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Nonlinear stability of a Vlasov equation for magnetic plasmas

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.
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Contributor : Frédérique Charles Connect in order to contact the contributor
Submitted on : Friday, April 20, 2012 - 11:30:58 AM
Last modification on : Sunday, June 26, 2022 - 5:16:40 AM
Long-term archiving on: : Saturday, July 21, 2012 - 2:27:58 AM


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Frédérique Charles, Bruno Després, Benoît Perthame, Remi Sentis. Nonlinear stability of a Vlasov equation for magnetic plasmas. Kinetic and Related Models , AIMS, 2013, 6 (2), pp.269 - 290. ⟨10.3934/krm.2013.6.269⟩. ⟨hal-00689810⟩



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