Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems
Abstract
Explicit highorder noncanonical symplectic particleincell algorithms for classical particlefield systems governed by the VlasovMaxwell equations are developed. The algorithms conserve a discrete noncanonical symplectic structure derived from the Lagrangian of the particlefield system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with highorder interpolating differential forms for a cubic grid. The resulting timedomain Lagrangian assumes a noncanonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structurepreserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble subsystems, and highorder structurepreserving algorithms follow by combinations. The explicit, highorder, and conservative nature of the algorithms is especially suitable for longterm simulations of particlefield systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.
 Authors:
 School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
 (China)
 (United States)
 LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190 (China)
 Publication Date:
 OSTI Identifier:
 22489840
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; BERNSTEIN MODE; BOLTZMANNVLASOV EQUATION; COMPUTERIZED SIMULATION; DEGREES OF FREEDOM; ELECTROMAGNETIC FIELDS; ELECTRONS; GAUGE INVARIANCE; LAGRANGIAN FUNCTION; LANDAU DAMPING; NONLINEAR PROBLEMS; PLASMA WAVES; SUPERCOMPUTERS
Citation Formats
Xiao, Jianyuan, Liu, Jian, He, Yang, Zhang, Ruili, Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, Qin, Hong, Email: hongqin@ustc.edu.cn, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, and Sun, Yajuan. Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems. United States: N. p., 2015.
Web. doi:10.1063/1.4935904.
Xiao, Jianyuan, Liu, Jian, He, Yang, Zhang, Ruili, Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, Qin, Hong, Email: hongqin@ustc.edu.cn, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, & Sun, Yajuan. Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems. United States. doi:10.1063/1.4935904.
Xiao, Jianyuan, Liu, Jian, He, Yang, Zhang, Ruili, Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, Qin, Hong, Email: hongqin@ustc.edu.cn, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, and Sun, Yajuan. 2015.
"Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems". United States.
doi:10.1063/1.4935904.
@article{osti_22489840,
title = {Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems},
author = {Xiao, Jianyuan and Liu, Jian and He, Yang and Zhang, Ruili and Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026 and Qin, Hong, Email: hongqin@ustc.edu.cn and Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 and Sun, Yajuan},
abstractNote = {Explicit highorder noncanonical symplectic particleincell algorithms for classical particlefield systems governed by the VlasovMaxwell equations are developed. The algorithms conserve a discrete noncanonical symplectic structure derived from the Lagrangian of the particlefield system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with highorder interpolating differential forms for a cubic grid. The resulting timedomain Lagrangian assumes a noncanonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structurepreserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble subsystems, and highorder structurepreserving algorithms follow by combinations. The explicit, highorder, and conservative nature of the algorithms is especially suitable for longterm simulations of particlefield systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave.},
doi = {10.1063/1.4935904},
journal = {Physics of Plasmas},
number = 11,
volume = 22,
place = {United States},
year = 2015,
month =
}

Explicit highorder noncanonical symplectic particleincell algorithms for VlasovMaxwell systems
Explicit highorder noncanonical symplectic particleincell algorithms for classical particlefield systems governed by the VlasovMaxwell equations are developed. The algorithms conserve a discrete noncanonical symplectic structure derived from the Lagrangian of the particlefield system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with highorder interpolating differential forms for a cubic grid. The resulting timedomain Lagrangian assumes a noncanonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structurepreserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces fivemore » 
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