THE THEORY OF LONGITUDINAL PLASMA OSCILLATIONS IN THE FORMATION OF A RUNAWAY ELECTRON STREAM

Abstract

The theory of longitudinal oscillations accompanying the acceleration of electrons in a neutral plasma is investigated. Particular reference is made to an experiment with a plasma betatron supplemented by a strong longitudinal magnetic field. Various stability criteria are derived which show that for runaway electron streams of interestingly large intensity an interval of instability is always encountered during the initial acceleration. Calculations of the fluctuation energy built up during this interval have been made in order to determine the conditions for which the fluctuation energy is not expected to overtake the drift energy. For a two-stream plasma consisting of the runaway electron stream and a slow ion stream, it is found that even for relatively small accelerating electric fields rather intense runaway streams can escape disruption due to the instability (e.g. for E = 2000 volt m−1 runaway beam densities corresponding to currents of about 4000 amp, at relativistic energies, may be expected to escape disruption). However, if relatively few slow electrons are present in the beam the critical runaway beam density is drastically reduced. The effect of finite rise-time for the accelerating electric field is considered.