ASYMPTOTICS OF THE THREE DIMENSIONAL VLASOV EQUATION IN THE LARGE MAGNETIC FIELD LIMIT

Francis Filbet (1) , Luis Miguel Miguel Rodrigues (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivation of the guiding-center approximation in the general three dimensional setting under the action of large inhomogeneous magnetic fields. First order corrections are computed and justified as well, including electric cross field, magnetic gradient and magnetic curvature drifts. We also treat long time behaviors on two specific examples, the two dimensional case in carte-sian coordinates and a poloidal axi-symmetric geometry, the former for expository purposes. Algebraic manipulations that underlie concrete computations make the most of the linearity of the stiffest part of the system of characteristics instead of relying on any particular variational structure.

Mots clés: gyrokinetics; Vlasov equation; asymptotic analysis 2010 MSC: 35Q83; guiding center approximation; 78A35; 82D10; 35B40

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Francis Filbet, Luis Miguel Miguel Rodrigues. ASYMPTOTICS OF THE THREE DIMENSIONAL VLASOV EQUATION IN THE LARGE MAGNETIC FIELD LIMIT. Journal de l'École polytechnique — Mathématiques, 2020, 7, pp.1009-1067. ⟨10.5802/jep.134⟩. ⟨hal-01933746v3⟩