关于旋转粒子的独立绝热不变量的个数
On the number of independent adiabatic invariants for gyrating particles
摘要：
指出所建立的三个绝热不变量是刘维尔意义下的分离不变量。人们普遍认为，点电荷运动的绝热不变量不能超过三个。然而，额外的独立（非分离）绝热不变量确实存在。对于自由运动，角动量分量提供了两个额外的运动常数。这个结果可以推广到Hamilton Jacobi方程。如果存在整体对称性，则独立运动常数的数目减少。对于旋转粒子，忽略陀螺螺旋型不变量，可能存在四个“有用的”不变量。径向漂移不变量，对应于粒子的径向坐标的平均值，是受限回转粒子的运动常数。对于螺旋箍缩的特殊情况，其中每个陀螺中心在没有镜陷获的磁通量表面上移动，径向漂移不变量是陀螺中心的径向坐标。对于螺旋箍缩，由能量、平行速度和径向漂移不变量组成的运动常数组便于模拟平衡。局部麦克斯韦分布函数表示在这组不变量被证明提供MHD型的平衡，它是直接的模型的粒子和场分量的径向分布。
英文摘要：
It is pointed out that the three established adiabatic invariants are separating invariants in the sense of Liouville. It is widely claimed that no more than three adiabatic invariants can exist for the motion of a point charge. However, additional independent (not separating) adiabatic invariants do exist. For a force free motion, the components of angular momentum provide two additional constants of motion. This result can be generalized to the Hamilton Jacobi equation. The number of independent constants of motion is reduced if there is a global symmetry. For a gyrating particle, neglecting a gyro helix type of invariant, four 'useful' invariants could exist. A radial drift invariant, corresponding to the average of the radial coordinate of the particle, is a constant of motion for a confined gyrating particle. For the special case of a screw pinch where each gyro center moves on a magnetic flux surface without mirror trapping, the radial drift invariant is the radial coordinate of the gyro center. For a screw pinch, the set of constants of motion consising of the energy, parallel velocity and radial drift invariant is convenient to model the equilibrium. Local Maxwellian distribution functions expressed in this set of invariants are demonstrated to provide MHD-type of equilibria, for which it is straightforward to model the radial profiles of the particle and field components.
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