Linearized Theory of Plasma Oscillations

Abstract

The basic hydrodynamic and Maxwellian equations found in the linearized theory of plasma oscillations are derived. An attempt is made to elucidate the relations between different approaches for investigating linearized theory. The possible basic modes of plasma oscillations are discussed. Longitudinal oscillations are discussed. Longitudinal oscillations and the variation of pressure accompanying the longitudinal waves are considered. The influence of the introduction of damping terms in the equation of motion is discussed. The treatment of plasmas with nonzero magnetic fields is discussed relative tc motios perpendicular to the propagation direction of longitudinal waves and the case of transverse waves and motions parallel and perpendicular to their direction of propagation. The relation between Alfven's magntohydrodynamics and linearized theory of plasma oscillations was established. A kinetic theory treatment of plasma oscillations is given to show what restrictions on the shape of the velocity distribution of electrons are necessary for the hydrodynamic treatment to be valid. The cases treated by kinetic theory include: the distribution function in longitudinal oscillations, velocity distributions for transverse oscillations, and oscillations with a constant magnetic field. (C.J.G.)