High magnetic field equilibria for the Fokker–Planck–Landau equation

The subject matter of this paper concerns the equilibria of the Fokker–Planck–Landau equation under the action of strong magnetic fields. Averaging with respect to the fast cyclotronic motion when the Larmor radius is supposed to be finite leads to an integro-differential version of the Fokker–Planck–Landau collision kernel, combining perpendicular space coordinates (with respect to the magnetic lines) and velocity. We determine the equilibria of this gyroaveraged Fokker–Planck–Landau kernel and derive the macroscopic equations describing the evolution around these equilibria, in the parallel direction.