论文标题
使用明确解决的能量保存算法模拟螺距角度散射
Simulating Pitch Angle Scattering Using An Explicitly Solvable Energy Conserving Algorithm
论文作者
论文摘要
可以使用Langevin方程来模拟Lorentz运算符下演变的粒子分布函数以进行螺距角散射。这种方法经常用于基于粒子的蒙特卡洛模拟等离子体碰撞等。但是，大多数数值处理不能保证能源节约，这可能导致非物理伪像，例如数值加热和光谱畸变。我们为倾斜角散射的Langevin方程提供了一种新型的结构保存数值算法。与众所周知的鲍里斯算法相似，提出的数值方案在计算速度空间旋转时利用了Cayley变换的结构保存特性。所得算法是可以明确解决的，同时将速度的标准保留到机器精度。我们证明该方法的数值收敛顺序与传统的随机Euler-Maruyama方法相同。数值方案通过模拟粒子梁的螺距角散射并与分析溶液进行比较来基准测试。基准结果表明，与理论预测相吻合，展示了所提出的算法的显着长时间精度。
Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method. The numerical scheme is benchmarked by simulating the pitch angle scattering of a particle beam, and comparing with the analytical solution. Benchmark results show excellent agreement with theoretical predictions, showcasing the remarkable long time accuracy of the proposed algorithm.
