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

Numerical calculations of fast-wave current drive (FWCD) efficiency have generally been of two types: ray tracing or global wave calculations. Ray tracing shows that the projection of the wave number (k parallel) along the magnetic field can vary greatly over a ray trajectory, particularly when the launch point is above or below the equatorial plane. As the wave penetrates toward the center of the plasma, k parallel increases, causing a decrease in the parallel phase speed and a corresponding decrease in the current drive efficiency, gamma. But the assumptions of geometrical optics, namely short wavelength and strong single pass absorption, are not greatly applicable in FWCD scenarios. Eigenmode structure, which is ignored in ray tracing, can play an important role in determining electric field strength and Landau damping rates. In such cases, a full-wave or global solution for the wave fields is desirable. In full-wave calculations such as ORION, k parallel appear as a differential operator (rvec B x gradient) in the argument of the plasma dispersion function. Since this leads to a differential system of infinite order, such codes of necessity assume k(parallel) (approximately) k(var phi) = const, where k(var phi) is the toroidal wave number. Thus, it is not possible to correctly include effects of the poloidal magnetic field on k(parallel). The problem can be alleviated by expressing the electric field as a superposition of poloidal modes, in which case k(parallel) is purely algebraic. This paper describes a new full-wave calculation, Poloidal Ion Cyclotron Expansion Solution, which uses poloidal and toroidal mode expansions to solve the wave equation in general flux coordinates. The calculation includes a full solution for E(parallel) and uses a reduced-order form of the plasma conductivity tensor to eliminate numerical problems associated with resolution of the very short wavelength ion Bernstein wave.