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.

Monte Carlo 隐式模拟程序，即隐式 Stratonovich 随机微分方程 (ISSDE)，用于求解描述具有库仑碰撞的等离子体的随机微分方程 (SDE)。该程序的基本思想是 Fokker-Planck 方程和 Stratonovich SDE 之间的随机等价。分裂方法用于增加库仑碰撞带电粒子动力学算法的数值稳定性。考虑了洛伦兹等离子体、麦克斯韦等离子体和背景等离子体的任意分布函数的情况。隐式中点方法的采用保证了扩散项的能量守恒，从而与传统的 Runge-Kutta 方法相比提高了数值稳定性。ISSDE 使用 C++ 构建，具有标准接口和可扩展模块。利用ISSDE研究了非磁化等离子体中电子束的减速过程和磁化等离子体中的弛豫过程，表明了其正确性和可靠性。