Phase-space description of plasma waves. Part 1. Linear theory

Abstract

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

Phase-space description of plasma waves. Part 2. Nonlinear theory

“…Assuming linear theory to be valid, in Part 1 of this study (Biro & Ronnmark 1992) we derived a kinetic equation for the density of waves ^V(k.,r,t) in a plasma. Similar equations are well known from the theory of weak plasma turbulence, and have been proposed by, for example, Kadomtsev (1965), Sagdeev & Galeev (1969), Davidson (1972) and Melrose (1980).…”