Finite Larmor radius approximation for the Fokker-Planck-Landau equation

The subject matter of this paper 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 gyroaverage of the Fokker-Planck-Landau operator, which plays a major role in plasma physics. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, kinetic energy and dissipates the entropy.