Symplectic and energy-conserving algorithms for solving magnetic field trajectories.
Symplectic and energy-conserving algorithms for solving magnetic field trajectories.
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DOI：
10.1103/physreve.77.066401
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发表时间：
2008-06
期刊：
影响因子：
--
通讯作者：
S. Chin
中科院分区：
文献类型：
--
作者：
S. Chin
如果经典哈密顿算子是可分的，则经典演化算子的指数分裂得到辛积子。磁场中带电粒子的非正则演化算子的类似分裂产生了精确的节能算法。后一种算法不需要矢量势而直接计算磁场，并且比辛积分器更稳定，相位误差小得多。对于组合电场和磁场，这些非正则演化算子的分离算法既不是完全辛的，也不是完全的能量守恒，但它们在具有定性正确的轨迹和有界周期能量误差方面表现得完全像辛算法。这项工作表明，利用量子力学的角动量算符，可以系统地推导出在一般电场和磁场中求解粒子轨迹的任何阶的指数分裂算法。在这项工作中，算子分析的使用充分理解了电磁力之间的缠绕相互作用，并使推导高度非平凡的积分器成为可能。
The exponential splitting of the classical evolution operator yields symplectic integrators if the canonical Hamiltonian is separable. Similar splitting of the noncanonical evolution operator for a charged particle in a magnetic field produces exact energy-conserving algorithms. The latter algorithms evaluate the magnetic field directly with no need of a vector potential and are more stable with far less phase errors than symplectic integrators. For a combined electric and magnetic field, these algorithms from splitting the noncanonical evolution operator are neither fully symplectic nor exactly energy conserving, yet they behave exactly like symplectic algorithms in having qualitatively correct trajectories and bounded periodic energy errors. This work shows that exponential-splitting algorithms of any order for solving particle trajectories in a general electric and magnetic field can be systematically derived by use of the angular momentum operator of quantum mechanics. The use of operator analysis in this work fully comprehends the intertwining interaction between electric and magnetic forces and makes possible the derivation of highly nontrivial integrators.