Title :

Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations

Author(s) :

Herda, Maxime [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Rodrigues, Luis Miguel [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]

Journal title :

Kinetic and Related Models

Pages :

593-636

Publisher :

AIMS

Publication date :

2019

ISSN :

1937-5093

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Physique [physics]/Physique [physics]/Physique des plasmas [physics.plasm-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Frontières, numérique, dispersion.
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL