Linearized model Fokker-Planck collision operators for gyrokinetic   simulations. I. Theory
  A new analytically and numerically manageable model collision operator is developed specifically for turbulence simulations. The like-particle collision operator includes both pitch-angle scattering and energy diffusion and satisfies the physical constraints required for collision operators: it conserves particles, momentum and energy, obeys Boltzmann's H-theorem (collisions cannot decrease entropy), vanishes on a Maxwellian, and efficiently dissipates small-scale structure in the velocity space. The process of transforming this collision operator into the gyroaveraged form for use in gyrokinetic simulations is detailed. The gyroaveraged model operator is shown to have more suitable behavior at small scales in phase space than previously suggested models. A model operator for electron-ion collisions is also presented. 
I. G. Abel (Imperial), M. Barnes (Maryland), S. C. Cowley (Culham), W.   Dorland (Maryland), A. A. Schekochihin (Imperial)