Saturation of electrostatic instability in two-species plasma

Abstract

We explore the level of saturation of instabilities in a two-species plasma using a combination of matched asymptotic expansion and numerical computation. The plasma is assumed to be spatially periodic, and the domain size is chosen to allow a single mode to become unstable when a bump is added to the tail of the distribution of the lighter species. We consider two versions of the problem, arising when the mass ratio of the two species is either very small, or of the order of unity. For small mass ratios, the initial saturation level of the mode amplitude, as measured by the electric field disturbance, follows the ‘trapping scaling’. For mass ratios of order unity, nonlinear effects become important at the level predicted by Crawford and Jayaraman, but the instability does not saturate there and continues to grow. In both cases, the initial onset of nonlinearity does not reflect the longer- time evolution of the system. In fact, the system passes through multiple stages of evolution in which the electric field amplitude is not simply predicted; none of the previously published scalings are adequate. Eventually, for both cases, the distribution of the lighter ions becomes significantly rearranged, and much (though not all) of the destabilizing bump is flattened. A better predictor of the strength of the instability is given by the extent of these rearrangements.