Variable collision frequency effects on hose and sausage instabilities in relativistic electron beams

Abstract

A relativistic electron beam propagating in a dense gas typically ionizes the gas weakly, and the resulting plasma conductivity evolution strongly influences beam stability properties. We note in this paper that the electric field E and the plasma electron temperature Te usually decrease with distance ζ behind the beam head; as a result, the plasma electron neutral collision frequency νm decreases with ζ, which depresses the conductivity σ in the front of the beam and increases σ further back in the beam. We find that this variation of νm, which has generally been ignored in previous models, substantially modifies beam instability evolution. Hose instability growth tends to increase very rapidly in the beam head and taper off to an asymptotic value for large ζ, in contrast to the pure power law growth seen when νm and dσ/dζ are assumed to be constant. A second effect arises from local decreases in the perturbed conductivity σ, produced by perturbed electric field driven increases in the local collision frequency. This destabilizing effect causes the beam to behave as if the monopole conductivity σ0 were replaced by σ*=σ0 [1−(E/νm)(∂νm/∂E)]≡σ0(1−q̄). Analytical models for the case of constant q̄ illustrate the pattern of rapid hose instability growth in the beam head followed by a ‘‘plateau’’ in hose amplitudes that is also observed in hose simulations with the VIPER model. The destabilizing effect of variable νm on the perturbed conductivity also occurs for the resistive sausage instability. However, the model calculation presented here shows that the threshold for sausage instability is not likely to be reached for reasonable beam and plasma parameters.