ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

doi:10.19596/j.cnki.1001-246x.7843

计算物理 ›› 2019, Vol. 36 ›› Issue (3): 265-279.DOI: 10.19596/j.cnki.1001-246x.7843

ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

郑艺峰¹, 王雨雷¹, 刘健¹, 秦宏^1,2

1. 中国科学技术大学近代物理系和核科学与技术系, 合肥安徽 230026;
2. Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA

收稿日期:2018-02-08 修回日期:2018-06-25 出版日期:2019-05-25 发布日期:2019-05-25
通讯作者: 王雨雷,E-mail:wyulei@ustc.edu.cn
作者简介:郑艺峰(1991-),男,硕士研究生,从事等离子体先进几何算法模拟研究,E-mail:Zyifeng@mail.ustc.edu.cn
基金资助:
国家自然科学基金（NSFC-11575185，11575186）、国家磁约束聚变能源研究项目（2015GB111003）、国家重点研究发展计划（2016YFA0400600，2016YFA0400601，2016YFA0400602）、GeoAlgorithmic Plasma Simulator （GAPS）、中科院前沿科学重点研究项目（QYZDB-SSW-SYS004）资助项目

ISSDE: First-principles Implicit Simulations Based on Stratonovich SDE Approach of Coulumb Collision

ZHENG Yifeng¹, WANG Yulei¹, LIU Jian¹, QIN Hong^1,2

1. School of Nuclear and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China;
2. Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA

Received:2018-02-08 Revised:2018-06-25 Online:2019-05-25 Published:2019-05-25

摘要/Abstract

摘要： 开发一种适用于求解含库仑碰撞等离子体随机微分方程（SDE）的第一性原理隐式模拟程序——Implicit Stratonovich Stochastic Differential Equations （ISSDE）.该程序基于Fokker-Planck （FP）方程与Stratonovich SDE的等价性理论，通过精确求解Stratonovich SDE达到对FP方程的高效第一性原理计算的目标.ISSDE采用隐式格式保证求解的数值稳定性，同时可以保证粒子碰撞过程的能量守恒.ISSDE基于C++语言开发，具有标准接口和灵活的可扩展模组.通过模拟电子束在非磁化和磁化致密等离子体中的慢化过程验证ISSDE的正确性，并展示该程序在碰撞等离子体模拟中的应用.

关键词: Fokker-Planck方程, Stratonovich SDE, 隐式, 慢化过程

Abstract: A first-principles implicit simulation program, Implicit Stratonovich Stochastic Differential Equations (ISSDE), is constructed for stochastic differential equations which describes plasmas with Coulomb collision. Basic idea of the program is stochastic equivalence between Fokker-Planck equation and Stratonovich SDE. Implicit discrete method guarantees numerical stability and conservation of kinetic energy. ISSDE is built with C++ language, and is designed to possess standard interfaces and extendible modules. Slowing-down processes of electron beams in both unmagnetized and magnetized plasmas are studied, which shows correctness of ISSDE. It provides a powerful tool for collisional plasmas studies.

Key words: FP equation, Stratonovich SDE, implicit, slowing-down

中图分类号:

郑艺峰, 王雨雷, 刘健, 秦宏. ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟[J]. 计算物理, 2019, 36(3): 265-279.

ZHENG Yifeng, WANG Yulei, LIU Jian, QIN Hong. ISSDE: First-principles Implicit Simulations Based on Stratonovich SDE Approach of Coulumb Collision[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(3): 265-279.

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ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

ISSDE: First-principles Implicit Simulations Based on Stratonovich SDE Approach of Coulumb Collision

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