Appears in collection : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmas

The subject matter of this talk concerns the derivation of the Finite Larmor radius approximation, when collisions are taken into account. Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyro-average of the Fokker-Planck- Landau operator, which plays a major role in plasma physics. We determine its equilibria and derive the fluid approximation around them, leading to a new Euler type system of conservation laws. The main technique applies for studying highly anisotropic parabolic problems, for example the heat equation with disparate diffusion coeffcients with respect to the parallel and perpendicular directions.