Damping of Plasma Oscillations in the Linear Theory

Abstract

The problem of stable oscillations of an infinite plasma is re-examined from the standpoint of an integral equation for the electric potential in the plasma. The behavior of a plasma with a Lorentz distribution is solved completely. We show how one may compute, under suitable restriction, the initial velocity distribution when the electric potential has been specified for all time. We then solve for an initial velocity distribution which yields an electric potential which is nonoscillatory in character and damps as a Gaussian distribution in time; the initial velocity distribution is proved to be an entire function in velocity space. Since this result is contrary to that of Landau, we re-examine his method of determining the electric potential.