Gubarev Y.G.   Светоносов А.И.  

On the Instability for 1–D States of Dynamical Equilibrium of the Vlasov–Poisson Plasma

Reporter: Gubarev Y.G.

The Vlasov-Poisson plasma model is one of basic mathematical models of plasma physics. This is due to its simplicity, clarity and usefulness for solving of the problem of controlled thermonuclear fusion.
The Vlasov-Poisson plasma model is studied for a long time. However, only sufficient conditions of the stability for a number of dynamic equilibrium states with respect to perturbations of incomplete open-ended subclasses were established.
In this report, it is proved by the direct Lyapunov method that some 1-D states of dynamic equilibrium of the Vlasov-Poisson plasma are absolutely unstable in relation to the same 1-D small perturbations. At that, the known sufficient condition of the linear stability for these states is turned, and the range of its applicability is described. We obtained sufficient conditions of the linear practical instability, constructed the a priori exponential lower estimate and characterized initial data for growing small perturbations too.
According to authors, these results may be useful in the process of mathematical modeling of various physical phenomena in plasma and during the creation of pilot plants for controlled thermonuclear fusion.

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