Abstract: This report is devoted to considering the stability for exact stationary solutions to equations, which describe the spatial motions of an unbounded collisionless electroneutral fully ionized Vlasov-Maxwell plasma, in relation to small three-dimensional (3D) perturbations using the direct Lyapunov method. We have established a countable set of sufficient conditions for the linear practical instability of dynamic equilibrium states of the Vlasov-Maxwell plasma, which, when they are satisfied, yield an a priori exponential lower estimate for small 3D perturbations growing in time. Analytical examples have been constructed to support our results and indicate that the scope of applicability for the Newcomb-Gardner-Rosenbluth stability condition is limited to incomplete unclosed subclass of small perturbations under study. Furthermore, our findings align perfectly with the classical Earnshaw instability theorem and extend its area of use from electrostatics to electromagnetism and from theoretical mechanics to statistical one. Specifically, the sufficient conditions for linear practical instability found in this study are constructive in character since they may be used as a control and testing mechanism when carrying out physical investigations and performing numerical calculations during developing the operating modes on installations for the controlled thermonuclear fusion realization.

Cite: Zhang Q.
Instability for one partial class of three-dimensional dynamic equilibrium states for the Vlasov-Maxwell plasma
13th International Conference on Mathematical Modeling in Physical Sciences 30 Sep - 3 Oct 2024