Finite Larmor radius approximation for collisional magnetic confinement. Part II: the Fokker-Planck-Landau equation

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This paper is devoted to the finite Larmor radius approximation of the Fokker-Planck-Landau equation, which plays a major role in plasma physics. We obtain a completely explicit form for the gyroaverage of the Fokker-Planck-Landau kernel, accounting for diffusion and convolution with respect to both velocity and (perpendicular) position coordinates. We show that the new collision operator enjoys the usual physical properties; the averaged kernel balances the mass, momentum, and kinetic energy and dissipates the entropy, globally in velocity and perpendicular position coordinates.