非均匀非平稳各向异性等离子体中线性波action的朗道衰减
Linear wave action decay entailed by Landau damping in inhomogeneous, nonstationary and anisotropic plasma
摘要：
本文研究了电子波在无碰撞、非均匀、非平稳、各向异性等离子体中的线性传播。等离子体的特征在于它的分布函数，$f_H$，在零级波振幅。这个分布函数可以任意选择，只要它能解弗拉索夫方程，所有的流体力学量都是从这个分布函数导出的。然后，从线性化的电子运动方程和高斯定律，推导出波振幅的包络方程，假定其随时间和空间尺度的演化比波的振荡周期大得多。包络方程可以被转换成一个方程的波的作用，从惠瑟姆的变分原理，证明了行动衰减由于朗道阻尼。此外，在波数和频率变化的一阶朗道阻尼率推导。作为简要讨论，本文概括了许多以前的作品在这个问题上，提供了一个理论基础的启发式参数有关的行动衰减，也解决了传播的外部驱动波。
英文摘要：
This paper addresses the linear propagation of an electron wave in a collisionless, inhomogeneous, nonstationary and anisotropic plasma. The plasma is characterized by its distribution function, $f_H$, at zero order in the wave amplitude. This distribution function, from which are derived all the hydrodynamical quantities, may be chosen arbitrarily, provided that it solves Vlasov equation. Then, from the linearized version of the electrons equation of motion, and from Gauss law, is derived an envelope equation for the wave amplitude, assumed to evolve over time and space scales much larger than the oscillation periods of the wave. The envelope equation may be cast into an equation for the the wave action, derived from Whitham's variational principle, that demonstrates the action decay due to Landau damping. Moreover, the Landau damping rate is derived at first order in the variations of the wave number and frequency. As briefly discussed, this paper generalizes numerous previous works on the subject, provides a theoretical basis for heuristic arguments regarding the action decay, and also addresses the propagation of an externally driven wave.
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