用多参数Lie变换法推导陀螺中心轨迹方程
Deriving the trajectory equations of gyrocenter with a multi-parameter Lie transform method
摘要：
指出在电磁扰动存在的情况下，用现代陀螺运动理论导出的生成元的值被拉回变换不当地放大了，并且陀螺中心的轨迹方程中含有非旋度形式的扰动磁矢势项.这些项不是物理项，因为微扰磁矢势可以包含任意的规范项。本文用多参数李变换方法代替了现代陀螺动力学理论中的单参数李变换方法。可以考虑系统的所有特征尺度。该方法借助于一种线性相消规则，将陀螺角$θ$与其余自由度解耦，直到参数的二阶为Larmor半径与平衡磁场横向尺度之比。采用这种新方法，这些非物理项不再出现在轨迹方程中。
英文摘要：
It's pointed out that the values of the generators derived by the modern gyrokinetic theory are inappropriately amplified by the pullback transform with the existence of electromagnetic perturbation, and the trajectory equations of the gyrocenter include terms containing the perturbative magnetic vector potential not in the form of its curl. These terms are not physical ones, as the perturbative magnetic vector potential could include an arbitrary gauge term. In this paper, instead of the single-parameter Lie transform method utilized by the modern gyrokinetic theory, a multi-parameter Lie transform method is utilized. All characteristic scales of the system can be taken into account. With the assistance of a kind of linear cancellation rule, the new method can decouple the gyroangle $θ$ from the remaining degrees of freedom up to the second order of the parameter as the ratio between the Larmor radius and the transverse length scale of the equilibrium magnetic field. With this new method, those nonphysical terms don't appear anymore in the trajectory equations.
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