Analysis of Transport Phenomena by a Three-Dimensional Fokker-Planck Code

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In order to describe the transport phenomena in a tokamak plasma in terms of the velocity distribution function, a drift-kinetic formulation has been developed to derive coupled three-dimensional Fokker-Planck equations. The three-dimensional Fokker-Planck numerical code has been extended to include the spatial diffusion due to Coulomb collisions and electromagnetic fluctuations.1. From the analysis of the drift orbit, the change of characteristic radius due to the velocity modification through Coulomb collision or wave-particle interaction has been analytically calculated. The velocity diffusion term, the spatial diffusion term and the cross terms in the Fokker-Planck equation are derived from the collision term. The periodicity of the collisionless drift orbit enables us to Fourier-expand the distribution function. Poloidal angle dependence of the distribution has been included for the first time.2. The bounce-averaged three-dimensional Fokker-Planck code has been employed to study the heating and current drive by the RF waves. Taking account of the spatial diffusion of the fast electrons, the radial profile of the driven current as well as the current drive efficiency have been obtained.3. By employing the full implicit method, the numerical stability of the three-dimensional Fokker-Planck code has been drastically improved. The upper-limit of the input power in the RF current drive is much enlarged compared with the alternative directional implicit method.