Full-wave calculation of fast-wave current drive in tokamaks including k(parallel) variations

When fast waves propagate inward from the edge of a tokamak toward the plasma center, the k(perpendicular) spectrum produced by the antenna is not maintained but is shifted and deformed due to the presence of the finite poloidal magnetic field. This k(perpendicular) shift causes a variation in the parallel phase speed of the wave and can therefore have a strong effect on electron damping and current drive efficiency. In this paper, we include this effect in a new full-wave calculation (PICES) which represents the wave fields as a superposition of poloidal modes, thereby reducing k(perpendicular) to an algebraic operator. The wave equation is solved in general flux coordinates, including a full (non-perturbative) solution for E(perpendicular) and a reduced-order dielectric formulation to eliminate short-wavelength ion Bernstein modes. A simplified current drive model which includes particle trapping is used to estimate the effect of the k(perpendicular) shift on current drive efficiency in ITER and D3-D. Results suggest that when single-pass absorption is weak, reflected power may drive current nearly as efficiently as that absorbed on the first pass.