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Title: Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

Abstract

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field 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:
; ; ;  [1];  [1];  [2]
  1. School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
  2. 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
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 22; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; BERNSTEIN MODE; BOLTZMANN-VLASOV 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, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, and Sun, Yajuan. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell 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, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, & Sun, Yajuan. Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems. United States. https://doi.org/10.1063/1.4935904
Xiao, Jianyuan, Liu, Jian, He, Yang, Zhang, Ruili, Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, Qin, Hong, Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, and Sun, Yajuan. 2015. "Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems". United States. https://doi.org/10.1063/1.4935904.
@article{osti_22489840,
title = {Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell 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 and Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 and Sun, Yajuan},
abstractNote = {Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field 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},
url = {https://www.osti.gov/biblio/22489840}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 11,
volume = 22,
place = {United States},
year = {2015},
month = {11}
}