Abstract: In this paper, we consider the linear stability problem for spatial dynamic equilibrium states of a two-component Vlasov-Poisson plasma in a cylindrically symmetrical statement. By using the direct Lyapunov method, we demonstrate that cylindrically symmetrical dynamic equilibria of two-component Vlasov-Poisson plasma are absolutely unstable in relation to small cylindrically symmetrical perturbations. We obtain sufficient conditions for linear practical instability of exact stationary solutions to the Vlasov-Poisson equations. The Newcomb-Gardner-Rosenbluth sufficient condition for linear stability of exact stationary solutions to the Vlasov-Poisson equations is reversed, and we deduce the a priori exponential lower estimate for growing small perturbations.

Cite: Gubarev Y.G. , Luo J.
On instability for cylindrically symmetrical dynamic equilibria of two-component Vlasov-Poisson plasma in linear approximation
14th International Conference on Mathematical Modeling in Physical Sciences 20-23 Oct 2025