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A set of key properties for an ideal dissipation scheme in gyrokineticsimulations is proposed, and implementation of a model collision operatorsatisfying these properties is described. This operator is based on the exactlinearized test-particle collision operator, with approximations to thefield-particle terms that preserve conservation laws and an H-Theorem. Itincludes energy diffusion, pitch-angle scattering, and finite Larmor radiuseffects corresponding to classical (real-space) diffusion. The numericalimplementation in the continuum gyrokinetic code GS2 is fully implicit andguarantees exact satisfaction of conservation properties. Numerical results arepresented showing that the correct physics is captured over the entire range ofcollisionalities, from the collisionless to the strongly collisional regimes,without recourse to artificial dissipation.

Linearized model Fokker-Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests