Quasi-Linear Theory of Plasma Waves

Abstract

The quasi-linear theory of plasma waves in a collision-free plasma is formulated in such a way that corrections to the adiabatic assumption and those due to nonlinear effects can be readily estimated in terms of the properties of the initial spatially homogeneous part of the distribution function. Decaying Fourier components of the electric field are treated in a uniform way with unstable Fourier components. It is shown that the case of a three-dimensional plasma is qualitatively different from a one-dimensional plasma, the former leading to a decay to zero of the fluctuating electric field.