Low Field Regime for the Relativistic Vlasov-Maxwell-Fokker-Planck System; the One and One Half Dimensional Case

Mihai Bostan (1, 2) , Thierry Goudon (3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 CALVI - Scientific computation and visualization
3 SIMPAF - SImulations and Modeling for PArticles and Fluids

We study the asymptotic regime for the relativistic Vlasov-Maxwell-Fokker-Planck system which corresponds to a mean free path small compared to the Debye length, chosen as an observation length scale, combined to a large thermal velocity assumption. We are led to a convection-diffusion equation, where the convection velocity is obtained by solving a Poisson equation. The analysis is performed in the one and one half dimensional case and the proof combines dissipation mechanisms and finite speed of propagation properties.

Mots clés: Vlasov-Maxwell-Fokker-Planck system; Asymptotic behavior; Diffusion approximation

Domaines: Equations aux dérivées partielles [math.AP]

Mihai Bostan, Thierry Goudon. Low Field Regime for the Relativistic Vlasov-Maxwell-Fokker-Planck System; the One and One Half Dimensional Case. Kinetic and Related Models , 2008, 1 (1), pp.139-170. ⟨10.3934/krm.2008.1.139⟩. ⟨hal-00594960⟩