Second-order radio frequency kinetic theory with applications to flow drive and heating in tokamak plasmas

A comprehensive kinetic theory is developed to treat radio frequency (rf) driven plasma flow in one-dimensional geometry. The kinetic equation is expanded to second order in the perturbing rf electric field. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength. Moments of the second-order distribution function give time-averaged expressions for the rf-driven particle transport, forces, and heating, including the wave kinetic flux. On the transport time scale, the rf force in the poloidal direction is balanced by neoclassical viscosity, and the force in the radial direction is balanced by ambipolar electric fields. Comparison is made with previous theories which have relied on incompressible fluid approximations and a Reynolds stress model for the rf pressure. Substantial differences are seen in situations involving the ion Bernstein wave, which is compressional in nature. Linear electron Landau damping and magnetic pumping, by themselves, do not lead to significant poloidal flow. But ion cyclotron damping of either fast magnetosonic waves or ion Bernstein waves can drive significant flow at power levels typical of plasma heating experiments.