Nonlinear fluxes and forces from radio-frequency waves with application to driven flows in tokamaks

Nonlinear rf-driven sheared flows are of interest for turbulence control and basic physics experiments. Short-wavelength slow modes are required for efficient coupling of wave momentum to the plasma, requiring a kinetic hot-plasma theory. Here, a guiding-center formulation is developed which calculates the nonlinear particle and energy fluxes, energy absorption, and nonlinear forces on the plasma using a kinetic moment approach that is valid to first order in the ratio of the gyroradius compared to the wave envelope scale length and the plasma equilibrium scale length. Both the stress tensor and Lorentz force contribute to the net force on a fluid element. The forces driving flux-surface-averaged flows in a tokamak are extracted from the parallel and toroidal components. It is shown that flux-surface-averaged flows are driven by two classes of terms: direct absorption of wave momentum and dissipative stresses. Furthermore, the general kinetic expression for the force is shown to reduce to the standard cold-fluid ponderomotive force in an appropriate limit, but in this limit no flows are driven.