Transport equations with disparate advection fields. Application to the gyrokinetic models in plasma physics
Résumé
The subject matter of this paper concerns the asymptotic regimes for transport equations with advection fields having components of very disparate orders of magnitude. Such models arise in the magnetic confinement context, where charged particles move under the action of strong magnetic fields. According to the different possible orderings between the typical physical scales (Larmor radius, Debye length, cyclotronic frequency, plasma frequency) we distinguish several regimes: guiding-center approximation, finite Larmor radius regime, etc. The main purpose is to derive the limit models: we justify rigorously the convergence towards these limit models and we investigate the well-posedness of them.