Binary-pairing Monte-Carlo methods are widely used in particle-in-cell codes to capture effects of small angle Coulomb collisions. These methods preserve momentum and energy exactly when the simulation particles have equal weights. However, when the interacting particles are of varying weight, these physical conservation laws are only preserved on average. Here, we 1) extend these methods to weighted particles such that the scattering physics is correct on average, and 2) describe a new method for adjusting the particle velocities post scatter to restore exact conservation of momentum and energy. The efficacy of the model is illustrated with various test problems.
Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
本文为等离子体动力学模型中库仑碰撞的离散化提供了新的见解。基于以前的工作[Carrillo et al. J. Comp. Phys. X 7：100066（2020），Hirvijoki and Burby Phys. Plasmas 27（8）：082307（2020）]，我提出了标准Landau碰撞算子和静电回旋Landau算子的确定性离散时间能量和正性保持，熵耗散标记粒子方案。在标准朗道算子的情况下，该方案还保留了离散时间的动力学动量。这些改进，[Carrillo et al. J. Comp. Phys. X 7：100066（2020），Hirvijoki and Burby Phys. Plasmas 27（8）：082307（2020）]中的结构保持离散化到离散时间的扩展，通过利用所涉及的碰撞算子和所谓的离散梯度积分器的底层metriplectic结构而成为可能。
An $O(\log N)$ Monte Carlo method for periodic Coulomb systems
Center for Computational Mathematics, Flatiron Institute, Simons Foundation（西蒙斯基金会平顿研究所计算数学中心）；School of Mathematical Sciences, MOE-LSC and CMA-Shanghai, Shanghai Jiao Tong University（上海交通大学数学科学学院，教育部重点实验室与上海计算数学与应用数学研究院）
Direct simulation Monte Carlo schemes for Coulomb interactions in plasmas
Université de Toulouse（图卢兹大学；UPS，INSA，UT1，UTM；图卢兹数学研究所）；UPS, INSA, UT1, UTM（加州大学洛杉矶分校数学系）；Institut de Mathématiques de Toulouse（费拉拉大学数学系和CMCS）；Mathematics Department, University of California, Los Angeles (UCLA)；Mathematics Department and CMCS, University of Ferrara
