磁场中带电粒子运动的李变换微扰理论修正
Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field
AI总结：
针对磁场中带电粒子引导中心运动的传统李变换微扰理论的排序不一致问题，修正相关近恒等变换规则，实现漂移运动一阶描述，解决两类处理方法的不一致问题。
摘要：
本文指出，针对磁场中带电粒子引导中心运动的传统李变换微扰理论存在排序不一致问题，需要进行修正，原因有两点。首先，必须考虑回旋相位的时间变化与其他相空间坐标的时间变化之间的排序差异。其次，需要注意函数导数的参数极限并不等价于极限函数的导数这一重要事实。考虑到这些情况后，本文对与拉格朗日量相关的一种1-形式的近恒等变换规则进行了修正。采用修正后的近恒等变换规则，带电粒子的漂移运动可在一阶近似下描述，而非像传统公式那样需要通过繁琐的展开过程在二阶及更高阶近似下才能描述。这一结果解决了磁场中带电粒子运动的拉格朗日微扰理论中直接处理方法与李变换处理方法之间的不一致问题。
英文摘要：
It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering difference between the temporal variation of gyrophase and that of the other phase space coordinates needs to be taken into account. Second, it is also important to note that the parametric limit of the derivative of a function is not equivalent to the derivative of the limit function. When these facts are taken into account, the near identity transformation rule for one form related to the Lagrangian is modified. With the modified near identity transformation rule, the drift motion of charged particles can be described in the first order, instead of in the second order and beyond through a tedious expansion process as in the conventional formulation. This resolves the discrepancy between the direct and Lie transform treatments in the Lagrangian perturbation theory for charged particle motion in a magnetic field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
