非定域绝热理论I. action分布函数
Nonlocal adiabatic theory. I. The action distribution function
摘要：
在本文中，我们解决了带电粒子的运动所采取的正弦静电波，其振幅和相速度变化缓慢的时间足够新绝热理论的应用。此外，我们限制的情况下，只有少数分界线交叉发生，使绝热不变量，$\mathcal{I}$，保持几乎恒定。我们在这里坚持这样一个事实，即$\mathcal{I}$不同于动力作用$I$。特别是，我们表明，$\mathcal{I}$依赖于整个时间的波的变化的历史，而行动通常被定义为一个本地的波的振幅和相速度的函数。此外，我们提供了几个数值结果，显示如何行动的分布函数，$f(I)$，随时间变化，我们解释了如何推导出解析。然后将推导推广到弱非均匀波的情形。
英文摘要：
In this paper, we address the motion of charged particles acted upon by a sinusoidal electrostatic wave, whose amplitude and phase velocity vary slowly enough in time for neo-adiabatic theory to apply. Moreover, we restrict to the situation when only few separatrix crossings have occurred, so that the adiabatic invariant, $\mathcal{I}$, remains nearly constant. We insist here on the fact that $\mathcal{I}$ is different from the dynamical action, $I$. In particular, we show that $\mathcal{I}$ depends on the whole time history of the wave variations, while the action is usually defined as a local function of the wave amplitude and phase velocity. Moreover, we provide several numerical results showing how the action distribution function, $f(I)$, varies with time, and we explain how to derive it analytically. The derivation is then generalized to the situation when the wave is weakly inhomogeneous.
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