Longitudinal plasma oscillations

The present paper is a coherent account of various aspects of longitudinal oscillations in one and two component plasmas. A discussion is offered of dispersion equations, conditions necessary for the growth or decay of oscillations, the physical mechanisms of growing or damping, and the possibility of arbitrary steady-state solutions. The physical situation is described in terms of Poisson's equation and the Boltzmann equation, while the mathematical description is in terms of solutions of an initial-value problem in the small amplitude (linearized) approximation. Some general results are derived for an arbitrary unperturbed velocity distribution of electrons and ions. From these expressions the customary results for a stationary plasma in thermal equilibrium can readily be obtained. For simplicity, one dimensional motion of a simple one component plasma is treated in detail; appropriate generalizations for two or more component plasmas (electrons and ions) are, however, indicated in text. Collisions between particles and non-linear effects are not considered, nor are the effects of external electric or magnetic fields.