On self-consistent waves and their stability in warm plasma. Part 1.Construction of the self-consistent waves

Abstract

Following a prescription invoked by Clemmow for cold plasma, we show how the method can be extended for a warm plasma so that self-consistent, large-amplitude, nonlinear waves can be obtained in an otherwise homogeneous, stationary system. Results are given for situations in the presence of an imbedded constant magnetic field. The relationship of phase and amplitude for such waves is more complex than in the cold plasma since the resultsobtained depend to a surprising degree on the form of the distribution functions invoked for the warm plasma, as we demonstrate by specffic example. We have pursued this problem for two reasons: first, Clemmow has noted that the need has arisen for a detailed investigation of the behaviour of large amplitude waves in plasma; secondly, the self- consistent, large-amplitude waves catalogued by Clemmow in the case of a cold plasma, have recently been shown to be highly unstable. The question then arises of a possible stabilizing influence in the case of a warm plasma. In this paper we investigate the first part of this problem: construction of self-consistent waves in warm plasma.