On the theory of stationary waves in plasmas

Abstract

Existing theories of stationary plasma oscillations lead to a dispersion equation (2), involving an integration across a pole. It is here shown that this difficulty is of purely mathematical origin, and can be overcome by a proper treatment. This treatment leads to a complete set of stationary solutions, which are much more numerous than the usual plasma oscillations. In particular, their wave lengths and frequencies are not connected by a dispersion equation, but independently assume all real values. Special superpositions of these stationary solutions correspond to the usual plasma oscillations. They constitute slightly damped plane waves, which do obey the dispersion equation (2), the integral being interpreted as a Cauchy principal value. An arbitrary initial distribution behaves (after a short transient time) like a superposition of such waves, as far as the density is concerned.