HAL : hal-00689810, version 1

arXiv : 1204.4613

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Nonlinear stability of a Vlasov equation for magnetic plasmas

Frédérique Charles 1, Bruno Després 1, Benoît Perthame 1, Remi Sentis 2

(20/04/2012)

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.

1 :	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 :	Direction des applications militaires (CEA/DAM)
	CEA

Domaine

:

Mathématiques/Equations aux dérivées partielles

Mots Clés : Vlasov equations – Plasma physics – Kinetic averaging lemma – Maxwell's equations.

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Contributeur : Frédérique Charles <>

Soumis le : Vendredi 20 Avril 2012, 11:30:58

Dernière modification le : Vendredi 20 Avril 2012, 15:05:24