Linear Instability of Three-Dimensional Dynamic Equilibrium States for Two-Component Vlasov–Poisson Plasma

The problem of controlling plasma is one of the most essential challenges in the creation of experimental facilities for thermonuclear fusion. In this study, a mathematical model of a two-component Vlasov–Poisson plasma is used to study the stability of spatial dynamic equilibria in this plasma. Applying the direct Lyapunov method, we obtain results that demonstrate that three-dimensional (3D) dynamic equilibrium states of the Vlasov–Poisson plasma are absolutely unstable with respect to small spatial perturbations. The sufficient conditions for linear practical instability are obtained for the 3D dynamic equilibria of a two-component Vlasov–Poisson plasma. An a priori exponential lower estimate is constructed, and initial data are found for small spatial perturbations that grow with time. Finally, analytical examples are presented for exact stationary solutions to the mathematical model of Vlasov–Poisson plasma and the growing small 3D perturbations superimposed on these solutions.