论文标题
相对论轨迹和旋转动力学的显式批量保护数值方案
Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics
论文作者
论文摘要
使用Lorentz-BMT方程在Baylis的Clifford代数表示中制定了一类显式数值方案，以解决电磁场中颗粒的相对论动力学和自旋。已经证明，这些数值方法让人联想到跨越和verlet方法，共享许多重要的属性：它们是能量持续的，音量支持和二阶收敛的。通过对恒定均匀的电动力场中的已知分析溶液进行基准测试，从经验上分析了这些特性。证明，与鲍里斯推动器相比，恒定磁场中的数值误差长时间模拟，其角误差随时间而线性增加。最后，在平面波场配置中研究了粒子的复杂自旋动力学。
A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy-conserving, volume-conserving and second order convergent. These properties are analysed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane wave field configuration.
