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A new analytically and numerically manageable model collision operator isdeveloped specifically for turbulence simulations. The like-particle collisionoperator includes both pitch-angle scattering and energy diffusion andsatisfies the physical constraints required for collision operators: itconserves particles, momentum and energy, obeys Boltzmann's H-theorem(collisions cannot decrease entropy), vanishes on a Maxwellian, and efficientlydissipates small-scale structure in the velocity space. The process oftransforming this collision operator into the gyroaveraged form for use ingyrokinetic simulations is detailed. The gyroaveraged model operator is shownto have more suitable behavior at small scales in phase space than previouslysuggested models. A model operator for electron-ion collisions is alsopresented.

Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory