论文标题
明确可解决的能源持续算法用于磁化等离子体中的音调角散射
An Explicitly Solvable Energy-Conserving Algorithm for Pitch-Angle Scattering in Magnetized Plasmas
论文作者
论文摘要
我们为随机微分方程（SDE）开发了一种明确可解决的能量持持续算法（ESEC）算法，该方程描述了磁化等离子体中的音调角散射过程。 Cayley变换用于计算确定性的旋转和随机散射，从而提供算法可显式解决并确切地保护能量。 SDE对于音高角散射的异常特性是其系数在零速度上发散，并且不满足全局Lipschitz条件。因此，当应用标准数值方法（例如Euler-Maruyama（EM））时，很难建立数值收敛。对于拟议的ESEC算法，其能源保存的财产使我们能够克服这一障碍。我们严格地证明ESEC算法是1/2阶的强烈收敛。详细的数值研究证实了这一结果。对于具有恒定磁场的磁化等离子体中的俯仰角散射的情况，对分析解决方案进行了基准测试，并找到了出色的协议。
We develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.
