Anomalous effects on classical and neoclassical transport

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We have investigated the plasma transport due to fluctuations using a renormalization technique of statistical dynamics and obtained the following results :1.Employing a functional integral method, we have studied the particle diffusion in a stochastic magnetic field. With the ensemble average of a functional representation to a kinetic equation over the fluctuating magnetic field and the random variables modeling the Coulomb collisions, a closed set of equations for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation is derived within the framework of the direct-interaction approximation (DIA). It is found from these equations that the cross-field diffusion coefficients can be obtained by solving nonlinear ordinary differential equations. We have explicitly calculated diffusion coefficients for various parameters in the shearless and sheared configurations.2.We have theoretically studied the effect of fluctuations on the bootstr … More ap current in tokamaks. Based upon a closed set of equations for the ensemble-averaged distribution function and the response function, we have derived a radial diffusion equation for the bootstrap current density. The anomalous radial diffusion due to fluctuations as well as the finite-banana width effect is shown to significantly modify the conventional bootstrap current near the magnetic axis. It is also shown that this modification leads to the possibility of a completely bootstrapped tokamak. The radial diffusion equation for the rf-driven current density is also obtained using the similar method.3.Applying the DIA to subensemble-averaged functions instead of conventional ensemble-averaged ones, we have derived a closed set of equations for a subensemble-averaged distribution function and its response function. This closure theory approximately provides the Lagrangian description by incorporating particle trajectory effect. The running diffusion coefficient in turbulent plasma is shown to be calculated by solving a nonlinear ordinary differential equation together with an equation for deterministic particle trajectories. Less