Resonances and oscillatory behavior near multi-species plasma equilibria

Abstract

We consider dynamic multi-species plasma equilibria whose variables depend on a single spatial coordinate and linear perturbations of these. The linearized system may be reduced to a second-order one satisfied by the respective fluid streamfunctions. For the two-species case, the electron mass is a parameter small enough for a WKB asymptotic analysis to be justified. It turns out that the points where either the ion or electron equilibrium velocity equals the ratio between the temporal and transversal frequencies of the perturbation are turning or singular points of the system, connecting exponentially increasing or decreasing solutions to oscillatory ones. The crucial role of singular points in the balance between the different contributions to the electron kinetic energy is explored.