Nonlinear stability of a Vlasov equation for magnetic plasmas

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