Plasma Oscillations: II. Kinetic theory of waves in plasmas

Abstract

This work is the second part (and chapter VI) of a three-part series reviewing the subject of plasma oscillations. Part I (Nuclear Fusion 1 (1960) 3) was devoted to the macroscopic theory of plasmas in general, and plasma waves in particular, in both collision-free and collision-dominated plasmas, with and without magnetic fields, in some cases with boundaries and spatial gradients. The present article is concerned mostly with the kinetic theory of collision-free plasmas in the absence of magnetic fields, boundaries and spatial gradients and with neglect of the coupling with the radiation field. It is this area that has been most extensively expounded and that can be adapted to a heuristic theory of the non-equilibrium statistical mechanics of plasmas. The plan of the work is as follows: First the small longitudinal oscillations of an infinite homogeneous collisionless plasma are considered. Clearly the model requires that the frequency of collisions, Coulomb or other, be much smaller than the characteristic frequencies and growth rates of the system. The general theory is applied to an investigation of the stability of such systems and the polarization of its environment by a test charge. The latter provides the basic data for a heuristic theory of the non-equilibrium statistical mechanics of plasmas, which yields, for instance, a derivation of the Fokker-Planck equation with polarization corrections and a treatment of fluctuation phenomena in plasmas. This last is applied to the theory of the experimentally interesting phenomenon of the scattering of light by plasmas. The phenomenon of Landau damping has been treated both by the Laplace-transform technique and the normal-mode technique, and the equivalence of both methods has been shown. A special class of finite-amplitude electrostatic waves has been treated, and its relation to the normal modes of the linearized equations has been given. Also plasma oscillations of a large number of electron beams are considered, and the limit of an infinite number of beams is shown to yield the results of a plasma with a continuous velocity distribution.