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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https://hal.archives-ouvertes.fr/hal-00689810
Contributeur : Frédérique Charles <>
Soumis le : vendredi 20 avril 2012 - 11:30:58
Dernière modification le : lundi 29 mai 2017 - 14:25:07
Document(s) archivé(s) le : samedi 21 juillet 2012 - 02:27:58

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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. 〈http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8318〉. 〈10.3934/krm.2013.6.269〉. 〈hal-00689810〉

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