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

TL;DR

This paper derives and justifies reduced anisotropic models for strongly magnetized plasma dynamics described by Vlasov-Fokker-Planck equations, highlighting the complex perpendicular behavior and providing rigorous mathematical analysis.

Contribution

It introduces formally derived asymptotic models for strongly magnetized plasma and proves their well-posedness and solution control through anisotropic hypocoercive estimates.

Findings

Asymptotic models capture non-trivial perpendicular plasma dynamics.

Well-posedness of the derived models is established.

Rigorous justification of the models is provided with solution control.

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.