MultiScale Analysis for Linear First Order PDEs. The Finite Larmor Radius Regime

International audience; The subject matter of this paper concerns the asymptotic analysis of mathematical models for strongly magnetized plasmas. We concentrate on the finite Larmor radius regime with non uniform magnetic field in three dimensions. We determine the limit model and establish convergence results for any initial conditions, not necessarily well prepared. This study relies on a two-scale approach, based on the mean ergodic theorem, which allows us to separate between the fast and slow dynamics. The method adapts to many models. In particular it is possible to incorporate collision operators and to compute the effective diffusion matrices of the limit models. The average advection field and average diffusion matrix field appear as the long time limit for some parabolic problems, which allows us to obtain good approximations of the limit models, in the case of non uniform magnetic fields (when exact formulae are not available).