Current-drive theory in the presence of fluctuations

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We have theoretically studied the current drive due to radio-frequency (rf) waves in the presence of electric and magnetic fluctuations and have obtained the following results:1. Starting from the relativistic Fokker-Planck equation in the presence of fluctuations and using the direct-interaction approximation (DIA), we have derived the equation for the ensemble-averaged distribution function, which can be used as a basic equation in developing the computational code for the rf current drive.2. We have found that the use of adjoint equation leads us to the more analytical method compared with directly solving the equation for the ensemble-averaged distribution function. By means of this adjoint method, the mean-squared width and the radial profile of rf-driven current density are explicitly calculated for various values of the collision frequency, and the amplitude and correlation lengths of fluctuations.3. The radial diffusion equation for the rf-driven current density and the analytic expression for the diffusion coefficient in this equation are presented. The explicitly calculated results show that the current profiles obtained by using the adjoint equation and the radial diffusion equation agree well in the range of interesting parameters.4. The spatially local (spatial Markovian) approximation is used in the formulations of 1-3. In order to study the spatial nonlocal effect, we have reformulated the theory without the use of local approximation, and have derived the integro-differential equation for the rf-driven current density. The effect of spatial nonlocality on the profiles of rf-driven current density is show to be not significant in the wide range of parameters.5. Using the idea of the subensemble averaged instead of conventional ensemble average, we have extended the DIA, and have applied to the rf-current-drive theory. I n th i s formulation, we can incorporate the effect of particle trapping in the fluctuating electric and magnetic filed.