Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equationsReport as inadecuate




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1 ICJ - Institut Camille Jordan Villeurbanne 2 IRMAR - Institut de Recherche Mathématique de Rennes

Abstract : We consider various sets of Vlasov-Fokker-Planck equations modeling the dynamics of charged particles in a plasma under the effect of a strong magnetic field. For each of them in a regime where the strength of the magnetic field is effectively stronger than that of collisions we first formally derive asymptotically reduced models. In this regime, strong anisotropic phenomena occur; while equilibrium along magnetic field lines is asymptotically reached our asymptotic models capture a non trivial dynamics in the perpendicular directions. We do check that in any case the obtained asymptotic model defines a well-posed dynamical system and when self consistent electric fields are neglected we provide a rigorous mathematical justification of the formally derived systems. In this last step we provide a complete control on solutions by developing anisotropic hypocoercive estimates.

Keywords : gyrokinetic theory hypocoercivity Vlasov equation Fokker-Planck operator Maxwell-Boltzmann distribution Gibbs equilibrium plasma physics disparate mass strong magnetic field





Author: Maxime Herda - Luis Miguel Rodrigues -

Source: https://hal.archives-ouvertes.fr/



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