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Adaptive time-stepping Monte Carlo integration of Coulomb collisions

机译：自适应时间踩踏蒙特卡罗集合的库仑碰撞

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AbstractWe report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell–Jüttner statistics. The implementation is based on the Beliaev–Budker collision integral which allows both the test particle and the background plasma to be relativistic. The integration method supports adaptive time stepping, which is shown to greatly improve the computational efficiency. The Monte Carlo method is implemented for both the three-dimensional particle momentum space and the five-dimensional guiding center phase space.Detailed description is provided for both the physics and implementation of the operator. The focus is in adaptive integration of stochastic differential equations, which is an overlooked aspect among existing Monte Carlo implementations of Coulomb collision operators. We verify that our operator converges to known analytical results and demonstrate that careless implementation of the adaptive time step can lead to severely erroneous results.The operator is provided as a self-contained Fortran 95 module and can be included into existing orbit-following tools that trace either the full Larmor motion or the guiding center dynamics. The adaptive time-stepping algorithm is expected to be useful in situations where the collision frequencies vary greatly over the course of a simulation. Examples include the slowing-down of fusion products or other fast ions, and the Dreicer generation of runaway electrons as well as the generation of fast ions or electrons with ion or electron cyclotron resonance heating.
机译：<！[cdata [ Abstract 我们报告了一个可访问和强大的工具，用于评估obeys Maxwell-jüttner统计数据的等离子体中的库仑冲突对测试粒子的影响。该实施基于Beliaev-Budker碰撞积分，其允许测试粒子和背景等离子体均为相对论。集成方法支持自适应时间踩踏，这被示出大大提高计算效率。 Monte Carlo方法是为三维粒子动量空间和五维引导中心相空间实现的。 提供了用于操作员的物理和实现的详细描述。重点是随机微分方程的自适应集成，这是库仑碰撞运算符的现有蒙特卡罗实现中的被忽略的方面。我们确认我们的操作员会聚到已知的分析结果，并证明了自适应时间步骤的粗心执行可能导致严重错误的结果。 操作员作为自包含Fortran 95模块提供，并且可以包含在追踪完整的Larmor运动或引导中心动态的现有轨道上的工具中。预期自适应时间步进算法在碰撞频率在模拟过程中变化的情况下是有用的。实例包括融合产物或其他快速离子的减速，以及失控电子的干燥器产生以及具有离子或电子回旋共振加热的快速离子或电子。

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