The efficiency of fast wave current drive for a weakly relativistic plasma

Current drive by fast waves (FWCD) is an important candidate for steady‐state operation of tokamaks. Major experiments using this scheme are being carried out on DIII‐D. There has been considerable study of the theoretical efficiency of FWCD. In Refs. 4 and 5, the nonrelativistic efficiency of FWCD at arbitrary frequencies was studied. For DIII‐D parameters, the results can be considerably different from the Landau and Alfven limits. At the high temperatures of reactors and DIII‐D upgrade, relativistic effects become important. In this paper, the relativistic FWCD efficiency for arbitrary frequencies is studied. Assuming that the plasma is weakly relativistic, i.e., Te/mc2 is small, an analytic expression for FWCD is obtained for high resonant energies (uph/uTe≫1). Comparisons with the results from a numerical code ADJ and the nonrelativistic results shall be made and analytical fits in the whole range of velocities shall be presented.