非定域绝热理论II。多维非均匀等离子体中电子等离子体波的非线性频移
Nonlocal adiabatic theory. II. Nonlinear frequency shift of an electron plasma wave in a multidimensional inhomogeneous plasma
摘要：
在这篇文章中，我们提供了一个一般的推导的非线性频移，$δω$，正弦电子等离子体波（EPW），变化缓慢，足以在配套文件中得出的结果，在行动的分布函数，应用。我们首先考虑的情况下，当EPW单调增长，然后单调衰减的均匀等离子体。在这种情况下，我们在波的频率，它不收敛回其线性值作为波衰减到小振幅的滞后。然后，我们解决的$δω$的EPW，保持增长的一维（1-D）非均匀等离子体的推导。我们发现，通常情况下，频移不仅取决于当地的EPW振幅和波数。它还取决于密度变化的整个历史，正如波所经历的那样。在多维不均匀等离子体中，由$δω$假定的值通常不同于在1-D中导出的值，因为由于横向电子运动，除了等离子体不均匀性之外，还必须考虑$δω$中的滞后。因此，除非EPW在均匀的一维等离子体中保持增长，否则不能导出作为局部波振幅和波数的函数的$δω$ \textit{a priori}。由于作用量分布函数的非定域性，$δω$依赖于EPW振幅和等离子体密度变化的整个历史。
英文摘要：
In this article, we provide a general derivation of the nonlinear frequency shift, $δω$, for a sinusoidal electron plasma wave (EPW) that varies slowly enough for the results derived in the companion paper, on the action distribution function, to apply. We first consider the situation when the EPW monotonously grows and then monotonously decays in a homogeneous plasma. In this situation, we show a hysteresis in the wave frequency, which does not converge back to its linear value as the wave decays to small amplitudes. We then address the derivation of $δω$ for an EPW that keeps growing in a one-dimensional (1-D) inhomogeneous plasma. We show that, usually, the frequency shift does not only depend on the local EPW amplitude and wavenumber. It also depends on the whole history of the density variations, as experienced by the wave. In a multidimensional inhomogeneous plasma, the values assumed by $δω$ are usually different from those derived in 1-D because, due to the transverse electron motion, one must account for the hysteresis in $δω$ in addition to plasma inhomogeneity. Hence, unless the EPW keeps growing in a homogeneous one-dimensional plasma, one cannot derive $δω$ \textit{a priori} as a function of the local wave amplitude and wavenumber. Due to the nonlocality in the action distribution function, $δω$ depends on the whole history of the variations of the EPW amplitude and plasma density.
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