Radio-frequency current drive theory in the presence of fluctuations

The effect of low-frequency fluctuations on the radio-frequency- (rf-) induced current has been investigated by using a renormalization technique of statistical dynamics. With the application of the functional integral method to a Fokker-Planck equation in the presence of fluctuations, a closed set of equations is derived for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation. The nonlinear terms in these equations, which describe the radial anomalous transport for resonant particles, have a nonlocal feature not only in time but also in configuration and momentum spaces. The local approximation to these nonlinear terms quite simplifies the governing equations. For a steady-state current drive in the presence of fluctuations, the rf-induced current profile and its radial width are studied with the use of the local approximation to the nonlinear terms. The nonlocal effect in momentum space is also discussed for the weak and strong turbulent limits. This effect on the current profile width is found to be important for the weak turbulence although it can be neglected for the strong turbulence