A weakly relativistic Fokker-Planck operator for electron-electron collision was first used by Karney and Fisch to calculate the efficiencies of current drive by waves with fast phase velocity [C. F. F. Karney and N. J. Fisch, Phys. Fluids 28, 116 (1985)]. The present work extends Karney and Fisch's work by expressing the weakly relativistic collision operator in potential form, and working out a general Legendre expansion of the potential functions. This general Legendre expansion reproduces the results in Karney and Fisch's paper and is useful in implementing the weakly relativistic operator in Fokker-Planck codes. To justify the use of the weakly relativistic collision operator for current drive applications under ITER conditions, a comparison is made of current drive efficiencies predicted by this operator and a fully relativistic collision operator. Good agreement between efficiencies predicted by these two models is found. This suggests that the weakly relativistic collision operator is sufficiently precise for modeling the current drive schemes under ITER conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3551739]
