ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

doi:10.1088/1674-1056/abefc7

中国物理B ›› 2021, Vol. 30 ›› Issue (9): 95201-095201.doi: 10.1088/1674-1056/abefc7

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

Yifeng Zheng(郑艺峰), Jianyuan Xiao(肖建元)^†, Yanpeng Wang(王彦鹏), Jiangshan Zheng(郑江山), and Ge Zhuang(庄革)

School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China

收稿日期:2020-11-16 修回日期:2021-03-15 接受日期:2021-03-18 出版日期:2021-08-19 发布日期:2021-08-19
通讯作者: Jianyuan Xiao E-mail:xiaojy@ustc.edu.cn
基金资助:
Project supported by the National MCF Energy R&D Program of China (Grant No. 2018YFE0304100), the National Key Research and Development Program of China (Grant Nos. 2016YFA0400600, 2016YFA0400601, and 2016YFA0400602), and the National Natural Science Foundation of China (Grant Nos. NSFC-11805273 and NSFC-11905220).

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

Yifeng Zheng(郑艺峰), Jianyuan Xiao(肖建元)^†, Yanpeng Wang(王彦鹏), Jiangshan Zheng(郑江山), and Ge Zhuang(庄革)

School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China

Received:2020-11-16 Revised:2021-03-15 Accepted:2021-03-18 Online:2021-08-19 Published:2021-08-19
Contact: Jianyuan Xiao E-mail:xiaojy@ustc.edu.cn
Supported by:
Project supported by the National MCF Energy R&D Program of China (Grant No. 2018YFE0304100), the National Key Research and Development Program of China (Grant Nos. 2016YFA0400600, 2016YFA0400601, and 2016YFA0400602), and the National Natural Science Foundation of China (Grant Nos. NSFC-11805273 and NSFC-11905220).

摘要/Abstract

摘要： A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations (ISSDE), is developed for solving stochastic differential equations (SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker-Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge-Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.

关键词: Fokker-Planck equation, Stratonovich SDE, implicit, slowing down process

Abstract: A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations (ISSDE), is developed for solving stochastic differential equations (SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker-Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge-Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.

Key words: Fokker-Planck equation, Stratonovich SDE, implicit, slowing down process

中图分类号: (Electron collisions)

52.20.Fs

52.25.Xz (Magnetized plasmas) 52.40.Mj (Particle beam interactions in plasmas) 52.50.Gj (Plasma heating by particle beams)

Yifeng Zheng(郑艺峰), Jianyuan Xiao(肖建元), Yanpeng Wang(王彦鹏), Jiangshan Zheng(郑江山), and Ge Zhuang(庄革). ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision[J]. 中国物理B, 2021, 30(9): 95201-095201.

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ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

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