Variable Collision Frequency Effects on Hose and Sausage Instabilities in Relativistic Electron Beams

摘要

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. The electric field E and the plasma electron temperature T sub e usually decrease with the distance zeta behind the beam head; as a result, the plasma electron-neutral collision frequency Nu sub m decreases with zeta, which depresses the conductivity sigma in the front of the beam and increases sigma further back in the beam. This variation of nu sub m, 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 zeta in contrast to the pure power law growth seen when d(sigma)/d (zeta) are assumed to be constant. A second effect arises from local decreases in the perturbed conductivity sigma I 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 sigma sub 0 were replaced. Analytical models for the case of constant perturbation illustrate the pattern of rapid hose instability growth in the beam head followed by a plateu in hose amplitudes that is also observed in hose simulations with the VIPER model. The destabilizing effect of variable nu sub m 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.