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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];  [2];  [1];  [3];  [4]
  1. School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
  2. (China)
  3. (United States)
  4. 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; 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, E-mail: hongqin@ustc.edu.cn, 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, E-mail: hongqin@ustc.edu.cn, 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. doi:10.1063/1.4935904.
Xiao, Jianyuan, Liu, Jian, He, Yang, Zhang, Ruili, Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, Qin, Hong, E-mail: hongqin@ustc.edu.cn, 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. doi: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, E-mail: hongqin@ustc.edu.cn 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},
journal = {Physics of Plasmas},
number = 11,
volume = 22,
place = {United States},
year = 2015,
month =
}
  • 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 arXiv: 1505.06076 (2015)], which produces fivemore » 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. (C) 2015 AIP Publishing LLC.« less
  • Particle-in-cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretising its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g. 10(9), degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinearmore » Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.« less
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  • An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.