Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space
Abstract
Here, spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method.
- Authors:
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1467122
- Alternate Identifier(s):
- OSTI ID: 1481149
- Report Number(s):
- LA-UR-18-23813
Journal ID: ISSN 2296-987X; 27
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Published Article
- Journal Name:
- Frontiers in Astronomy and Space Sciences
- Additional Journal Information:
- Journal Name: Frontiers in Astronomy and Space Sciences Journal Volume: 5; Journal ID: ISSN 2296-987X
- Publisher:
- Frontiers Media SA
- Country of Publication:
- Switzerland
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Heliospheric and Magnetospheric Physics; Mathematics; Magnetic Fusion Energy; plasma; kinetic; spectral; Hermite; turbulence
Citation Formats
Roytershteyn, Vadim, and Delzanno, Gian Luca. Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space. Switzerland: N. p., 2018.
Web. doi:10.3389/fspas.2018.00027.
Roytershteyn, Vadim, & Delzanno, Gian Luca. Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space. Switzerland. https://doi.org/10.3389/fspas.2018.00027
Roytershteyn, Vadim, and Delzanno, Gian Luca. Tue .
"Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space". Switzerland. https://doi.org/10.3389/fspas.2018.00027.
@article{osti_1467122,
title = {Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space},
author = {Roytershteyn, Vadim and Delzanno, Gian Luca},
abstractNote = {Here, spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method.},
doi = {10.3389/fspas.2018.00027},
journal = {Frontiers in Astronomy and Space Sciences},
number = ,
volume = 5,
place = {Switzerland},
year = {Tue Aug 28 00:00:00 EDT 2018},
month = {Tue Aug 28 00:00:00 EDT 2018}
}
https://doi.org/10.3389/fspas.2018.00027
Works referenced in this record:
On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods
journal, January 2016
- Camporeale, E.; Delzanno, G. L.; Bergen, B. K.
- Computer Physics Communications, Vol. 198
Discontinuous Galerkin algorithms for fully kinetic plasmas
journal, January 2018
- Juno, J.; Hakim, A.; TenBarge, J.
- Journal of Computational Physics, Vol. 353
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
journal, June 1990
- Hammett, Gregory W.; Perkins, Francis W.
- Physical Review Letters, Vol. 64, Issue 25
Multi-dimensional, fully-implicit, spectral method for the Vlasov–Maxwell equations with exact conservation laws in discrete form
journal, November 2015
- Delzanno, G. L.
- Journal of Computational Physics, Vol. 301
Towards adaptive kinetic-fluid simulations of weakly ionized plasmas
journal, February 2012
- Kolobov, V. I.; Arslanbekov, R. R.
- Journal of Computational Physics, Vol. 231, Issue 3
Identification of Kinetic AlfvÉN wave Turbulence in the Solar wind
journal, January 2012
- Salem, C. S.; Howes, G. G.; Sundkvist, D.
- The Astrophysical Journal, Vol. 745, Issue 1
Electron Physics in 3-D Two-Fluid 10-Moment Modeling of Ganymede's Magnetosphere
journal, April 2018
- Wang, Liang; Germaschewski, Kai; Hakim, Ammar
- Journal of Geophysical Research: Space Physics, Vol. 123, Issue 4
Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model
journal, December 2007
- Sugiyama, Tooru; Kusano, Kanya
- Journal of Computational Physics, Vol. 227, Issue 2
SpectralPlasmaSolver: a Spectral Code for Multiscale Simulations of Collisionless, Magnetized Plasmas
journal, May 2016
- Vencels, Juris; Delzanno, Gian Luca; Manzini, Gianmarco
- Journal of Physics: Conference Series, Vol. 719
The energy conserving particle-in-cell method
journal, August 2011
- Markidis, Stefano; Lapenta, Giovanni
- Journal of Computational Physics, Vol. 230, Issue 18
An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
journal, August 2011
- Chen, G.; Chacón, L.; Barnes, D. C.
- Journal of Computational Physics, Vol. 230, Issue 18
A prospectus on kinetic heliophysics
journal, May 2017
- Howes, Gregory G.
- Physics of Plasmas, Vol. 24, Issue 5
Generation of magnetic holes in fully kinetic simulations of collisionless turbulence
journal, May 2015
- Roytershteyn, Vadim; Karimabadi, Homa; Roberts, Aaron
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 2041
Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection
journal, January 2015
- Wang, Liang; Hakim, Ammar H.; Bhattacharjee, A.
- Physics of Plasmas, Vol. 22, Issue 1
Three Dimensional Anisotropic Spectra of Turbulence at Subproton Scales in the Solar Wind
journal, September 2010
- Sahraoui, F.; Goldstein, M. L.; Belmont, G.
- Physical Review Letters, Vol. 105, Issue 13
Anisotropy in Space Plasma Turbulence: Solar Wind Observations
journal, September 2011
- Horbury, T. S.; Wicks, R. T.; Chen, C. H. K.
- Space Science Reviews, Vol. 172, Issue 1-4
The Fluid-Kinetic Particle-in-Cell method for plasma simulations
journal, August 2014
- Markidis, Stefano; Henri, Pierre; Lapenta, Giovanni
- Journal of Computational Physics, Vol. 271
Toward a Theory of Astrophysical Plasma Turbulence at Subproton Scales
journal, October 2013
- Boldyrev, Stanislav; Horaites, Konstantinos; Xia, Qian
- The Astrophysical Journal, Vol. 777, Issue 1
Specification of the near-Earth space environment with SHIELDS
journal, October 2018
- Jordanova, V. K.; Delzanno, G. L.; Henderson, M. G.
- Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 177
Ultrahigh performance three-dimensional electromagnetic relativistic kinetic plasma simulation
journal, May 2008
- Bowers, K. J.; Albright, B. J.; Yin, L.
- Physics of Plasmas, Vol. 15, Issue 5
Foundations of nonlinear gyrokinetic theory
journal, April 2007
- Brizard, A. J.; Hahm, T. S.
- Reviews of Modern Physics, Vol. 79, Issue 2
Solar wind Turbulent Spectrum at Plasma Kinetic Scales
journal, November 2012
- Alexandrova, O.; Lacombe, C.; Mangeney, A.
- The Astrophysical Journal, Vol. 760, Issue 2
Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995
- Goldreich, P.; Sridhar, S.
- The Astrophysical Journal, Vol. 438
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries
book, January 1997
- Balay, Satish; Gropp, William D.; McInnes, Lois Curfman
- Modern Software Tools for Scientific Computing
Extended magnetohydrodynamics with embedded particle‐in‐cell simulation of Ganymede's magnetosphere
journal, February 2016
- Tóth, Gábor; Jia, Xianzhe; Markidis, Stefano
- Journal of Geophysical Research: Space Physics, Vol. 121, Issue 2
A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
journal, January 1947
- Crank, J.; Nicolson, P.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 43, Issue 1
The Solar Wind as a Turbulence Laboratory
journal, January 2005
- Bruno, Roberto; Carbone, Vincenzo
- Living Reviews in Solar Physics, Vol. 2
Electron Acceleration in the Heart of the Van Allen Radiation Belts
journal, July 2013
- Reeves, G. D.; Spence, H. E.; Henderson, M. G.
- Science, Vol. 341, Issue 6149
Nature of Subproton Scale Turbulence in the Solar Wind
journal, May 2013
- Chen, C. H. K.; Boldyrev, S.; Xia, Q.
- Physical Review Letters, Vol. 110, Issue 22
Spectral velocity discretizations for the Vlasov-Maxwell equations
journal, January 1996
- Holloway, James Paul
- Transport Theory and Statistical Physics, Vol. 25, Issue 1
Kinetic Alfvén wave revisited
journal, July 1999
- Hollweg, Joseph V.
- Journal of Geophysical Research: Space Physics, Vol. 104, Issue A7
Two-way coupling of a global Hall magnetohydrodynamics model with a local implicit particle-in-cell model
journal, July 2014
- Daldorff, Lars K. S.; Tóth, Gábor; Gombosi, Tamas I.
- Journal of Computational Physics, Vol. 268
Viriato : A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics
journal, September 2016
- Loureiro, N. F.; Dorland, W.; Fazendeiro, L.
- Computer Physics Communications, Vol. 206
Electron-scale reduced fluid models with gyroviscous effects
journal, July 2017
- Passot, T.; Sulem, P. L.; Tassi, E.
- Journal of Plasma Physics, Vol. 83, Issue 4
Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
journal, May 2009
- Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
- The Astrophysical Journal Supplement Series, Vol. 182, Issue 1
The Design and Implementation of FFTW3
journal, February 2005
- Frigo, M.; Johnson, S. G.
- Proceedings of the IEEE, Vol. 93, Issue 2
A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind: DISSIPATION OF THE SOLAR WIND
journal, May 2008
- Howes, G. G.; Cowley, S. C.; Dorland, W.
- Journal of Geophysical Research: Space Physics, Vol. 113, Issue A5
Intermittent Dissipation at Kinetic Scales in Collisionless Plasma Turbulence
journal, November 2012
- Wan, M.; Matthaeus, W. H.; Karimabadi, H.
- Physical Review Letters, Vol. 109, Issue 19
Fourier-Hermite Solutions of the Vlasov Equations in the Linearized Limit
journal, January 1967
- Grant, Frederick C.
- Physics of Fluids, Vol. 10, Issue 4
Theory of Space Plasma Microinstabilities
book, January 2009
- Gary, S. Peter
- Cambridge University Press
Works referencing / citing this record:
Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations
journal, August 2019
- Liang, Haoming; Cassak, Paul A.; Servidio, Sergio
- Physics of Plasmas, Vol. 26, Issue 8
Numerical Study of Inertial Kinetic-Alfvén Turbulence
journal, January 2019
- Roytershteyn, Vadim; Boldyrev, Stanislav; Delzanno, Gian Luca
- The Astrophysical Journal, Vol. 870, Issue 2