Another classical property of the Fokker-Planck operator is the relaxation towards a Maxwellian equilibrium. The entropy dissipation rate [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is given by the following lemma whose proof is left to the reader.
We expect that averaging the collision operator will lead to a similar operator, satisfying the usual physical properties : particle, momentum, energy conservations and the relaxation towards a local Maxwellian equilibrium. It turns out that a linearized and gyroaveraged collision operator has been written in , but the implementation of this operator see[m.sub.s] very hard.
We establish the particle, momentum, energy conservations and the relaxation towards a local Maxwellian equilibrium. Therefore this reduced collision operator is well adapted for gyrokinetic simulations.