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

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.

to appear in Kinetic and Related Models

References in corpus (3)

• On massless electron limit for a multispecies kinetic system with external magnetic field
• On the gyrokinetic limit for the two-dimensional Vlasov-Poisson system
• Invariant Measures for a Stochastic Fokker-Planck Equation

Cited by in corpus (4)

• Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
• Determining a parabolic system by boundary observation of its non-negative solutions with biological applications
• Long time behavior for collisional strongly magnetized plasma in three space dimensions
• Asymptotically preserving particle-in-cell methods for inhomogenous strongly magnetized plasmas