Nonlinear stability of a Vlasov equation for magnetic plasmas

Frédérique Charles; Bruno Després; Benoît Perthame; Rémis Sentis

doi:10.3934/krm.2013.6.269

Article Contents

2013, Volume 6, Issue 2: 269-290. Doi: 10.3934/krm.2013.6.269

This issue Previous Article Large deviations for the solution of a Kac-type kinetic equation Next Article The moment guided Monte Carlo method for the Boltzmann equation

Nonlinear stability of a Vlasov equation for magnetic plasmas

1.
UPMC-Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 4, pl. Jussieu F75252 Paris cedex 05
2.
INRIA Rocquencourt, BANG project-team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex

Received: April 2012

Revised: November 2012

Published: June 2013

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: 35B35, 35L60, 82D10.

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