The unstable modes of a two-component electron plasma

Abstract

In this paper we investigate the linear generation of electrostatic waves in a homogeneous, collisionless, unmagnetized plasma with two Maxwellian electron components, one drifting with respect to the other. The ions are assumed to be infinitely massive. It is shown that such a system may be unstable to a beam mode rather than the well-known Langmuir mode, if the drifting electron component is sufficiently dense and has a sufficiently low temperature. This ‘electron-beam instability’ is driven by the free energy in the particle distribution, and the associated phase velocity is greater than the electron thermal speed. The dispersion characteristics of the electron-beam instability and the Langmuir instability at the critical drift velocity for wave growth are determined for a wide range of parameters. The results of our investigation are applied to electron beams producing hard X-ray emission in solar flares, and it is argued that such beams may be unstable to the generation of electrostatic waves at frequencies below the electron plasma frequency.