Two-flow instability of particular class of one-dimensional dynamic equilibrium states of Vlasov-Poisson plasma

Abstract

The problem on linear stability of the subclass of one–dimensional (1D) states of dynamic equilibrium boundless electrically neutral collisionless plasma in electrostatic approximation (the Vlasov–Poisson plasma) is studied. By the direct Lyapunov method, we prove that these equilibrium states are absolutely unstable relative to small 1D perturbations when the Vlasov–Poisson plasma contains electrons and a single species of ions which stationary distribution functions are isotropic on the physical space but dependent on velocity. We state sufficient conditions for linear practical instability; for small 1D perturbations growing over time, we construct the a priori exponential lower estimate and describe the initial data. In addition, we construct the analytical example of the studied 1D states of dynamic equilibrium and their small perturbations of the same type of symmetry growing over time according to the obtained estimate.