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General formulas for adiabatic invariants in nearly periodic Hamiltonian systems
Journal of Plasma Physics ( IF 2.5 ) Pub Date : 2020-12-17 , DOI: 10.1017/s002237782000080x
J. W. Burby , J. Squire

While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.

中文翻译:

近周期性哈密顿系统中绝热不变量的一般公式

虽然众所周知,每个几乎周期性的哈密顿系统都具有绝热不变量,但现有的计算绝热不变量级数项的方法效率低下。最流行的方法涉及非唯一近恒等坐标变换的繁重中间计算,即使绝热不变量本身是唯一定义的标量。S. Omohundro 开发的一种鲜为人知的方法避免了计算坐标变换的中间序列,但也效率低下,因为它涉及其自己的复杂中间计算序列。为了提高未来绝热不变量计算的效率,我们为绝热不变量级数中的前几项推导出了普遍适用、易于计算的公式。为了证明这些公式的实用性,
更新日期:2020-12-17
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