Реферат: The Vlasov - Poisson model provides a fundamental mathematical framework for describing collisionless, unbounded, electrically neutral plasma in the electrostatic approximation and plays a central role in the theoretical exploration of controlled thermonuclear fusion. The stability of dynamic equilibrium states for this plasma remains a challenging fundamental problem. Classical stability theory (in particular, the sufficient Newcomb - Gardner - Rosenbluth (NGR) condition) guarantees linear stability for dynamic equilibria with monotonically decreasing (single-peaked) distribution functions. The Newcomb - Gardner spectral theorem rules out temporally growing normal-mode perturbations for such equilibrium states, while the Penrose criterion extends these results to a broader class of multi-peaked distribution functions. In this work, we investigate linear stability for a subclass of one-dimensional (1D) dynamic equilibria of the Vlasov - Poisson plasma consisting of electrons and a single ion species. By means of the direct Lyapunov method, we rigorously prove an absolute instability for this subclass of dynamic equilibria, establish sufficient conditions for practical linear instability, and derive an a priori exponential lower estimate on the growth of small 1D perturbations. Our results provide a precise characterization of the limitations for a number of the classical stability statements (namely, for the NGR sufficient condition, the Newcomb - Gardner spectral theorem, and the Penrose criterion). Also, we construct analytical counterexamples that expose the essence of limitations for these statements.

Библиографическая ссылка: Gubarev Y. , Li A.
Study of Linear Two‑Stream Instability for Dynamic Equilibria of the Vlasov - Poisson Plasma in One‑Dimensional Formulation
15th International Conference on Mathematical Modeling in Physical Sciences 02-05 Nov 2026