论文标题
测试粒子模拟的保守特征：I。在酒杯坐标中的规范和非规范指南中心模型
Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates
论文作者
论文摘要
Boozer中的指导中心（GC）Lagrangian可以通过消除包含磁场载体的磁场载体的协变量$ b_ {ψ_{\ rm p}} $的术语来将其置于规范的形式中。考虑在存在具有固定振幅，固定频率和单个环形模式数字$ n $的剪切alfvén波场的情况下，我们显示使用有或没有$ b_ {ψ_{\ rm p}} $的模拟实际上实际上是相同的谐振和非共振gc orbits。数值结果与理论分析（在附录中呈现）一致，该分析表明，具有$ b_ {ψ_{\ rm p}} $保留的未删节的GC Lagrangian保留的运动方程，具有汉密尔顿流动的两个关键特性：（i）相位空间保护，II）能量，（II）。作为反例，我们还显示了能源保护（II）或保护法（i）和（ii）都通过省略某些小术语而破坏的情况。在测试模拟代码的保守性特征时，发现不类似等离子体的正常模式的扰动是有益的。当人们使用非正常模式检查波颗粒相互作用时，偏差会增强，因此更容易发现。
The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating a term containing the covariant component $B_{Ψ_{\rm P}}$ of the magnetic field vector with respect to the poloidal flux function $Ψ_{\rm P}$. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency and a single toroidal mode number $n$, we show that simulations using the code ORBIT with and without $B_{Ψ_{\rm P}}$ yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the Appendix), which show that the unabridged GC Lagrangian with $B_{Ψ_{\rm P}}$ retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation, and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) & (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen)modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.
