Abstract: We consider the linear stability problem for dynamic equilibria of two-component Vlasov-Poisson plasma in cylindrically symmetrical statement. The hydrodynamic substitution of independent variables is performed in order to transform the Vlasov-Poisson equations to an infinite system of gas-dynamic equations. It is important that exact stationary solutions to gas-dynamic equations are equivalent to exact stationary solutions to the Vlasov-Poisson equations. The sufficient condition of linear stability for exact stationary solutions to the Vlasov-Poisson equations is studied. Previously, this condition was not reversed either for small or, especially, for finite perturbations. To fulfill such reversion in the linear approximation, these gas-dynamic equations are linearized near their exact stationary solutions. The a priori exponential estimate from below is constructed for a subclass of small cylindrically symmetrical perturbations of exact stationary solutions to gas-dynamic equations, which grow over time and are described by the field of Lagrangian displacements. The countable set of sufficient conditions for linear practical instability is obtained. Thus, the Newcomb-Gardner-Rosenbluth sufficient condition for linear stability of exact stationary solutions to the Vlasov-Poisson equations is reversed. Moreover, a formal nature of this condition is revealed with respect to the considered small perturbations. As a result, by the direct Lyapunov method, an absolute instability for exact stationary solutions to the mathematical model of two-component Vlasov-Poisson plasma in relation to small cylindrically symmetrical perturbations is proved.

Cite: Gubarev Y.G. , Luo J.
Study of Linear Stability for Cylindrically Symmetrical States of Dynamic Equilibrium of Two-component Vlasov-Poisson Plasma
12th International Conference on Mathematical Modeling in Physical Sciences 28-31 Aug 2023