Application of the averaging method to the gyrokinetic plasma

Emmanuel Frénod (1, 2, 3)

1 LEMEL - Laboratoire d'Etude et Modélisation des Environnements littoraux
2 CALVI - Scientific computation and visualization
3 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885

we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on the solution to a non oscillating ordinary differential equation with an oscillating correction added to it. The expression of the non oscillating ordinary differential equations are defined by a recurrence relation. We then apply this result to problems where charged particles are submitted to large magnetic field.

Mots clés: singular pertubation; averaging method; Two-scale analysis; asymptotic expansion

Domaines: Analyse fonctionnelle [math.FA]; Physique des plasmas [physics.plasm-ph]; Analyse numérique [math.NA]

Emmanuel Frénod. Application of the averaging method to the gyrokinetic plasma. Asymptotic Analysis, 2006, 46, pp.1--28. ⟨10.48550/arXiv.math/0702763⟩. ⟨hal-00133404⟩