Nonlinear stability of a Vlasov equation for magnetic plasmas

TL;DR

This paper analyzes a simplified Vlasov-Maxwell model for magnetic plasmas, demonstrating its nonlinear stability and existence, which aids in understanding plasma behavior in fusion devices without full computational complexity.

Contribution

It introduces and proves the nonlinear stability and existence of a simplified Vlasov-Maxwell model incorporating the Hall effect for magnetic plasmas.

Findings

Model is nonlinear stable based on energy dissipation.

Existence of solutions is rigorously proven.

Provides a mathematically validated simplified plasma model.

Abstract

The mathematical description of laboratory fusion plasmas produced in Tokamaks is still challenging. Complete models for electrons and ions, as Vlasov-Maxwell systems, are computationally too expensive because they take into account all details and scales of magneto-hydrodynamics. In particular, for most of the relevant studies, the mass electron is negligible and the velocity of material waves is much smaller than the speed of light. Therefore it is useful to understand simplified models. Here we propose and study one of those which keeps both the complexity of the Vlasov equation for ions and the Hall effect in Maxwell's equation. Based on energy dissipation, a fundamental physical property, we show that the model is nonlinear stable and consequently prove existence.