On massless electron limit for a multispecies kinetic system with external magnetic field

Maxime Herda (1, 2)

1 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy
2 MMCS - Modélisation mathématique, calcul scientifique

We consider a three-dimensional kinetic model for a two species plasma consisting of electrons and ions confined by an external nonconstant magnetic field. Then we derive a kinetic-fluid model when the mass ratio me/mi tends to zero. Each species initially obeys a Vlasov-type equation and the electrostatic coupling follows from a Poisson equation. In our modeling, ions are assumed non-collisional while a Fokker-Planck collision operator is taken into account in the electron equation. As the mass ratio tends to zero we show convergence to a new system where the macroscopic electron density satisfies an anisotropic drift-diffusion equation. To achieve this task, we overcome some specific technical issues of our model such as the strong effect of the magnetic field on electrons and the lack of regularity at the limit. With methods usually adapted to diffusion limit of collisional kinetic equations and including renormalized solutions, relative entropy dissipation and velocity averages, we establish the rigorous derivation of the limit model.

Mots clés: velocity averaging lemma; Vlasov-Poisson-Fokker-Planck system; renormalized solutions; magnetic field; Vlasov-Poisson system; plasma physics; Multispecies kinetic equations

Domaines: Equations aux dérivées partielles [math.AP]; Physique des plasmas [physics.plasm-ph]

Maxime Herda. On massless electron limit for a multispecies kinetic system with external magnetic field. Journal of Differential Equations, 2016, 260 (11), pp.7861-7891. ⟨10.1016/j.jde.2016.02.005⟩. ⟨hal-01147365v2⟩