ion acoustic (IA) speed obtained from their linear dispersion relation, whereas when it exceeds IA speed, it is necessary to include the kinetic effects in the model.

  1. Investigation of the effect of flow shear and the ITG on gyrokinetic MAST turbulence

    NASA Astrophysics Data System (ADS)

    van Wyk, Louis; Highcock, Edmund; Field, Anthony; Schekochihin, Alexander; Roach, Colin

    2015-11-01

    We study the effect of flow shear γE and ion temperature gradient a /LTi on L-mode turbulence in MAST using gyrokinetic simulations. These parameters play a crucial role in regulating and driving turbulence and together with the ratio of the safety factor to the inverse aspect ratio, q / ɛ , define a ``zero-turbulence manifold'' (ZTM) that represents the critical values needed to sustain turbulence. Nonlinear simulations show that by varying γE and a /LTi within experimental errors the turbulence crosses the ZTM, implying that the experiment operates close to marginality. In this parameter regime flow shear is very effective at regulating the turbulence, which is found to be subcritical. Finally the structure of the turbulence was studied: statistical parameters such as radial, perpendicular and parallel correlation lengths and the correlation time were calculated and found to be in reasonable agreement with experimental results obtained using Beam Emission Spectroscopy. Work supported by STFC and CCFE. Computing time provided by IFERC grant MULTEIM, The Hartree Centre, and EPSRC grants EP/ H002081/1 and EP/L000237/1.

  2. The anisotropic redistribution of free energy for gyrokinetic plasma turbulence in a Z-pinch

    NASA Astrophysics Data System (ADS)

    Navarro, Alejandro Bañón; Teaca, Bogdan; Jenko, Frank

    2016-04-01

    For a Z-pinch geometry, we report on the nonlinear redistribution of free energy across scales perpendicular to the magnetic guide field, for a turbulent plasma described in the framework of gyrokinetics. The analysis is performed using a local flux-surface approximation, in a regime dominated by electrostatic fluctuations driven by the entropy mode, with both ion and electron species being treated kinetically. To explore the anisotropic nature of the free energy redistribution caused by the emergence of zonal flows, we use a polar coordinate representation for the field-perpendicular directions and define an angular density for the scale flux. Positive values for the classically defined (angle integrated) scale flux, which denote a direct energy cascade, are shown to be also composed of negative angular sections, a fact that impacts our understanding of the backscatter of energy and the way in which it enters the modeling of sub-grid scales for turbulence. A definition for the flux of free energy across each perpendicular direction is introduced as well, which shows that the redistribution of energy in the presence of zonal flows is highly anisotropic.

  3. A study of self organized criticality in ion temperature gradient mode driven gyrokinetic turbulence

    SciTech Connect

    Mavridis, M.; Isliker, H.; Vlahos, L.; Görler, T.; Jenko, F.; Told, D.

    2014-10-15

    An investigation on the characteristics of self organized criticality (Soc) in ITG mode driven turbulence is made, with the use of various statistical tools (histograms, power spectra, Hurst exponents estimated with the rescaled range analysis, and the structure function method). For this purpose, local non-linear gyrokinetic simulations of the cyclone base case scenario are performed with the GENE software package. Although most authors concentrate on global simulations, which seem to be a better choice for such an investigation, we use local simulations in an attempt to study the locally underlying mechanisms of Soc. We also study the structural properties of radially extended structures, with several tools (fractal dimension estimate, cluster analysis, and two dimensional autocorrelation function), in order to explore whether they can be characterized as avalanches. We find that, for large enough driving temperature gradients, the local simulations exhibit most of the features of Soc, with the exception of the probability distribution of observables, which show a tail, yet they are not of power-law form. The radial structures have the same radial extent at all temperature gradients examined; radial motion (transport) though appears only at large temperature gradients, in which case the radial structures can be interpreted as avalanches.

  4. Global gyrokinetic simulations of the H-mode tokamak edge pedestal

    SciTech Connect

    Wan, Weigang; Parker, Scott E.; Chen, Yang; Groebner, Richard J.; Yan, Zheng; Pankin, Alexei Y.; Kruger, Scott E.

    2013-05-15

    Global gyrokinetic simulations of DIII-D H-mode edge pedestal show two types of instabilities may exist approaching the onset of edge localized modes: an intermediate-n, high frequency mode which we identify as the “kinetic peeling ballooning mode (KPBM),” and a high-n, low frequency mode. Our previous study [W. Wan et al., Phys. Rev. Lett. 109, 185004 (2012)] has shown that when the safety factor profile is flattened around the steep pressure gradient region, the high-n mode is clearly kinetic ballooning mode and becomes the dominant instability. Otherwise, the KPBM dominates. Here, the properties of the two instabilities are studied by varying the density and temperature profiles. It is found that the KPBM is destabilized by density and ion temperature gradient, and the high-n mode is mostly destabilized by electron temperature gradient. Nonlinear simulations with the KPBM saturate at high levels. The equilibrium radial electric field (E{sub r}) reduces the transport. The effect of the parallel equilibrium current is found to be weak.

  5. Comparisons between global and local gyrokinetic simulations of an ASDEX Upgrade H-mode plasma

    NASA Astrophysics Data System (ADS)

    Navarro, Alejandro Bañón; Told, Daniel; Jenko, Frank; Görler, Tobias; Happel, Tim

    2016-04-01

    We investigate by means of local and global nonlinear gyrokinetic GENE simulations an ASDEX Upgrade H-mode plasma. We find that for the outer core positions (i.e., ρ tor ≈ 0.5 - 0.7 ), nonlocal effects are important. For nominal input parameters local simulations over-predict the experimental heat fluxes by a large factor, while a good agreement is found with global simulations. This was a priori not expected, since the values of 1 / ρ ⋆ were large enough that global and local simulations should have been in accordance. Nevertheless, due to the high sensitivity of the heat fluxes with respect to the input parameters, it is still possible to match the heat fluxes in local simulations with the experimental and global results by varying the ion temperature gradient within the experimental uncertainties. In addition to that, once an agreement in the transport quantities between local (flux-matched) and global simulations is achieved, an agreement for other quantities, such as density and temperature fluctuations, is also found. The case presented here clearly shows that even in the presence of global size-effects, the local simulation approach is still a valid and accurate approach.

  6. Gyrokinetic theory and simulation of angular momentum transport

    SciTech Connect

    Waltz, R. E.; Staebler, G. M.; Candy, J.; Hinton, F. L.

    2007-12-15

    A gyrokinetic theory of turbulent toroidal angular momentum transport as well as modifications to neoclassical poloidal rotation from turbulence is formulated starting from the fundamental six-dimensional kinetic equation. The gyro-Bohm scaled transport is evaluated from toroidal delta-f gyrokinetic simulations using the GYRO code [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. The simulations recover two pinch mechanisms in the radial transport of toroidal angular momentum: The slab geometry ExB shear pinch [Dominguez and Staebler, Phys. Fluids B 5, 387 (1993)] and the toroidal geometry 'Coriolis' pinch [Peeters, Angioni, and Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. The pinches allow the steady state null stress (or angular momentum transport flow) condition required to understand intrinsic (or spontaneous) toroidal rotation in heated tokamak without an internal source of torque [Staebler, Kinsey, and Waltz, Bull. Am. Phys. Soc. 46, 221 (2001)]. A predicted turbulent shift in the neoclassical poloidal rotation [Staebler, Phys. Plasmas 11, 1064 (2004)] appears to be small at the finite relative gyroradius (rho-star) of current experiments.

  7. Gyrokinetic Simulation of Residual Stress from Diamagnetic Velocity Shears

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Staebler, G. M.; Solomon, W. M.

    2010-11-01

    Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the parallel velocity (and parallel velocity itself) vanishes. Previously [1] we demonstrated with gyrokinetic (GYRO) simulations that TAM pinching from the diamagnetic level shear in the ExB velocity could provide the residual stress needed for spontaneous toroidal rotation. Here we show that the shear in the diamagnetic velocities themselves provide comparable residual stress (and level of stabilization). The sign of the residual stress, quantified by the ratio of TAM flow to ion power flow (M/P), depends on the signs of the various velocity shears as well as ion (ITG) versus electron (TEM) mode directed turbulence. The residual stress from these temperature and density gradient diamagnetic velocity shears is demonstrated in global gyrokinetic simulation of ``null'' rotation DIIID discharges by matching M/P profiles within experimental error. 8pt [1] R.E. Waltz, G.M. Staebler, J. Candy, and F.L. Hinton, Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009).

  8. Linear multispecies gyrokinetic flux tube benchmarks in shaped tokamak plasmas

    NASA Astrophysics Data System (ADS)

    Merlo, G.; Sauter, O.; Brunner, S.; Burckel, A.; Camenen, Y.; Casson, F. J.; Dorland, W.; Fable, E.; Görler, T.; Jenko, F.; Peeters, A. G.; Told, D.; Villard, L.

    2016-03-01

    Verification is the fundamental step that any turbulence simulation code has to be submitted in order to assess the proper implementation of the underlying equations. We have carried out a cross comparison of three flux tube gyrokinetic codes, GENE [F. Jenko et al., Phys. Plasmas 7, 1904 (2000)], GKW [A. G. Peeters et al., Comput. Phys. Commun. 180, 2650 (2009)], and GS2 [W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)], focusing our attention on the effect of realistic geometries described by a series of MHD equilibria with increasing shaping complexity. To simplify the effort, the benchmark has been limited to the electrostatic collisionless linear behaviour of the system. A fully gyrokinetic model has been used to describe the dynamics of both ions and electrons. Several tests have been carried out looking at linear stability at ion and electron scales, where for the assumed profiles Ion Temperature Gradient (ITG)/Trapped Electron Modes and Electron Temperature Gradient modes are unstable. The capability of the codes to handle a non-zero ballooning angle has been successfully benchmarked in the ITG regime. Finally, the standard Rosenbluth-Hinton test has been successfully carried out looking at the effect of shaping on Zonal Flows (ZFs) and Geodesic Acoustic Modes (GAMs). Inter-code comparison as well as validation of simulation results against analytical estimates has been accomplished. All the performed tests confirm that plasma elongation strongly stabilizes plasma instabilities as well as leads to a strong increase in ZF residual and GAM damping.

  9. Understanding the nonlinear dynamics of driven particles in supercooled liquids in terms of an effective temperature

    SciTech Connect

    Schroer, Carsten F. E.; Heuer, Andreas

    2015-12-14

    In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.

  10. Understanding the nonlinear dynamics of driven particles in supercooled liquids in terms of an effective temperature

    NASA Astrophysics Data System (ADS)

    Schroer, Carsten F. E.; Heuer, Andreas

    2015-12-01

    In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.

  11. Full-f gyrokinetic simulations for neoclassical toroidal viscosity in a perturbed tokamak configuration

    NASA Astrophysics Data System (ADS)

    Matsuoka, Seikichi; Idomura, Yasuhiro; Satake, Shinsuke

    2014-10-01

    A magnetic field perturbation in tokamak plasmas plays a key role in determining the intrinsic rotation and velocity shear, since even a small perturbation can break the axisymmetry in the toroidal direction and induces the finite neoclassical toroidal viscosity (NTV). A simulation study for the NTV evaluation in an axisymmetric tokamak with a small resonant magnetic field perturbation using the full-f gyrokinetic Eulerian code GT5D is presented. The magnetic field perturbation is included in the particle orbit of GT5D only through the Hamiltonian by replacing the axisymmetric magnetic field with the sum of the axisymmetric field and the perturbation, which enables us to perform GT5D simulations without changing the symplectic structure of the single-particle Lagrangian constructed for the equilibrium (axisymmetric) magnetic field. Numerical results are benchmarked with those obtained by the neoclassical transport code, FORTEC-3D, which solves the drift kinetic equation by two-weight δf Monte Carlo method. The NTV of GT5D with a single-helicity perturbation is found to have a similar peaked profile around the resonant surface as that of FORTEC-3D.

  12. A gyro-kinetic model for trapped electron and ion modes

    NASA Astrophysics Data System (ADS)

    Drouot, Thomas; Gravier, Etienne; Reveille, Thierry; Ghizzo, Alain; Bertrand, Pierre; Garbet, Xavier; Sarazin, Yanick; Cartier-Michaud, Thomas

    2014-10-01

    In tokamak plasmas, it is recognized that ITG (ion temperature gradient instability) and trapped electron modes (TEM) are held responsible for turbulence giving rise to anomalous transport. The present work focuses on the building of a model including trapped kinetic ions and trapped kinetic electrons. For this purpose, the dimensionality is reduced by averaging the motion over the cyclotron motion and the "banana" orbits, according to the fact that the instabilities are characterized by frequencies of the order of the low trapped particle precession frequency. Moreover, a set of action-angle variables is used. The final model is 4D (two-dimensional phase space parametrized by the two first adiabatic invariants namely the particle energy and the trapping parameter). In this paper, the trapped ion and electron modes (TIM and TEM) are studied by using a linear analysis of the model. This work is currently performed in order to include trapped electrons in an existing semi lagrangian code for which TIM modes are already taken into account. This study can be considered as a first step in order to include kinetic trapped electrons in the 5D gyrokinetic code GYSELA [J. Abiteboul et al., ESAIM Proc. 32, 103 (2011)]. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

  13. Search for the Missing L-mode Edge Transport and Possible Breakdown of Gyrokinetics

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.

    2012-10-01

    While GYRO simulations of typical core (0 < r/a < 0.7) DIII-D L-modes seems to be in good agreement with experiment, simulated low-k (kθρs< 1) transport and turbulence intensity is more than 5-fold lower than experimentally inferred levels in the near edge L-mode (r/a=0.7-0.95) DIII-D shot 128913 [1]. Global edge slice GYRO simulations of this and the well-studied discharge 101391 [2] are presented here to document the shortfall. TGLF transport code simulations over a large L-mode database indicate this short fall is not atypical so that L-mode edges transit to H-like pedestal profiles contrary to experiment. High edge e-i collisionality stabilizes the TEM modes so that diffusivities (χ) decrease like T^7/2/n to the cold edge. The very high magnetic shear and density gradients stabilize the ITG despite the very high temperature gradient drive and high q. High-k ETG can make-up for the shortfall in the electron but increases ion transport very little. Near L-edge transport is highly local. Focusing on local simulations at r/a=0.9, the ion channel short fall can exceed 10-fold. An artificial 10-fold increase in collisionality is needed to reach the expected resistive g-mode scaling with χ increasing like nT-1/2. Identical GYRO drift kinetic ion simulations (suppressing the gyroaverage) are close to experiment levels suggesting a possible breakdown of low-frequency gyrokinetics. Formulation of a nonlinear theory of 6D drift-cyclotron kinetics following the fast time scale of the gyrophase to test the breakdown of 5D gyrokinetics with reduced model simulations is presented. 6pt [1] C. Holland, A.E. White, et al., Phys. Plasmas 16, 052301 (2009). [2] R.E. Waltz, J. Candy, C.C. Petty, Phys. Plasmas 13, 072304 (2006).

  14. Linear and nonlinear wave-particle interactions. Ph.D. Thesis

    SciTech Connect

    Ho, A.Y.

    1994-12-31

    In part 1, a quasi-particle approach is adopted to examine the effect of ionospheric irregularities on the propagation of beacon satellite signals through the ionosphere. The experimental data corresponding to the Bottomside Sinusoidal (BSS) irregularity is used to validate the approach. Good agreement in the scintillation index S4 is found. It is demonstrated that a traveling BSS irregularity can indeed cause a scintillation in the transionospheric signal in agreement with the experimental measurements. The theory is then used to make a prediction for future experimental observations. In part 2, the authors show that when an energetic proton originally trapped by the geomagnetic mirror field near the equator interacts with a Kinetic Alfven Wave (KAW), its trajectory may become chaotic. As a result of this chaotic motion, the proton will escape from its confines and either precipitate into the polar region or drift downward into the lower altitude region. A cyclotron average is first used to reduce the number of degrees of freedom of the system from 2.5 to 1.5 so that the chaoticity of the system can be revealed by Poincare surface of section method. Next, a Lyapunov exponent analysis for limited cases of initial conditions provides a quantitative measure of chaos. In the chaotic region, the longitudinal motion of the proton is shown to involve irregular oscillation in excursion amplitude leading to proton diffusion into the loss cone. The proton also drifts radially via a nonzero average E x B drift velocity acquired in the interaction with the wave. In part 3, an experiment is performed to study the electromagnetic wave absorption and scattering properties of the structured and lossy plasma for use in a radar cloaking device. Measurements of microwave attenuation and scattering by a hollow cathode produced plasma column show greater than 20 dB attenuation in transmission for wave frequency range of 3.5 to 11 GHz.

  15. Tsunami Simulator Integrating the Smoothed-Particle Hydrodynamics Method and the Nonlinear Shallow Water Wave Model with High Performance Computer

    NASA Astrophysics Data System (ADS)

    Suwa, T.; Imamura, F.; Sugawara, D.; Ogasawara, K.; Watanabe, M.; Hirahara, T.

    2014-12-01

    A tsunami simulator integrating a 3-D fluid simulation technology that runs on large-scale parallel computers using smoothed-particle hydrodynamics (SPH) method has been developed together with a 2-D tsunami propagation simulation technique using a nonlinear shallow water wave model. We use the 2-D simulation to calculate tsunami propagation of scale of about 1000km from epicenter to near shore. The 3-D SPH method can be used to calculate the water surface and hydraulic force that a tsunami can exert on a building, and to simulate flooding patterns at urban area of at most km scale. With our simulator we can also see three dimensional fluid feature such as complex changes a tsunami undergoes as it interacts with coastal topography or structures. As a result it is hoped that, e.g. , effect of the structures to dissipate waves energy passing over it can be elucidated. The authors utilize the simulator in the third of five fields of the Strategic Programs for Innovative Research, "Advanced Prediction Researches for Natural Disaster Prevention and Reduction," or the theme "Improvement of the tsunami forecasting system on the HPCI computer." The results of tsunami simulation using the K computer will be reported. We are going to apply it to a real problem of the disaster prevention in future.

  16. Investigation of tearing instability using GeFi particle simulation model

    NASA Astrophysics Data System (ADS)

    Wang, X. Y.; Lin, Y.; Chen, L.; Lu, X.; Kong, W.

    2011-12-01

    The gyrokinetic (GK) electron and fully kinetic ion (GeFi) simulation model of Lin et al. [Plasmas Phys. Controlled Fusion 53, 054013 (2011)] has been thoroughly benchmarked and validated for a two-dimensional (2D) Harris current sheet with a finite guide field. First, a gyrokinetic eigenmode theory for the collisionless tearing mode in the small Larmor radius limit is presented. The linear eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are benchmarked against those from the GK eigenmode analysis in the limit of L ≫ρi>ρe, where L is the current sheet half-width, ρi is ion Larmor radius, and ρe is electron Larmor radius. Second, to valid the GeFi model, both the linear and nonlinear tearing instabilities obtained from the GeFi simulations are compared with the Darwin particle-in-cell (PIC) simulation. The validation of the GeFi model for laboratory and space plasmas is also discussed. Meanwhile, the GeFi simulation is carried out to investigate both the linear and nonlinear tearing instabilities for cases with a broad range of L and guide magnetic field BG. It is found that in a wide current sheet with L > 4.5ρeK, the nonlinear saturation level of the island half-width is ws ≃ 3ρeK, where ρeK = ρeB0/Bx0, B0 is the strength of the asymptotic magnetic field, and Bx0 is the antiparallel field. On the other hand, in a thin current sheet with L < 2.5ρeK, ws ≃ 2.2 L. In addition, a high frequency electrostatic drift mode is found to coexist with the tearing mode.

  17. Development of PUNDA (Parametric Universal Nonlinear Dynamics Approximator) Models for Self-Validating Knowledge-Guided Modelling of Nonlinear Processes in Particle Accelerators \\& Industry

    SciTech Connect

    Sayyar-Rodsari, Bijan; Schweiger, Carl; Hartman, Eric

    2007-10-07

    The difficult problems being tackled in the accelerator community are those that are nonlinear, substantially unmodeled, and vary over time. Such problems are ideal candidates for model-based optimization and control if representative models of the problem can be developed that capture the necessary mathematical relations and remain valid throughout the operation region of the system, and through variations in system dynamics. The goal of this proposal is to develop the methodology and the algorithms for building high-fidelity mathematical representations of complex nonlinear systems via constrained training of combined first-principles and neural network models.

  18. Final Technical Report: Global Field Aligned Mesh and Gyrokinetic Field Solver in a Tokamak Edge Geometry

    SciTech Connect

    Cummings, Julian C.

    2013-05-15

    This project was a collaboration between researchers at the California Institute of Technology and the University of California, Irvine to investigate the utility of a global field-aligned mesh and gyrokinetic field solver for simulations of the tokamak plasma edge region. Mesh generation software from UC Irvine was tested with specific tokamak edge magnetic geometry scenarios and the quality of the meshes and the solutions to the gyrokinetic Poisson equation were evaluated.

  19. Electron heat transport from stochastic fields in gyrokinetic simulationsa)

    NASA Astrophysics Data System (ADS)

    Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.

    2011-05-01

    GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as βe is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of βe. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, dm [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.

  20. Electron heat transport from stochastic fields in gyrokinetic simulations

    SciTech Connect

    Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.

    2011-05-15

    GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as {beta}{sub e} is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of {beta}{sub e}. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, d{sub m}[A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.

  1. Gyrokinetic studies of microinstabilities in the reversed field pinch

    SciTech Connect

    Carmody, D.; Pueschel, M. J.; Terry, P. W.

    2013-05-15

    An analytic equilibrium, the Toroidal Bessel Function Model, is used in conjunction with the gyrokinetic code GYRO to investigate the nature of microinstabilities in a reversed field pinch plasma. The effect of the normalized electron plasma pressure β on the characteristics of the microinstabilities is studied. At a β of 4.5%, a transition between an ion temperature gradient (ITG) and a microtearing mode is observed. Suppression of the ITG mode occurs as in the tokamak, through coupling to shear Alfvén waves, with a critical β for stability higher than its tokamak equivalent due to a shorter parallel connection length. A steep dependence of the microtearing growth rate on the temperature gradient suggests high profile stiffness. There is evidence for a collisionless microtearing mode. The properties of this mode are investigated, and it is found that electron curvature drift plays an important role in the instability.

  2. Gyrokinetic modeling: A multi-water-bag approach

    SciTech Connect

    Morel, P.; Gravier, E.; Besse, N.; Klein, R.; Ghizzo, A.; Bertrand, P.; Garbet, X.; Ghendrih, P.; Grandgirard, V.; Sarazin, Y.

    2007-11-15

    Predicting turbulent transport in nearly collisionless fusion plasmas requires one to solve kinetic (or, more precisely, gyrokinetic) equations. In spite of considerable progress, several pending issues remain; although more accurate, the kinetic calculation of turbulent transport is much more demanding in computer resources than fluid simulations. An alternative approach is based on a water-bag representation of the distribution function that is not an approximation but rather a special class of initial conditions, allowing one to reduce the full kinetic Vlasov equation into a set of hydrodynamic equations while keeping its kinetic character. The main result for the water-bag model is a lower cost in the parallel velocity direction since no differential operator associated with some approximate numerical scheme has to be carried out on this variable v{sub parallel}. Indeed, a small bag number is sufficient to correctly describe the ion temperature gradient instability.

  3. Three-dimensional gyrokinetic simulation of the relaxation of a magnetized temperature filament

    SciTech Connect

    Sydora, R. D.; Morales, G. J.; Maggs, J. E.; Van Compernolle, B.

    2015-10-15

    An electromagnetic, 3D gyrokinetic particle code is used to study the relaxation of a magnetized electron temperature filament embedded in a large, uniform plasma of lower temperature. The study provides insight into the role played by unstable drift-Alfvén waves observed in a basic electron heat transport experiment [D. C. Pace et al., Phys. Plasmas 15, 122304 (2008)] in which anomalous cross-field transport has been documented. The simulation exhibits the early growth of temperature-gradient-driven, drift-Alfvén fluctuations that closely match the eigenmodes predicted by linear theory. At the onset of saturation, the unstable fluctuations display a spiral spatial pattern, similar to that observed in the laboratory, which causes the rearrangement of the temperature profile. After saturation of the linear instability, the system exhibits a markedly different behavior depending on the inclusion in the computation of modes without variation along the magnetic field, i.e., k{sub z} = 0. In their absence, the initial filament evolves into a broadened temperature profile, self-consistent with undamped, finite amplitude drift-Alfvén waves. But the inclusion of k{sub z} = 0 modes causes the destruction of the filament and damping of the drift-Alfvén modes leading to a final state consisting of undamped convective cells and multiple, smaller-scale filaments.

  4. 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).

  5. Laser-based measurements of magnetic fluctuation-induced particle transport and nonlinear mode interactions in the Madison Symmetric Torus reversed-field pinch

    NASA Astrophysics Data System (ADS)

    Yates, Travis Fred

    Magnetic fluctuation-induced particle transport and density fluctuations have been investigated in the Madison Symmetric Torus (MST) reversed-filed pinch using a far infrared (FIR) laser based interferometer-polarimetry system. An extensive study focuses on the particle transport and density fluctuations during the sawtooth crash where the stochastic magnetic field is largest. Particle flux arising from the inieraction between density fluctuations and magnetic fluctuations has been measured to be significant at the reversal surface where modes with poloidal mode number m = 0 are resonant. The particle flux is comparable to that measured in the core where m = 1 modes dominate. The origin of density fluctuations has been studied experimentally. It is found that density fluctuations not only result from linear advection but also non-linear three-wave interactions. This is different from the previously reported results that indicated that the edge density fluctuations originate from linear advection. The results reported here reveal that m = 0 modes play an important role in density fluctuations and particle flux. An experiment where m = 0 modes are greatly reduced, by removing the reversal surface from the plasma, indicates that particle flux and density fluctuations are reduced significantly, which further confirms the importance of edge resonant modes in particle transport.

  6. Simulation of linear and nonlinear Landau damping of lower hybrid waves

    NASA Astrophysics Data System (ADS)

    Qi, Lei; Wang, X. Y.; Lin, Y.

    2013-06-01

    The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k∥/k ,Ti/Te, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear damping rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.

  7. Gyrokinetic Stability Studies of the Microtearing Mode in the National Spherical Torus Experiment H-mode

    SciTech Connect

    Baumgaertel, J. A.; Redi, M. H.; Budny, R. V.; Rewoldt, G.; Dorland, W.

    2005-10-19

    Insight into plasma microturbulence and transport is being sought using linear simulations of drift waves on the National Spherical Torus Experiment (NSTX), following a study of drift wave modes on the Alcator C-Mod Tokamak. Microturbulence is likely generated by instabilities of drift waves, which cause transport of heat and particles. Understanding this transport is important because the containment of heat and particles is required for the achievement of practical nuclear fusion. Microtearing modes may cause high heat transport through high electron thermal conductivity. It is hoped that microtearing will be stable along with good electron transport in the proposed low collisionality International Thermonuclear Experimental Reactor (ITER). Stability of the microtearing mode is investigated for conditions at mid-radius in a high density NSTX high performance (H-mode) plasma, which is compared to the proposed ITER plasmas. The microtearing mode is driven by the electron temperature gradient, and believed to be mediated by ion collisions and magnetic shear. Calculations are based on input files produced by TRXPL following TRANSP (a time-dependent transport analysis code) analysis. The variability of unstable mode growth rates is examined as a function of ion and electron collisionalities using the parallel gyrokinetic computational code GS2. Results show the microtearing mode stability dependence for a range of plasma collisionalities. Computation verifies analytic predictions that higher collisionalities than in the NSTX experiment increase microtearing instability growth rates, but that the modes are stabilized at the highest values. There is a transition of the dominant mode in the collisionality scan to ion temperature gradient character at both high and low collisionalities. The calculations suggest that plasma electron thermal confinement may be greatly improved in the low-collisionality ITER.

  8. Non-linear, non-monotonic effect of nano-scale roughness on particle deposition in absence of an energy barrier: Experiments and modeling

    PubMed Central

    Jin, Chao; Glawdel, Tomasz; Ren, Carolyn L.; Emelko, Monica B.

    2015-01-01

    Deposition of colloidal- and nano-scale particles on surfaces is critical to numerous natural and engineered environmental, health, and industrial applications ranging from drinking water treatment to semi-conductor manufacturing. Nano-scale surface roughness-induced hydrodynamic impacts on particle deposition were evaluated in the absence of an energy barrier to deposition in a parallel plate system. A non-linear, non-monotonic relationship between deposition surface roughness and particle deposition flux was observed and a critical roughness size associated with minimum deposition flux or “sag effect” was identified. This effect was more significant for nanoparticles (<1 μm) than for colloids and was numerically simulated using a Convective-Diffusion model and experimentally validated. Inclusion of flow field and hydrodynamic retardation effects explained particle deposition profiles better than when only the Derjaguin-Landau-Verwey-Overbeek (DLVO) force was considered. This work provides 1) a first comprehensive framework for describing the hydrodynamic impacts of nano-scale surface roughness on particle deposition by unifying hydrodynamic forces (using the most current approaches for describing flow field profiles and hydrodynamic retardation effects) with appropriately modified expressions for DLVO interaction energies, and gravity forces in one model and 2) a foundation for further describing the impacts of more complicated scales of deposition surface roughness on particle deposition. PMID:26658159

  9. Non-linear, non-monotonic effect of nano-scale roughness on particle deposition in absence of an energy barrier: Experiments and modeling

    NASA Astrophysics Data System (ADS)

    Jin, Chao; Glawdel, Tomasz; Ren, Carolyn L.; Emelko, Monica B.

    2015-12-01

    Deposition of colloidal- and nano-scale particles on surfaces is critical to numerous natural and engineered environmental, health, and industrial applications ranging from drinking water treatment to semi-conductor manufacturing. Nano-scale surface roughness-induced hydrodynamic impacts on particle deposition were evaluated in the absence of an energy barrier to deposition in a parallel plate system. A non-linear, non-monotonic relationship between deposition surface roughness and particle deposition flux was observed and a critical roughness size associated with minimum deposition flux or “sag effect” was identified. This effect was more significant for nanoparticles (<1 μm) than for colloids and was numerically simulated using a Convective-Diffusion model and experimentally validated. Inclusion of flow field and hydrodynamic retardation effects explained particle deposition profiles better than when only the Derjaguin-Landau-Verwey-Overbeek (DLVO) force was considered. This work provides 1) a first comprehensive framework for describing the hydrodynamic impacts of nano-scale surface roughness on particle deposition by unifying hydrodynamic forces (using the most current approaches for describing flow field profiles and hydrodynamic retardation effects) with appropriately modified expressions for DLVO interaction energies, and gravity forces in one model and 2) a foundation for further describing the impacts of more complicated scales of deposition surface roughness on particle deposition.

  10. Automated classification of single airborne particles from two-dimensional angle-resolved optical scattering (TAOS) patterns by non-linear filtering

    NASA Astrophysics Data System (ADS)

    Crosta, Giovanni Franco; Pan, Yong-Le; Aptowicz, Kevin B.; Casati, Caterina; Pinnick, Ronald G.; Chang, Richard K.; Videen, Gorden W.

    2013-12-01

    Measurement of two-dimensional angle-resolved optical scattering (TAOS) patterns is an attractive technique for detecting and characterizing micron-sized airborne particles. In general, the interpretation of these patterns and the retrieval of the particle refractive index, shape or size alone, are difficult problems. By reformulating the problem in statistical learning terms, a solution is proposed herewith: rather than identifying airborne particles from their scattering patterns, TAOS patterns themselves are classified through a learning machine, where feature extraction interacts with multivariate statistical analysis. Feature extraction relies on spectrum enhancement, which includes the discrete cosine FOURIER transform and non-linear operations. Multivariate statistical analysis includes computation of the principal components and supervised training, based on the maximization of a suitable figure of merit. All algorithms have been combined together to analyze TAOS patterns, organize feature vectors, design classification experiments, carry out supervised training, assign unknown patterns to classes, and fuse information from different training and recognition experiments. The algorithms have been tested on a data set with more than 3000 TAOS patterns. The parameters that control the algorithms at different stages have been allowed to vary within suitable bounds and are optimized to some extent. Classification has been targeted at discriminating aerosolized Bacillus subtilis particles, a simulant of anthrax, from atmospheric aerosol particles and interfering particles, like diesel soot. By assuming that all training and recognition patterns come from the respective reference materials only, the most satisfactory classification result corresponds to 20% false negatives from B. subtilis particles and <11% false positives from all other aerosol particles. The most effective operations have consisted of thresholding TAOS patterns in order to reject defective ones

  11. Multiplex protein pattern unmixing using a non-linear variable-weighted support vector machine as optimized by a particle swarm optimization algorithm.

    PubMed

    Yang, Qin; Zou, Hong-Yan; Zhang, Yan; Tang, Li-Juan; Shen, Guo-Li; Jiang, Jian-Hui; Yu, Ru-Qin

    2016-01-15

    Most of the proteins locate more than one organelle in a cell. Unmixing the localization patterns of proteins is critical for understanding the protein functions and other vital cellular processes. Herein, non-linear machine learning technique is proposed for the first time upon protein pattern unmixing. Variable-weighted support vector machine (VW-SVM) is a demonstrated robust modeling technique with flexible and rational variable selection. As optimized by a global stochastic optimization technique, particle swarm optimization (PSO) algorithm, it makes VW-SVM to be an adaptive parameter-free method for automated unmixing of protein subcellular patterns. Results obtained by pattern unmixing of a set of fluorescence microscope images of cells indicate VW-SVM as optimized by PSO is able to extract useful pattern features by optimally rescaling each variable for non-linear SVM modeling, consequently leading to improved performances in multiplex protein pattern unmixing compared with conventional SVM and other exiting pattern unmixing methods. PMID:26592652

  12. ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS

    SciTech Connect

    WALTZ RE; CANDY J; HINTON FL; ESTRADA-MILA C; KINSEY JE

    2004-10-01

    A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or a globally with physical profile variation. Rohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, plasma pinches and impurity flow, and simulations at fixed flow rather than fixed gradient are illustrated and discussed.

  13. ADVANCES IN COMPREHENSIVE GYROKINETIC SIMULATIONS OF TRANSPORT IN TOKAMAKS

    SciTech Connect

    WALTZ,R.E; CANDY,J; HINTON,F.L; ESTRADA-MILA,C; KINSEY,J.E

    2004-10-01

    A continuum global gyrokinetic code GYRO has been developed to comprehensively simulate core turbulent transport in actual experimental profiles and enable direct quantitative comparisons to the experimental transport flows. GYRO not only treats the now standard ion temperature gradient (ITG) mode turbulence, but also treats trapped and passing electrons with collisions and finite {beta}, equilibrium ExB shear stabilization, and all in real tokamak geometry. Most importantly the code operates at finite relative gyroradius ({rho}{sub *}) so as to treat the profile shear stabilization and nonlocal effects which can break gyroBohm scaling. The code operates in either a cyclic flux-tube limit (which allows only gyroBohm scaling) or globally with physical profile variation. Bohm scaling of DIII-D L-mode has been simulated with power flows matching experiment within error bars on the ion temperature gradient. Mechanisms for broken gyroBohm scaling, neoclassical ion flows embedded in turbulence, turbulent dynamos and profile corrugations, are illustrated.

  14. Gyrokinetic simulation of driftwave instability in field-reversed configuration

    NASA Astrophysics Data System (ADS)

    Fulton, D. P.; Lau, C. K.; Schmitz, L.; Holod, I.; Lin, Z.; Tajima, T.; Binderbauer, M. W.

    2016-05-01

    Following the recent remarkable progress in magnetohydrodynamic (MHD) stability control in the C-2U advanced beam driven field-reversed configuration (FRC), turbulent transport has become one of the foremost obstacles on the path towards an FRC-based fusion reactor. Significant effort has been made to expand kinetic simulation capabilities in FRC magnetic geometry. The recently upgraded Gyrokinetic Toroidal Code (GTC) now accommodates realistic magnetic geometry from the C-2U experiment at Tri Alpha Energy, Inc. and is optimized to efficiently handle the FRC's magnetic field line orientation. Initial electrostatic GTC simulations find that ion-scale instabilities are linearly stable in the FRC core for realistic pressure gradient drives. Estimated instability thresholds from linear GTC simulations are qualitatively consistent with critical gradients determined from experimental Doppler backscattering fluctuation data, which also find ion scale modes to be depressed in the FRC core. Beyond GTC, A New Code (ANC) has been developed to accurately resolve the magnetic field separatrix and address the interaction between the core and scrape-off layer regions, which ultimately determines global plasma confinement in the FRC. The current status of ANC and future development targets are discussed.

  15. Web Interface Connecting Gyrokinetic Turbulence Simulations with Tokamak Fusion Data

    NASA Astrophysics Data System (ADS)

    Suarez, A.; Ernst, D. R.

    2005-10-01

    We are developing a comprehensive interface to connect plasma microturbulence simulation codes with experimental data in the U.S. and abroad. This website automates the preparation and launch of gyrokinetic simulations utilizing plasma profile and magnetic equilibrium data. The functionality of existing standalone interfaces, such as GS2/PREP [D. R. Ernst et al., Phys. Plasmas 11(5) 2637 (2004)], in use for several years for the GS2 code [W. Dorland et al., Phys. Rev. Lett. 85(26) 5579 (2000)], will be extended to other codes, including GYRO [J. Candy / R.E. Waltz, J. Comput. Phys.186, (2003) 545]. Data is read from mdsplus and TRANSP [\\underline {http://w3.pppl.gov/transp}] and can be viewed using a java plotter, Webgraph, developed for this project by previous students Geoffrey Catto and Bo Feng. User sessions are tracked and saved to allow users to access their previous simulations, which can be used as templates for future work.

  16. Full-f gyrokinetic simulation over a confinement time

    SciTech Connect

    Idomura, Yasuhiro

    2014-02-15

    A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the radial electric field shear but also on the radial electric field itself. Based on the toroidal angular momentum conservation, it is found that in the steady null momentum transport state, the turbulent residual stress is cancelled by the neoclassical counterpart, which is greatly enhanced in the presence of turbulent fluctuations.

  17. 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.

  18. 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.

  19. Gyrokinetic simulation of momentum transport with residual stress from diamagnetic level velocity shears

    SciTech Connect

    Waltz, R. E.; Staebler, G. M.; Solomon, W. M.

    2011-04-15

    Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium ExB velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or ''profile shear'' in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) ExB and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a ''null'' toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the ExB shear and parallel velocity (Coriolis force) pinching components from the larger ''diffusive'' parallel velocity shear driven component and

  20. An efficient mixed-precision, hybrid CPU-GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm

    SciTech Connect

    Chen, Guangye; Chacon, Luis; Barnes, Daniel C

    2012-01-01

    Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been developed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230, 18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver and is capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle orbit integrations from the field solver, while remaining fully self-consistent. This provides great flexibility, and dramatically improves the solver efficiency by reducing the degrees of freedom of the associated nonlinear system. However, it requires a particle push per nonlinear residual evaluation, which makes the particle push the most time-consuming operation in the algorithm. This paper describes a very efficient mixed-precision, hybrid CPU-GPU implementation of the implicit PIC algorithm. The JFNK solver is kept on the CPU (in double precision), while the inherent data parallelism of the particle mover is exploited by implementing it in single-precision on a graphics processing unit (GPU) using CUDA. Performance-oriented optimizations, with the aid of an analytical performance model, the roofline model, are employed. Despite being highly dynamic, the adaptive, charge-conserving particle mover algorithm achieves up to 300 400 GOp/s (including single-precision floating-point, integer, and logic operations) on a Nvidia GeForce GTX580, corresponding to 20 25% absolute GPU efficiency (against the peak theoretical performance) and 50-70% intrinsic efficiency (against the algorithm s maximum operational throughput, which neglects all latencies). This is about 200-300 times faster than an equivalent serial CPU implementation. When the single-precision GPU particle mover is combined with a double-precision CPU JFNK field solver, overall performance gains 100 vs. the double-precision CPU-only serial version are obtained, with no apparent loss of

  1. Simplified models for the nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

    NASA Astrophysics Data System (ADS)

    Galant, Grzegorz; Zaleśny, Jarosław; Lisak, Mietek; Berczyński, Paweł; Berczyński, Stefan

    2011-05-01

    An analytical model that is based on purely differential equations of the nonlinear dynamics of two plasma modes driven resonantly by high-energy ions near the instability threshold is presented here. The well-known integro-differential model of Berk and Breizman (BB) extended to the case of two plasma modes is simplified here to a system of two coupled nonlinear differential equations of fifth order. The effects of the Krook, diffusion and dynamical friction (drag) relaxation processes are considered, whereas shifts in frequency and wavenumber between the modes are neglected. In spite of these simplifications the main features of the dynamics of the two plasma modes are retained. The numerical solutions to the model equations show competition between the two modes for survival, oscillations, chaotic regimes and 'blow-up' behavior, similar to the BB model.

  2. Quenching of leading jets and particles: The p⊥ dependent Landau-Pomeranchuk-Migdal effect from nonlinear k⊥ factorization

    NASA Astrophysics Data System (ADS)

    Nikolaev, N. N.; Schäfer, W.

    2006-07-01

    We report the first derivation of radiative nuclear stopping (the Landau-Pomeranchuk-Migdal effect) for leading jets at fixed values of the transverse momentum p in the beam fragmentation region of hadron-nucleus collisions from Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC). The major novelty of this work is a derivation of the missing virtual radiative pQCD correction to these processes—the real-emission radiative corrections are already available in the literature. We manifestly implement the unitarity relation, which in the simplest form requires that upon summing over the virtual and real-emission corrections the total number of scattered quarks must exactly equal unity. For the free-nucleon target, the leading jet spectrum is shown to satisfy the familiar linear Balitsky-Fadin-Kuraev-Lipatov leading log⁡-(1)/(x) (LL(1)/(x)) evolution. For nuclear targets, the nonlinear k⊥-factorization for the LL-(1)/(x) evolution of the leading jet spectrum is shown to exactly match the equally nonlinear LL(1)/(x) evolution of the collective nuclear glue—there emerges a unique linear k⊥-factorization relation between the two nonlinear evolving nuclear observables. We argue that within the standard dilute uncorrelated nucleonic gas treatment of heavy nuclei, in the finite energy range from RHIC to LHC, the leading jet spectrum can be evolved in the LL(1)/(x) Balitsky-Kovchegov approximation. We comment on the extension of these results to, and their possible Reggeon field theory interpretation for, midrapidity jets.

  3. 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.

  4. Validation studies of gyrokinetic ITG and TEM turbulence simulations in a JT-60U tokamak using multiple flux matching

    NASA Astrophysics Data System (ADS)

    Nakata, Motoki; Honda, Mitsuru; Yoshida, Maiko; Urano, Hajime; Nunami, Masanori; Maeyama, Shinya; Watanabe, Tomo-Hiko; Sugama, Hideo

    2016-08-01

    Quantitative validation studies of flux-tube gyrokinetic Vlasov simulations on ion and electron heat transport are carried out for the JT-60U tokamak experiment. The ion temperature gradient (ITG) and/or trapped electron modes (TEM) driven turbulent transport and zonal flow generations are investigated for an L-mode plasma in the local turbulence limit with a sufficiently small normalized ion thermal gyroradius and weak mean radial electric fields. Nonlinear turbulence simulations by the GKV code successfully reproduce radial profiles of the ion and electron energy fluxes in the core region. The numerical results show that the TEM-driven zonal flow generation in the outer region is more significant than that in the core region with ITG- and ITG–TEM-dominated turbulence, leading to moderate transport shortfall of the ion energy flux. Error levels in the prediction of the ion and electron temperature gradient profiles in the core region are estimated as less than +/- 30% , based on a multiple flux matching technique, where the simulated ion and electron energy fluxes are simultaneously matched to the experimental values.

  5. Comparative gyrokinetic analysis of JET baseline H-mode core plasmas with carbon wall and ITER-like wall

    NASA Astrophysics Data System (ADS)

    Tegnered, D.; Strand, P.; Nordman, H.; Giroud, C.; Kim, Hyun-Tae; Maddison, G. P.; Romanelli, M.; Szepesi, G.; Contributors, JET

    2016-04-01

    Following the change of plasma facing components at JET from a carbon wall (CW) to a metal ITER-like wall (ILW) a deterioration of global confinement has been observed for H-mode baseline experiments. The deterioration has been correlated with a degradation of pedestal confinement with lower electron temperatures at the top of the edge barrier region. In order to investigate the change in core confinement, heat transport due to Ion Temperature Gradient (ITG)/Trapped Electron Mode (TEM) turbulence is investigated using the gyrokinetic code GENE. Two pairs of CW and ILW discharges that are matched according to several global parameters are simulated at mid radius. The simulations included effects of collisions, finite β, realistic geometries, and impurities. A sensitivity study is performed with respect to the key dimensionless parameters in the matched pairs. The combined effect of the relative change in these parameters is that the ITG mode is destabilized in the ILW discharges compared to the CW discharges. This is also reflected in nonlinear simulations where the ILW discharges show higher normalized ion and electron heat fluxes and larger stiffness. The ion energy confinement time within ρ =0.5 is found to be comparable while the electron confinement time is shorter for the ILW discharges. The core confinement in the ILW discharges is expected to improve if the edge pedestal is recovered since that would favourably change the key plasma parameters that now serve to destabilize them.

  6. Special section containing papers presented at the 13th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems (Beijing, China, 17-20 September 2013) Special section containing papers presented at the 13th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems (Beijing, China, 17-20 September 2013)

    NASA Astrophysics Data System (ADS)

    Lin, Z.

    2014-10-01

    -ion density relaxes to similar profiles for all injection angles. Further verification and validation of these reduced models by existing tokamak experiments and nonlinear simulations are needed. Impressive progress in first-principles simulations of Alfvén eigenmodes and energetic particle transport was prominently featured at the meeting. Rigorous verification and validation have been successfully carried out for global gyrokinetic simulations of Alfvén eigenmodes with kinetic effects of thermal plasmas and non-perturbative contributions by energetic particles. The gyrokinetic turbulence simulation provides an indispensable new capability for studying the nonlinear physics of energetic particles and Alfvén eigenmodes by incorporating important physics of radial variations and toroidal mode coupling. For example, gyrokinetic simulations have found nonlinear oscillations of Alfvén eigenmode amplitude and frequency consistent with experimental observations. With better understanding of linear and nonlinear properties of Alfvén eigenmodes, a fruitful future direction is the self-consistent simulation of energetic particle transport, which requires long time simulations of nonlinear interactions between multiple Alfvén eigenmodes. A significant step in this direction has been taken by MHD-gyrokinetic hybrid simulations, which have demonstrated that fast ion profile is flattened by enhanced transport due to resonance overlaps in multiple interacting Alfvén eigenmodes with realistic amplitudes. A very interesting physics here is that the re-distribution of the energetic particle profile by an initially dominant Alfvén eigenmode leads to the excitation of other Alfvén eigenmodes. The broaden phase space volume for the extraction of free energy can then drive large fluctuation amplitudes and enhanced energetic particle transport. Some experimental evidences of such indirect interaction of multiple modes through energetic particles were observed in JT-60U and ASDEX

  7. Wave-particle dynamics of waveform and defect evolutions in undulated nonlinear self-excited dust acoustic waves

    SciTech Connect

    Tsai, Jun-Yi; Tsai, Ya-Yi; I, Lin

    2015-01-15

    The wave-particle dynamics for the evolutions of defects and surrounding pitchfork type waveforms of a weakly disordered self-excited dust acoustic wave is experimentally investigated in an rf dusty plasma system. Particle trajectories are tracked and correlated with waveform evolution to construct an Eulerian-Lagrangian wave-particle dynamical picture. It is found that the local accumulation and depletion of particles in the wave crest and rear, respectively, determines the local crest speed, and the growth and decay of the local crest height, which in turn determine the waveform evolution. The local crest height and the focusing and defocusing of particle trajectories due to the transverse force fields from the tilted wave crest and the non-uniform crest height along the wave crest are the key factors to determine the above particle accumulation and depletion. It explains the observations such as the lower speed of smaller crests, the straightening of the leading front of the pitchfork waveform associated with the transverse motion of defect to the open side, and the vertical defect gliding in the wave frame through the detachment of the strongly kinked pitchfork branch followed by its reconnection with the trailing crest.

  8. Verification of Gyrokinetic (delta)f Simulations of Electron Temperature Gradient Turbulence

    SciTech Connect

    Nevins, W M; Parker, S E; Chen, Y; Candy, J; Dimits, A; Dorland, W; Hammett, G W; Jenko, F

    2007-05-07

    The GEM gyrokinetic {delta}f simulation code [Chen, 2003] [Chen, 2007] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [Nevins, 2006]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.

  9. Gyrokinetic Simulation of Global and Local Alfv'en Eigenmodes Driven by Neutral Beam Injection in DIII-D

    NASA Astrophysics Data System (ADS)

    Bass, E. M.; Waltz, R. E.

    2012-10-01

    In ITER, convection of fusion-produced alpha particles by energetic particle (EP)-driven Alfv'en eigenmodes (AEs) risks wall damage and loss of alpha heating needed for ignition. We examine beam-excited AEs and induced quasilinear transport in a DIII-D AE experiment using the gyrokinetic code GYRO [1]. Global, linear eigenvalue simulations show reverse-shear AEs (RSAEs), toroidal AEs, and beta-induced AEs interacting over one (equilibrium time scale) RSAE frequency sweep. Eigenfunction modifications over MHD, including a poloidal twist and broad AE footprint observed in electron cyclotron emission imaging [2], show the value of a kinetic approach. Under a simple quasilinear saturation assumption, a sequence of comparatively inexpensive local simulations quantitatively recreates some global features, notably the quasilinear transport footprint. Accordingly, we present here a stiff EP transport model where AEs limit the EP density gradient to the local stability threshold, and a TGLF-driven quasilinear model elsewhere. The model gives some``worst case'' predictions of the AE-limited alpha profile in ITER.[4pt] [1] J. Candy and R.E. Waltz, Phys. Rev. Lett. 91, 045001 (2003). [2] B.J. Tobias, et al., Phys. Rev. Lett. 106, 075003 (2011).

  10. Kinetic (particle-in-cell) simulation of nonlinear laser absorption in a finite-size plasma with a background inhomogeneous magnetic field

    SciTech Connect

    Mehdian, H. Kargarian, A.; Hajisharifi, K.

    2015-06-15

    In this paper, the effect of an external inhomogeneous magnetic field on the high intensity laser absorption rate in a sub-critical plasma has been investigated by employing a relativistic electromagnetic 1.5 dimensional particle-in-cell code. Relying on the effective nonlinear phenomena such as phase-mixing and scattering, this study shows that in a finite-size plasma the laser absorption increases with inhomogeneity of the magnetic field (i.e., reduction of characteristic length of inhomogeneous magnetic field, λ{sub p}) before exiting a considerable amount of laser energy from the plasma due to scattering process. On the other hand, the presence of the external inhomogeneous magnetic field causes the maximum absorption of laser to occur at a shorter time. Moreover, study of the kinetic results associated with the distribution function of plasma particles shows that, in a special range of the plasma density and the characteristic length of inhomogeneous magnetic field, a considerable amount of laser energy is transferred to the particles producing a population of electrons with kinetic energy along the laser direction.

  11. Nonlinear Hysteretic Torsional Waves.

    PubMed

    Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V

    2015-07-31

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters. PMID:26274421

  12. Nonlinear Hysteretic Torsional Waves

    NASA Astrophysics Data System (ADS)

    Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

    2015-07-01

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

  13. Gyrokinetic full f analysis of electric field dynamics and poloidal velocity in the FT2-tokamak configuration

    SciTech Connect

    Leerink, S.; Heikkinen, J. A.; Janhunen, S. J.; Kiviniemi, T. P.; Nora, M.; Ogando, F.

    2008-09-15

    The ELMFIRE gyrokinetic simulation code has been used to perform full f simulations of the FT-2 tokamak. The dynamics of the radial electric field and the creation of poloidal velocity in the presence of turbulence are presented.

  14. Nonlinear particle dynamics in the magnetotail: A laboratory study 1. The experimental configuration and numerical simulation. Interim report

    SciTech Connect

    Walker, D.; Bowles, J.; Holland, D.; Chen, J.; Siefring, C.

    1995-09-25

    The authors have performed the initial stages of an experiment designed to investigate particle dynamics in the magnetotail. The results of this experiment lend support to the idea that particle scattering from the magnetotail neutral sheet is not random but that there exist resonances in the number and direction of scattered particles as a function of energy. The effort began with construction and testing of the magnetic field configuration necessary to simulate the quitetime magnetotail field: a neutral sheet magnetic field profile B0(z)x with a superimposed normal field B(2)z. Once complete, electrons of variable energy were injected into the field region created and the scattered current collected by back-scattered and forward-scattered collection plates was analyzed as a function of electron energy. The experiment was used to test the hypothesis that single particle scattering from a neutral sheet type profile as described can be coherent and can, at times, demonstrate resonance effects as a function of energy.

  15. Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

    NASA Astrophysics Data System (ADS)

    Jia, Guozhang; Xiang, Nong; Wang, Xueyi; Huang, Yueheng; Lin, Yu

    2016-01-01

    The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparable to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ˜ 3ωLH, where ωLH represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ˜ 1.3ωLH), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.

  16. Nonlinear propagation of dust-ion-acoustic solitary waves in an unmagnetized dusty plasma with trapped particle distribution

    NASA Astrophysics Data System (ADS)

    Rahman, O.

    2015-12-01

    The nonlinear propagation of dust-ion-acoustic (DIA) solitary waves (SWs) in an unmagnetized four-component dusty plasma containing electrons and negative ions obeying vortex-like (trapped) velocity distribution, cold mobile positive ions and arbitrarily charged stationary dust has been theoretically investigated. The properties of small but finite amplitude DIASWs are studied by employing the reductive perturbation technique. It has been found that owing to the departure from the Maxwellian electron and Maxwellian negative ion distribution to a vortex-like one, the dynamics of such DIASWs is governed by a modified Korteweg-de Vries (mKdV) equation which admits SW solution under certain conditions. The basic properties (speed, amplitude, width, etc.) of such DIASWs are found to be significantly modified by the presence of trapped electron and trapped negative ions. The implications of our results to space and laboratory dusty electronegative plasmas (DENPs) are briefly discussed.

  17. Flow of polydisperse gas-particle mixture in a duct followed by coagulation in a nonlinear wave field

    NASA Astrophysics Data System (ADS)

    Tukmakov, A. L.; Bayanov, R. I.; Tukmakov, D. A.

    2015-05-01

    Numerical simulation of the flow of an aerosol of polydisperse composition in a plane duct, where the resonance acoustic oscillations are generated, which are directed across the flow, has been carried out. The peculiarities of the flow, which is followed by coagulation and alteration of the distribution of particles over their sizes, have been described. The carrying medium has been modeled with the aid of the system of Navier-Stokes equations for compressible heat-conducting gas. The polydisperse phase dynamics is described by the systems of equations involving the equations of continuity, conservation of the momentum and internal energy. Equations of the motion of carrying medium and disperse fractions are written with allowance for interphase exchange by the momentum and energy. A Lagrangian model has been used to describe the coagulation process. The dispersion alteration in the gas-particle flow under the action of acoustic oscillations, which are resonant for the duct cross section, is analyzed.

  18. Smooth Particle Hydrodynamics with nonlinear Moving-Least-Squares WENO reconstruction to model anisotropic dispersion in porous media

    NASA Astrophysics Data System (ADS)

    Avesani, Diego; Herrera, Paulo; Chiogna, Gabriele; Bellin, Alberto; Dumbser, Michael

    2015-06-01

    Most numerical schemes applied to solve the advection-diffusion equation are affected by numerical diffusion. Moreover, unphysical results, such as oscillations and negative concentrations, may emerge when an anisotropic dispersion tensor is used, which induces even more severe errors in the solution of multispecies reactive transport. To cope with this long standing problem we propose a modified version of the standard Smoothed Particle Hydrodynamics (SPH) method based on a Moving-Least-Squares-Weighted-Essentially-Non-Oscillatory (MLS-WENO) reconstruction of concentrations. This scheme formulation (called MWSPH) approximates the diffusive fluxes with a Rusanov-type Riemann solver based on high order WENO scheme. We compare the standard SPH with the MWSPH for different a few test cases, considering both homogeneous and heterogeneous flow fields and different anisotropic ratios of the dispersion tensor. We show that, MWSPH is stable and accurate and that it reduces the occurrence of negative concentrations compared to standard SPH. When negative concentrations are observed, their absolute values are several orders of magnitude smaller compared to standard SPH. In addition, MWSPH limits spurious oscillations in the numerical solution more effectively than classical SPH. Convergence analysis shows that MWSPH is computationally more demanding than SPH, but with the payoff a more accurate solution, which in addition is less sensitive to particles position. The latter property simplifies the time consuming and often user dependent procedure to define the initial dislocation of the particles.

  19. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell algorithm

    NASA Astrophysics Data System (ADS)

    Chen, G.; Chacón, L.

    2015-12-01

    For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V.

  20. Global gyrokinetic simulations of trapped-electron mode and trapped-ion mode microturbulence

    NASA Astrophysics Data System (ADS)

    Drouot, T.; Gravier, E.; Reveille, T.; Sarrat, M.; Collard, M.; Bertrand, P.; Cartier-Michaud, T.; Ghendrih, P.; Sarazin, Y.; Garbet, X.

    2015-08-01

    This paper presents a reduced kinetic model, which describes simultaneously trapped-ion (TIM) and trapped-electron (TEM) driven modes. Interestingly, the model enables the study of a full f problem for ion and electron trapped particles at very low numerical cost. The linear growth rate obtained with the full f nonlinear code Trapped Element REduction in Semi Lagrangian Approach is successfully compared with analytical predictions. Moreover, nonlinear results show some basic properties of collisionless TEM and TIM turbulence in tokamaks. A competition between streamer-like structures and zonal flows is observed for TEM and TIM turbulence. Zonal flows are shown to play an important role in suppressing the nonlinear transport and strongly depend on the temperature ratio Te/Ti .

  1. 3D electrostatic gyrokinetic electron and fully kinetic ion simulation of lower-hybrid drift instability of Harris current sheet

    DOE PAGESBeta

    Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu

    2016-07-07

    The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location wheremore » $$\\vec{k}$$• $$\\vec{B}$$ =0, consistent with previous analytical and simulation studies. Here, $$\\vec{B}$$ is the equilibrium magnetic field and $$\\vec{k}$$ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at $$\\vec{k}$$ •$$\\vec{B}$$ ≠0. Additionally, the simulation results indicate that varying mi/me, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.« less

  2. 3D electrostatic gyrokinetic electron and fully kinetic ion simulation of lower-hybrid drift instability of Harris current sheet

    NASA Astrophysics Data System (ADS)

    Wang, Zhenyu; Lin, Yu; Wang, Xueyi; Tummel, Kurt; Chen, Liu

    2016-07-01

    The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me . In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me . The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where k →.B → =0 , consistent with previous analytical and simulation studies. Here, B → is the equilibrium magnetic field and k → is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at k →.B → ≠0 . In addition, the simulation results indicate that varying mi/me , the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.

  3. Gyrokinetic simulation of momentum transport with residual stress from diamagnetic level velocity shears

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Staebler, G. M.; Solomon, W. M.

    2011-04-01

    Residual stress refers to the remaining toroidal angular momentum (TAM) flux (divided by major radius) when the shear in the equilibrium fluid toroidal velocity (and the velocity itself) vanishes. Previously [Waltz et al., Phys. Plasmas 14, 122507 (2007); errata 16, 079902 (2009)], we demonstrated with GYRO [Candy and Waltz, J. Comp. Phys. 186, 545 (2003)] gyrokinetic simulations that TAM pinching from (ion pressure gradient supported or diamagnetic level) equilibrium E ×B velocity shear could provide some of the residual stress needed to support spontaneous toroidal rotation against normal diffusive loss. Here we show that diamagnetic level shear in the intrinsic drift wave velocities (or "profile shear" in the ion and electron density and temperature gradients) provides a comparable residual stress. The individual signed contributions of these small (rho-star level) E ×B and profile velocity shear rates to the turbulence level and (rho-star squared) ion energy transport stabilization are additive if the rates are of the same sign. However because of the additive stabilization effect, the contributions to the small (rho-star cubed) residual stress is not always simply additive. If the rates differ in sign, the residual stress from one can buck out that from the other (and in some cases reduce the stabilization.) The residual stress from these diamagnetic velocity shear rates is quantified by the ratio of TAM flow to ion energy (power) flow (M/P) in a global GYRO core simulation of a "null" toroidal rotation DIII-D [Mahdavi and Luxon, Fusion Sci. Technol. 48, 2 (2005)] discharge by matching M/P profiles within experimental uncertainty. Comparison of global GYRO (ion and electron energy as well as particle) transport flow balance simulations of TAM transport flow in a high-rotation DIII-D L-mode quantifies and isolates the E ×B shear and parallel velocity (Coriolis force) pinching components from the larger "diffusive" parallel velocity shear driven component and

  4. Nonlinear dynamics, rectification, and phase locking for particles on symmetrical two-dimensional periodic substrates with dc and circular ac drives.

    PubMed

    Reichhardt, C; Olson Reichhardt, C J; Hastings, M B

    2004-05-01

    We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of a omega/(2 pi), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a nonzero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity. PMID:15244891

  5. The nonlinear coupling between gyroradius scale turbulence and mesoscale magnetic islands in fusion plasmas

    SciTech Connect

    Hornsby, W. A.; Peeters, A. G.; Snodin, A. P.; Casson, F. J.; Camenen, Y.; Szepesi, G.; Siccinio, M.; Poli, E.

    2010-09-15

    The interaction between small scale turbulence (of the order of the ion Larmor radius) and mesoscale magnetic islands is investigated within the gyrokinetic framework. Turbulence, driven by background temperature and density gradients, over nonlinear mode coupling, pumps energy into long wavelength modes, and can result in an electrostatic vortex mode that coincides with the magnetic island. The strength of the vortex is strongly enhanced by the modified plasma flow response connected with the change in topology, and the transport it generates can compete with the parallel motion along the perturbed magnetic field. Despite the stabilizing effect of sheared plasma flows in and around the island, the net effect of the island is a degradation of the confinement. When density and temperature gradients inside the island are below the threshold for turbulence generation, turbulent fluctuations still persist through turbulence convection and spreading. The latter mechanisms then generate a finite transport flux and, consequently, a finite pressure gradient in the island. A finite radial temperature gradient inside the island is also shown to persist due to the trapped particles, which do not move along the field around the island. In the low collisionality regime, the finite gradient in the trapped population leads to the generation of a bootstrap current, which reduces the neoclassical drive.

  6. Consequences of using nonlinear particle trajectories to compute spatial diffusion coefficients. [for cosmic ray propagation in interstellar and interplanetary space

    NASA Technical Reports Server (NTRS)

    Goldstein, M. L.

    1977-01-01

    In a study of cosmic ray propagation in interstellar and interplanetary space, a perturbed orbit resonant scattering theory for pitch angle diffusion in a slab model of magnetostatic turbulence is slightly generalized and used to compute the diffusion coefficient for spatial propagation parallel to the mean magnetic field. This diffusion coefficient has been useful for describing the solar modulation of the galactic cosmic rays, and for explaining the diffusive phase in solar flares in which the initial anisotropy of the particle distribution decays to isotropy.

  7. Particle-In-Cell Simulations of a Nonlinear Transverse Electromagnetic Wave in a Pulsar Wind Termination Shock

    SciTech Connect

    Skjaeraasen, Olaf; Melatos, A.; Spitkovsky, A.; /KIPAC, Menlo Park

    2005-08-15

    A 2.5-dimensional particle-in-cell code is used to investigate the propagation of a large-amplitude, superluminal, nearly transverse electromagnetic (TEM) wave in a relativistically streaming electron-positron plasma with and without a shock. In the freestreaming, unshocked case, the analytic TEM dispersion relation is verified, and the streaming is shown to stabilize the wave against parametric instabilities. In the confined, shocked case, the wave induces strong, coherent particle oscillations, heats the plasma, and modifies the shock density profile via ponderomotive effects. The wave decays over {approx}> 10{sup 2} skin depths; the decay length scale depends primarily on the ratio between the wave frequency and the effective plasma frequency, and on the wave amplitude. The results are applied to the termination shock of the Crab pulsar wind, where the decay length-scale ({approx}> 0.05''?) might be comparable to the thickness of filamentary, variable substructure observed in the optical and X-ray wisps and knots.

  8. Gyrokinetic study of electromagnetic effects on toroidal momentum transport in tokamak plasmas

    SciTech Connect

    Hein, T.; Angioni, C.; Fable, E.; Candy, J.; Peeters, A. G.

    2011-07-15

    The effect of a finite {beta}{sub e} = 8{pi}n{sub e}T{sub e}/B{sup 2} on the turbulent transport of toroidal momentum in tokamak plasmas is discussed. From an analytical gyrokinetic model as well as local linear gyrokinetic simulations, it is shown that the modification of the parallel mode structure due to the nonadiabatic response of passing electrons, which changes the parallel wave vector k{sub ||} with increasing {beta}{sub e}, leads to a decrease in size of both the diagonal momentum transport as well as the Coriolis pinch under ion temperature gradient turbulence conditions, while for trapped electron modes, practically no modification is found. The decrease is particularly strong close to the onset of the kinetic ballooning modes. There, the Coriolis pinch even reverses its direction.

  9. Geodesic acoustic mode in anisotropic plasmas using double adiabatic model and gyro-kinetic equation

    SciTech Connect

    Ren, Haijun; Cao, Jintao

    2014-12-15

    Geodesic acoustic mode in anisotropic tokamak plasmas is theoretically analyzed by using double adiabatic model and gyro-kinetic equation. The bi-Maxwellian distribution function for guiding-center ions is assumed to obtain a self-consistent form, yielding pressures satisfying the magnetohydrodynamic (MHD) anisotropic equilibrium condition. The double adiabatic model gives the dispersion relation of geodesic acoustic mode (GAM), which agrees well with the one derived from gyro-kinetic equation. The GAM frequency increases with the ratio of pressures, p{sub ⊥}/p{sub ∥}, and the Landau damping rate is dramatically decreased by p{sub ⊥}/p{sub ∥}. MHD result shows a low-frequency zonal flow existing for all p{sub ⊥}/p{sub ∥}, while according to the kinetic dispersion relation, no low-frequency branch exists for p{sub ⊥}/p{sub ∥}≳ 2.

  10. Nature of turbulent transport across sheared zonal flows: insights from gyro-kinetic simulations

    SciTech Connect

    Sanchez, Raul; Newman, David E; Leboeuf, Jean-Noel; Decyk, Viktor

    2011-01-01

    The traditional view regarding the reduction of turbulence-induced transport across a stable sheared flow invokes a reduction of the characteristic length scale in the direction perpendicular to the flow as a result of the shearing and stretching of eddies caused by the differential pull exerted in the direction of the flow. A reduced effective transport coefficient then suffices to capture the reduction, that can then be readily incorporated into a transport model. However, recent evidence from gyrokinetic simulations of the toroidal ion-temperature-gradient mode suggests that the dynamics of turbulent transport across sheared flows changes in a more fundamental manner, and that the use of reduced effective transport coefficients fails to capture the full dynamics that may exhibit both subdiffusion and non-Gaussian statistics. In this contribution, after briefly reviewing these results, we propose some candidates for the physical mechanisms responsible for endowing transport with such non-diffusive characteristics, backing these proposals with new numerical gyrokinetic data

  11. Gyrokinetic simulation on the effect of radio frequency waves on ion-temperature-gradient-driven modes

    NASA Astrophysics Data System (ADS)

    Imadera, K.; Kishimoto, Y.; Sen, S.; Vahala, G.

    2016-02-01

    The ion-temperature-driven modes are studied in the presence of radio frequency waves by the use of the Gyro-Kinetic simulation Code. It is shown that the radio frequency waves through the ponderomotive force can stabilise the ion-temperature-gradient instabilities and contrary to the usual belief no radio frequency wave-induced flow generation hypothesis is required. This might be a major way to create a transport barrier in the fusion energy generation.

  12. Renormalized perturbation theory - Vlasov-Poisson system, weak turbulence limit, and gyrokinetics

    NASA Astrophysics Data System (ADS)

    Zhang, Y. Z.; Mahadjan, S. M.

    1988-10-01

    The self-consistency of the renormalized perturbation theory of Zhang and Mahajan (1985) is demonstrated by applying it to the Vlasov-Poisson system and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-beta gyrokinetic system. Comparison of this theory with other current theories is presented.

  13. On Higher-order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit

    SciTech Connect

    W.W. Lee and R.A. Kolesnikov

    2009-02-17

    In this paper, we present a simple iterative procedure for obtaining the higher order E x B and dE/dt (polarization) drifts associated with the gyrokinetic Vlasov-Poisson equations in the long wavelength limit of k⊥ρi ~ o(ε) and k⊥L ~ o(1), where ρi is the ion gyroradius, L is the scale length of the background inhomogeneity and ε is a smallness parameter. It can be shown that these new higher order k⊥ρi terms, which are also related to the higher order perturbations of the electrostatic potential Φ, should have negligible effects on turbulent and neoclassical transport in tokamaks, regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson's equation have been studied and shown to be unimportant as well. On the other hand, the terms of o(k2⊥ρi2) ~ o(ε) and k⊥L ~ o(1) can indeed have impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared with a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.

  14. Assessing the nonlinear response of fine particles to precursor emissions: Development and application of an extended response surface modeling technique v1.0

    DOE PAGESBeta

    Zhao, B.; Wang, S. X.; Xing, J.; Fu, K.; Fu, J. S.; Jang, C.; Zhu, Y.; Dong, X. Y.; Gao, Y.; Wu, W. J.; et al

    2015-01-30

    An innovative extended response surface modeling technique (ERSM v1.0) is developed to characterize the nonlinear response of fine particles (PM₂̣₅) to large and simultaneous changes of multiple precursor emissions from multiple regions and sectors. The ERSM technique is developed based on the conventional response surface modeling (RSM) technique; it first quantifies the relationship between PM₂̣₅ concentrations and the emissions of gaseous precursors from each single region using the conventional RSM technique, and then assesses the effects of inter-regional transport of PM₂̣₅ and its gaseous precursors on PM₂̣₅ concentrations in the target region. We apply this novel technique with a widelymore » used regional chemical transport model (CTM) over the Yangtze River delta (YRD) region of China, and evaluate the response of PM₂̣₅ and its inorganic components to the emissions of 36 pollutant–region–sector combinations. The predicted PM₂̣₅ concentrations agree well with independent CTM simulations; the correlation coefficients are larger than 0.98 and 0.99, and the mean normalized errors (MNEs) are less than 1 and 2% for January and August, respectively. It is also demonstrated that the ERSM technique could reproduce fairly well the response of PM₂̣₅ to continuous changes of precursor emission levels between zero and 150%. Employing this new technique, we identify the major sources contributing to PM₂̣₅ and its inorganic components in the YRD region. The nonlinearity in the response of PM₂̣₅ to emission changes is characterized and the underlying chemical processes are illustrated.« less

  15. Assessing the nonlinear response of fine particles to precursor emissions: Development and application of an extended response surface modeling technique v1.0

    SciTech Connect

    Zhao, B.; Wang, S. X.; Xing, J.; Fu, K.; Fu, J. S.; Jang, C.; Zhu, Y.; Dong, X. Y.; Gao, Y.; Wu, W. J.; Wang, J. D.; Hao, J. M.

    2015-01-30

    An innovative extended response surface modeling technique (ERSM v1.0) is developed to characterize the nonlinear response of fine particles (PM₂̣₅) to large and simultaneous changes of multiple precursor emissions from multiple regions and sectors. The ERSM technique is developed based on the conventional response surface modeling (RSM) technique; it first quantifies the relationship between PM₂̣₅ concentrations and the emissions of gaseous precursors from each single region using the conventional RSM technique, and then assesses the effects of inter-regional transport of PM₂̣₅ and its gaseous precursors on PM₂̣₅ concentrations in the target region. We apply this novel technique with a widely used regional chemical transport model (CTM) over the Yangtze River delta (YRD) region of China, and evaluate the response of PM₂̣₅ and its inorganic components to the emissions of 36 pollutant–region–sector combinations. The predicted PM₂̣₅ concentrations agree well with independent CTM simulations; the correlation coefficients are larger than 0.98 and 0.99, and the mean normalized errors (MNEs) are less than 1 and 2% for January and August, respectively. It is also demonstrated that the ERSM technique could reproduce fairly well the response of PM₂̣₅ to continuous changes of precursor emission levels between zero and 150%. Employing this new technique, we identify the major sources contributing to PM₂̣₅ and its inorganic components in the YRD region. The nonlinearity in the response of PM₂̣₅ to emission changes is characterized and the underlying chemical processes are illustrated.

  16. Investigation of tearing instability using GeFi particle simulation model

    SciTech Connect

    Wang, X. Y.; Lin, Y.; Lu, X.; Kong, W.; Chen, L.

    2011-12-15

    The gyrokinetic (GK) electron and fully kinetic ion (GeFi) simulation model of Lin et al.[Plasmas Phys. Controlled Fusion 53, 054013 (2011)] has been thoroughly benchmarked and validated for a two-dimensional (2D) Harris current sheet with a finite guide field. First, a gyrokinetic eigenmode theory for the collisionless tearing mode in the small Larmor radius limit is presented. The linear eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are benchmarked against those from the GK eigenmode analysis in the limit of L>>{rho}{sub i}>{rho}{sub e}, where L is the current sheet half-width, {rho}{sub i} is ion Larmor radius, and {rho}{sub e} is electron Larmor radius. Second, to valid the GeFi model, both the linear and nonlinear tearing instabilities obtained from the GeFi simulations are compared with the Darwin particle-in-cell (PIC) simulation. The validation of the GeFi model for laboratory and space plasmas is also discussed. Meanwhile, the GeFi simulation is carried out to investigate both the linear and nonlinear tearing instabilities for cases with a broad range of L and guide magnetic field B{sub G}. It is found that in a wide current sheet with L > 4.5{rho}{sub eK}, the nonlinear saturation level of the island half-width is w{sub s}{approx_equal} 3{rho}{sub eK}, where {rho}{sub eK} = {rho}{sub e}B{sub 0}/B{sub x0}, B{sub 0} is the strength of the asymptotic magnetic field, and B{sub x0} is the antiparallel field. On the other hand, in a thin current sheet with L < 2.5{rho}{sub eK}, w{sub s}{approx_equal} 2.2 L. In addition, a high frequency electrostatic drift mode is found to coexist with the tearing mode.

  17. Deep and high-resolution three-dimensional tracking of single particles using nonlinear and multiplexed illumination

    PubMed Central

    Perillo, Evan P.; Liu, Yen-Liang; Huynh, Khang; Liu, Cong; Chou, Chao-Kai; Hung, Mien-Chie; Yeh, Hsin-Chih; Dunn, Andrew K.

    2015-01-01

    Molecular trafficking within cells, tissues and engineered three-dimensional multicellular models is critical to the understanding of the development and treatment of various diseases including cancer. However, current tracking methods are either confined to two dimensions or limited to an interrogation depth of ∼15 μm. Here we present a three-dimensional tracking method capable of quantifying rapid molecular transport dynamics in highly scattering environments at depths up to 200 μm. The system has a response time of 1 ms with a temporal resolution down to 50 μs in high signal-to-noise conditions, and a spatial localization precision as good as 35 nm. Built on spatiotemporally multiplexed two-photon excitation, this approach requires only one detector for three-dimensional particle tracking and allows for two-photon, multicolour imaging. Here we demonstrate three-dimensional tracking of epidermal growth factor receptor complexes at a depth of ∼100 μm in tumour spheroids. PMID:26219252

  18. Deep and high-resolution three-dimensional tracking of single particles using nonlinear and multiplexed illumination

    NASA Astrophysics Data System (ADS)

    Perillo, Evan P.; Liu, Yen-Liang; Huynh, Khang; Liu, Cong; Chou, Chao-Kai; Hung, Mien-Chie; Yeh, Hsin-Chih; Dunn, Andrew K.

    2015-07-01

    Molecular trafficking within cells, tissues and engineered three-dimensional multicellular models is critical to the understanding of the development and treatment of various diseases including cancer. However, current tracking methods are either confined to two dimensions or limited to an interrogation depth of ~15 μm. Here we present a three-dimensional tracking method capable of quantifying rapid molecular transport dynamics in highly scattering environments at depths up to 200 μm. The system has a response time of 1 ms with a temporal resolution down to 50 μs in high signal-to-noise conditions, and a spatial localization precision as good as 35 nm. Built on spatiotemporally multiplexed two-photon excitation, this approach requires only one detector for three-dimensional particle tracking and allows for two-photon, multicolour imaging. Here we demonstrate three-dimensional tracking of epidermal growth factor receptor complexes at a depth of ~100 μm in tumour spheroids.

  19. Investigating profile stiffness and critical gradients in shaped TCV discharges using local gyrokinetic simulations of turbulent transport

    NASA Astrophysics Data System (ADS)

    Merlo, G.; Brunner, S.; Sauter, O.; Camenen, Y.; Görler, T.; Jenko, F.; Marinoni, A.; Told, D.; Villard, L.

    2015-05-01

    The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity (δ < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al 2014 Phys. Plasmas 21 055906) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al 2000 Phys. Plasmas 7 1904), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when δ < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.

  20. Self-consistent Nonlinear Analysis and 3D Particle-In-Cell Simulation of a W-band Gyro-TWT

    NASA Astrophysics Data System (ADS)

    Tang, Yong; Luo, Yong; Xu, Yong; Yan, Ran

    2014-10-01

    The self-consistent nonlinear analysis and CST 3D particle-in-cell (PIC) simulation of a W-band gyrotron traveling wave tube (gyro-TWT) are presented in this paper. Both the simulation results of the two codes are excellent agreement with each other. The gyro-TWT loaded with periodic lossy dielectric in the circuit for suppressing potential spurious oscillations. It is driven by a 70kV, 10A gyrating electron beam with velocity ratio of 1.0. PIC simulation results are: the maximum peak output power of 198kW, statured gain of 62.3dB and efficiency of 28.3% at 92.5GHz. Only the operating mode TE 01 is observed in the CST 3D simulation and the potential competing backward wave oscillations are effectively suppressed. The CST simulation also predicts that the device works stably under the condition of the beam current lower than 14A and B 0 /B g lower than 1.05. The simulated bandwidth with peak power greater than 100kW is 6.8GHz without axial velocity spread, and 4.1GHz with 6% axial velocity spread.

  1. Bidirectional quantum teleportation of unknown photons using path-polarization intra-particle hybrid entanglement and controlled-unitary gates via cross-Kerr nonlinearity

    NASA Astrophysics Data System (ADS)

    Heo, Jino; Hong, Chang-Ho; Lim, Jong-In; Yang, Hyung-Jin

    2015-05-01

    We propose an arbitrary controlled-unitary (CU) gate and a bidirectional quantum teleportation (BQTP) scheme. The proposed CU gate utilizes photonic qubits (photons) with cross-Kerr nonlinearities (XKNLs), X-homodyne detectors, and linear optical elements, and consists of the consecutive operation of a controlled-path (C-path) gate and a gathering-path (G-path) gate. It is almost deterministic and feasible with current technology when a strong coherent state and weak XKNLs are employed. Based on the CU gate, we present a BQTP scheme that simultaneously teleports two unknown photons between distant users by transmitting only one photon in a path-polarization intra-particle hybrid entangled state. Consequently, it is possible to experimentally implement BQTP with a certain success probability using the proposed CU gate. Project supported by the Ministry of Science, ICT&Future Planning, Korea, under the C-ITRC (Convergence Information Technology Research Center) Support program (NIPA-2013-H0301-13-3007) supervised by the National IT Industry Promotion Agency.

  2. Turbulence in the TORE SUPRA Tokamak: Measurements and Validation of Nonlinear Simulations

    SciTech Connect

    Casati, A.; Bourdelle, C.; Clairet, F.; Garbet, X.; Grandgirard, V.; Hoang, G. T.; Imbeaux, F.; Sabot, R.; Sarazin, Y.; Gerbaud, T.; Hennequin, P.; Guercan, Oe. D.; Honore, C.; Vermare, L.; Candy, J.; Waltz, R. E.; Heuraux, S.

    2009-04-24

    Turbulence measurements in TORE SUPRA tokamak plasmas have been quantitatively compared to predictions by nonlinear gyrokinetic simulations. For the first time, numerical results simultaneously match within experimental uncertainty (a) the magnitude of effective heat diffusivity, (b) rms values of density fluctuations, and (c) wave-number spectra in both the directions perpendicular to the magnetic field. Moreover, the nonlinear simulations help to revise as an instrumental effect the apparent experimental evidence of strong turbulence anisotropy at spatial scales of the order of ion-sound Larmor radius.

  3. An Enhanced Nonlinear Critical Gradient for Electron Turbulent Transport due to Reversed Magnetic Shear

    SciTech Connect

    Peterson, J. L.; Hammet, G. W.; Mikkelsen, D. R.; Yuh, H. Y.; Candy, J.; Guttenfelder, W.; Kaye, S. M.; LeBlanc, B.

    2011-05-11

    The first nonlinear gyrokinetic simulations of electron internal transport barriers (e-ITBs) in the National Spherical Torus Experiment show that reversed magnetic shear can suppress thermal transport by increasing the nonlinear critical gradient for electron-temperature-gradient-driven turbulence to three times its linear critical value. An interesting feature of this turbulence is non- linearly driven off-midplane radial streamers. This work reinforces the experimental observation that magnetic shear is likely an effective way of triggering and sustaining e-ITBs in magnetic fusion devices.

  4. Nonlinear Waves in Hall MHD: Analysis and Comparison to Known Linear Waves

    NASA Astrophysics Data System (ADS)

    Pino, Jesse; Mahajan, Swadesh; Dorland, William

    2004-11-01

    Recently, a novel set of nonlinear waves were found to satisfy the Hall-Magnetohydrodynamic (HMHD) equations. The Mahajan-Krishan solution is a generalization of the classic Walén Nonlinear Alvén wave, of the form b=±αv. The implications of this mode are studied, including polarization and superposition. In particular, the gyrokinetic limit (k_⊥≫ k_\\|) is used in an attempt to match the MK wave to known Kinetic Alfvén waves and introduce FLR effects.

  5. Gyrokinetic and global fluid simulations of tokamak microturbulence and transport

    SciTech Connect

    Dimits, A.M.; Byers, J.A.; Williams, T.J.; Cohen, B.I.; Xu, W.Q.; Cohen, R.H.; Crotinger, J.A.; Shestakov, A.I.

    1994-08-30

    Results are presented from the first systematic nonlinear kinetic simulation study of the swings and parameter dependences of toroidal ion-temperature-gradient (ITG) turbulence and transport, and from the first such study that includes sheared toroidal flows. Key results include the observation of clear gyroBohm scaling of the turbulent transport and of a surprisingly weak dependence of the transport on toroidal flow shear. Based on the simulation results, a parameterization of the transport is given that includes the dependence on all of the relevant physical parameters. The transition from local to nonlocal transport as a function of the profile scale length has been investigated using two-dimensional global fluid simulations of dissipative drift-wave turbulence. Local gyroBohm scaling is observed, except at very short profile scale lengths.

  6. Fully electromagnetic gyrokinetic eigenmode analysis of high-beta shaped plasmas

    SciTech Connect

    Belli, E. A.; Candy, J.

    2010-11-15

    A new, more efficient method to compute unstable linear gyrokinetic eigenvalues and eigenvectors has been developed for drift-wave analysis of plasmas with arbitrary flux-surface shape, including both transverse and compressional magnetic perturbations. In high-beta, strongly shaped plasmas like in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)], numerous branches of closely spaced unstable eigenmodes exist. These modes are difficult and time-consuming to adequately resolve with the existing linear initial-value solvers, which are further limited to the most unstable eigenmode. The new method is based on an eigenvalue approach and is an extension of the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], reusing the existing discretization schemes in both real and velocity-space. Unlike recent methods, which use an iterative solver to compute eigenvalues of the relatively large gyrokinetic response matrix, the present scheme computes the zeros of the much smaller Maxwell dispersion matrix using a direct method. In the present work, the new eigensolver is applied to gyrokinetic stability analysis of a high-beta, NSTX-like plasma. We illustrate the smooth transformation from ion-temperature-gradient (ITG)-like to kinetic-ballooning (KBM)-like modes, and the formation of hybrid ITG/KBM modes, and further demonstrate the existence of high-k Alfvenic drift-wave 'cascades' for which the most unstable mode is a higher excited state along the field line. A new compressional electron drift wave, which is driven by a combination of strong beta and pressure gradient, is also identified for the first time. Overall, we find that accurate calculation of stability boundaries and growth rates cannot, in general, ignore the compressional component {delta}B{sub ||} of the perturbation.

  7. Fully electromagnetic gyrokinetic eigenmode analysis of high-beta shaped plasmas

    NASA Astrophysics Data System (ADS)

    Belli, E. A.; Candy, J.

    2010-11-01

    A new, more efficient method to compute unstable linear gyrokinetic eigenvalues and eigenvectors has been developed for drift-wave analysis of plasmas with arbitrary flux-surface shape, including both transverse and compressional magnetic perturbations. In high-beta, strongly shaped plasmas like in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)], numerous branches of closely spaced unstable eigenmodes exist. These modes are difficult and time-consuming to adequately resolve with the existing linear initial-value solvers, which are further limited to the most unstable eigenmode. The new method is based on an eigenvalue approach and is an extension of the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], reusing the existing discretization schemes in both real and velocity-space. Unlike recent methods, which use an iterative solver to compute eigenvalues of the relatively large gyrokinetic response matrix, the present scheme computes the zeros of the much smaller Maxwell dispersion matrix using a direct method. In the present work, the new eigensolver is applied to gyrokinetic stability analysis of a high-beta, NSTX-like plasma. We illustrate the smooth transformation from ion-temperature-gradient (ITG)-like to kinetic-ballooning (KBM)-like modes, and the formation of hybrid ITG/KBM modes, and further demonstrate the existence of high-k Alfvénic drift-wave "cascades" for which the most unstable mode is a higher excited state along the field line. A new compressional electron drift wave, which is driven by a combination of strong beta and pressure gradient, is also identified for the first time. Overall, we find that accurate calculation of stability boundaries and growth rates cannot, in general, ignore the compressional component δB∥ of the perturbation.

  8. Fidelity of reduced and realistic electron mass ratio multi-scale gyrokinetic simulations of tokamak discharges

    NASA Astrophysics Data System (ADS)

    Howard, N. T.; Holland, C.; White, A. E.; Greenwald, M.; Candy, J.

    2015-06-01

    The first study using multi-scale (coupled ITG/TEM/ETG) gyrokinetic simulations at both reduced and realistic electron mass ratios, μ = (mD/me).5 = 20.0, 40.0 and 60.0, has been performed on a standard, Alcator C-Mod, L-mode discharge. Ion-scale (kθρs  ∼  1.0) and multi-scale (up to kθρe  ∼  0.8) gyrokinetic simulations are compared at different simulated mass ratios to investigate the fidelity of reduced electron mass ratio, multi-scale simulation through direct comparison with realistic mass ratio, multi-scale simulation. Detailed description of both the numerical setup and the turbulent scales required to obtain meaningful coupled ITG/TEM/ETG simulation is presented. Significant high-k driven (TEM/ETG) heat flux is found to exist at scales of approximately kθρe  ∼  0.1 at all mass ratios but can only be obtained by simulation capturing turbulence up to kθρe  ∼  1.0. At slightly reduced mass ratio, μ = 40.0, qualitative agreement with realistic mass simulation can be obtained in the studied discharge, consistent with intuition obtained from linear stability analysis. However, realistic electron mass is required for any robust quantitative comparison with experimental heat fluxes for the condition studied, as significant differences are observed at even slightly reduced electron mass ratio. The details of this numerical study are presented to provide a basis for future studies utilizing coupled ITG/TEM/ETG gyrokinetic simulation.

  9. Transport of Energetic Particles by Microturbulence in Magnetized Plasmas

    SciTech Connect

    Zhang Wenlu; Lin Zhihong; Chen Liu

    2008-08-29

    Transport of energetic particles by the microturbulence in magnetized plasmas is studied in gyrokinetic simulations of the ion temperature gradient turbulence. The probability density function of the ion radial excursion is found to be very close to a Gaussian, indicating a diffusive transport process. The particle diffusivity can thus be calculated from a random walk model. The diffusivity is found to decrease drastically for high energy particles due to the averaging effects of the large gyroradius and orbit width, and the fast decorrelation of the energetic particles with the waves.

  10. Gyrokinetic simulations of off-axis minimum-q profile corrugations

    SciTech Connect

    Waltz, R.E.; Austin, M.E.; Burrell, K.H.; Candy, J.

    2006-05-15

    Quasiequilibrium radial 'profile corrugations' in the electron temperature gradient are found at lowest-order singular surfaces in global gyrokinetic code simulations of both monotonic-q and off-axis minimum-q discharges. The profile corrugations in the temperature and density gradients are time-averaged components of zonal flows. The m/n=2/1 electron temperature gradient corrugation is measurably large and appears to trigger an internal transport barrier as the off-axis minimum-q=2 surfaces enter the plasma.

  11. Verification of gyrokinetic {delta}f simulations of electron temperature gradient turbulence

    SciTech Connect

    Nevins, W. M.; Parker, S. E.; Chen, Y.; Candy, J.; Dimits, A.; Dorland, W.; Hammett, G. W.; Jenko, F.

    2007-08-15

    The GEM gyrokinetic {delta}f simulation code [Y. Chen and S. Parker, J. Comput. Phys. 189, 463 (2003); and ibid.220, 839 (2007)] is shown to reproduce electron temperature gradient turbulence at the benchmark operating point established in previous work [W. M. Nevins, J. Candy, S. Cowley, T. Dannert, A. Dimits, W. Dorland, C. Estrada-Mila, G. W. Hammett, F. Jenko, M. J. Pueschel, and D. E. Shumaker, Phys. Plasmas 13, 122306 (2006)]. The electron thermal transport is within 10% of the expected value, while the turbulent fluctuation spectrum is shown to have the expected intensity and two-point correlation function.

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

    SciTech Connect

    Zarzoso, D. Casson, F. J.; Poli, E.; Hornsby, W. A.; Peeters, A. G.

    2015-02-15

    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 steady state for which the analytic theory is formulated.

  13. Nature of Transport across Sheared Zonal Flows in Electrostatic Ion-Temperature-Gradient Gyrokinetic Plasma Turbulence

    SciTech Connect

    Sanchez, R.; Newman, D. E.; Leboeuf, J.-N.; Decyk, V. K.; Carreras, B. A.

    2008-11-14

    It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.

  14. Nature of Transport across Sheared Zonal Flows in Electrostatic Ion-Temperature-Gradient Gyrokinetic Plasma Turbulence

    SciTech Connect

    Sanchez, Raul; Newman, David E; Leboeuf, Jean-Noel; Decyk, Viktor; Carreras, Benjamin A

    2008-01-01

    It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified.

  15. Effects of the magnetic equilibrium on gyrokinetic simulations of tokamak microinstabilities

    SciTech Connect

    Wan, Weigang; Chen, Yang; Parker, Scott E.; Groebner, Richard J.

    2015-06-15

    The general geometry of the experimental tokamak magnetic equilibrium is implemented in the global gyrokinetic simulation code GEM. Compared to the general geometry, the well used Miller parameterization of the magnetic equilibrium is a good approximation in the core region and up to the top of the pedestal. Linear simulations indicate that results with the two geometries agree for r/a ≤ 0.9. However, in the edge region, the instabilities are sensitive to the magnetic equilibrium in both the L-mode and the H-mode plasmas. A small variation of the plasma shaping parameters leads to large changes to the edge instability.

  16. ETG-dominated transport regimes in near-edge DIII-D L-mode plasmas: Validation of multiscale gyrokinetic simulations

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

    A prerequisite for the development of a self-consistent theoretical description of the L-H transition is the ability to quantitatively characterize near-edge L-mode plasmas. It is shown here for the first time that regimes exist in the L-mode near-edge that appear to be dominated by sub-ion-scale turbulence driven by electron temperature gradient (ETG) modes. These are results of gyrokinetic simulations of a DIII-D L-mode discharge in the near edge region (r/a = 0.8) with the GENE code (www.genecode.org). Instructed by a linear analysis, we performed nonlinear simulations of ITG and ETG turbulence, pointing to a dominance of ETG turbulence regarding the anomalous radial heat flux. Direct comparison with experimental data is encouraging. Respective multi-scale simulations, covering both ion and electron scales are underway and will be presented. Implications for L-H transition modeling will also be discussed. Work supported by the US Department of Energy (DOE) under DE-FG02-08ER54984 and DE-FC02-04ER54698, as well as NERSC, a DOE Office of Science User Facility supported under Contract No. DE-AC02-05CH11231.

  17. Gyrokinetic Studies of ETG Turbulence in NSTX, and Comparisons of Advection Algorithms

    NASA Astrophysics Data System (ADS)

    Hammett, G. W.; Peterson, J. L.; Mikkelsen, D. R.; Kaye, S. M.; Waltz, R. E.; Candy, J.

    2009-05-01

    Electron temperature gradient (ETG) driven turbulence has been predicted to be important in some parameter regimes. High-k fluctuations have recently been measured in the National Spherical Torus Experiment (NSTX), at kθρe˜0.1-0.4, in the range of ETG turbulence. We are undertaking studies of ETG turbulence for NSTX cases using the GYRO gyrokinetic code. Among other results, we will show the dependence of some of the linear ETG properties on magnetic shear, q, and ZeffTe/Ti. Microtearing may also be important in some cases. On another topic, we will compare various advection algorithms on simple 1-D and 2-D test problems. The edge region in a magnetic fusion device has very steep density variations, which can cause problems for standard advection algorithms. Gibb's phenomena can lead to negative overshoots in the density solution; however, modern high-order upwind methods, developed initially for shock capturing, can preserve positivity of density, making them useful for edge gyrokinetic simulations. W. Dorland, F. Jenko, et al., Phys. Rev. Lett. 85, 5579 (2000). E. Mazzucato, D. R. Smith, et al., Phys. Rev. Lett. 101, 075001 (2008)

  18. Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

    SciTech Connect

    Swamy, Aditya K.; Ganesh, R.; Chowdhury, J.; Brunner, S.; Vaclavik, J.; Villard, L.

    2014-08-15

    Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient η{sub e}. Scans at different β values show an inverse relationship between the η{sub e} threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.

  19. The linear tearing instability in three dimensional, toroidal gyro-kinetic simulations

    SciTech Connect

    Hornsby, W. A. Migliano, P.; Buchholz, R.; Kroenert, L.; Weikl, A.; Peeters, A. G.; Zarzoso, D.; Poli, E.; Casson, F. J.

    2015-02-15

    Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro-kinetic turbulence code, GKW. The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate, and frequency of the mode were investigated by varying the current profile, collisionality, and the pressure gradients. Both collisionless and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absence of a pressure gradient is observed, which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However, the island rotation reverses direction at high collisionality. The growth rate is found to follow a η{sup 1∕7} scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability analysis as performed by Hastie et al. using the same current and safety factor profiles but for cylindrical geometry, however, here a modification due to toroidal coupling and pressure effects is seen.

  20. Comparison of linear gyrokinetic and two-fluid stability analyses of DIII-D L-mode plasmas

    NASA Astrophysics Data System (ADS)

    Holland, C.; Bass, E. M.

    2014-10-01

    We present results from a linear stability study of the edge and near-edge regions of well-studied DIII-D tokamak L-mode discharges, using both the gyrokinetic-Maxwell equations (as implemented in the GYRO code) and a range of two-fluid models implemented in the BOUT++ code. The goal is to identify instabilities that may help explain the well-known systematic under-prediction of near-edge DIII-D transport and fluctuation levels by some gyrokinetic codes, in particular those driven by edge physics not included within the gyrokinetic models. We first compare local and global gyrokinetic stability results spanning the region of 0 . 7 <ΨN < 0 . 95 to corresponding predictions from Braginskii-like models implemented in BOUT++, focusing on the influence of magnetic shaping and collisionality scalings for a range of low- to moderate-n modes, consistent with the observed discrepancies in fluctuation spectra. The closed-field line results are then compared against equivalent results that extend across the separatrix to the open field line region 0 . 7 <ΨN < 1 . 05 , in order to assess whether inclusion of this region leads to any significant changes in linear stability. Progress on extending the linear analysis to inclusion of rotational and gyrofluid effects will also be reported.