标题： 托卡马克等离子体中用于精确单粒子轨道模拟的体积保持算法的相位稳定性分析 显示英文标题

标题： Phase Stability Analysis of Volume-preserving Algorithms for Accurate Single Particle Orbit Simulations in Tokamak Plasmas

摘要： 二阶保体积算法（VPAs）用于模拟电磁场中的带电粒子运动，通过使用矩阵分解方法已推广到旋转角度公式。 基于此方法，利用离散傅里叶变换（DFT）技术分析了这类VPAs的相位稳定性。 发现两种显著的VPAs，即$G_h^2$和Boris算法，分别在高频（回旋运动）和低频动力学（穿越/振荡运动）中表现出最佳的相位精度。 这些发现通过数值实验得到了经验验证。 从本研究中获得的见解使可以根据特定物理问题的特征频率选择适当的VPA，这可以显著提高数值精度并改善长期模拟的计算效率。 显示英文摘要

摘要： Second-order Volume-preserving algorithms (VPAs) for simulating charged particle motion in electromagnetic fields have been generalized to a rotating angle formulation by using the matrix decomposition methods. Based on this method, the phase stability of this class of VPAs has been analyzed by using the Discrete Fourier Transformations (DFT) technique. It is found that two prominent VPAs, namely the $G_h^2$ and the Boris algorithm, exhibit optimal phase precision for high-frequency (gyro motion) and low-frequency dynamics (transit/bounce motion), respectively. These findings have been empirically verified through numerical experiments. The insights gained from this study enable the selection of an appropriate VPA for practical simulations based on the characteristic frequencies of specific physics problems, which can substantially enhance numerical accuracy and improve computational efficiency for long-term simulations.