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

doi:10.1088/1674-1056/abefc7

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.

Keywords: Fokker-Planck equation Stratonovich SDE implicit slowing down process

Received: 16 November 2020
Revised: 15 March 2021
Accepted manuscript online: 18 March 2021

PACS:	52.20.Fs	(Electron collisions)
	52.25.Xz	(Magnetized plasmas)
	52.40.Mj	(Particle beam interactions in plasmas)
	52.50.Gj	(Plasma heating by particle beams)

Fund: 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).

Corresponding Authors: Jianyuan Xiao
E-mail: xiaojy@ustc.edu.cn

Cite this article:

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 2021 Chin. Phys. B 30 095201

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

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