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

Abstract

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 guidingcenter 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-surfaceaveraged 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.

Observation of ion cyclotron range of frequencies mode conversion plasma flow drive on Alcator C-Mod

“…The involvement of slow wave and resonant wave-ion interaction for flow drive has been suggested by previous theoretical work on rf flow drive [39,40,41,42]. In previous attempts of mode conversion flow drive experiments on Alcator C-Mod, e.g., as that reported in [43], we were not able to obtain conclusive evidence of flow drive, partially due to running plasmas with predominantly MC electron heating.…”

Nonlinear ICRF-plasma interactions

“…[58][59][60] This knowledge has stimulated theoretical work on the calculation of rf driven flows, beginning with the pioneering work of Craddock and Diamond 61 and continuing up to the present. 48,[62][63][64][65][66][67][68][69] A number of 1-D and ray tracing calculations established that local absorption of IBW power at a cyclotron resonance was accompanied by redistribution of momentum that resulted in sheared poloidal (bipolar) flows.…”

“…61,66 There are several elegant formalisms for calculating nonlinear plasma effects due to rf waves, including guiding center 73 and quiver kinetics 74 formulations. Recently, flow drive work 64,69 has been developed using a different formulation, that of the W matrix 75,76 developed to describe energy flow and absorption in the presence of nonlocality introduced by finite gyroradius effects. This formalism uses a global Fourier representation of the rf fields, and is well suited to implementation in Fourier based codes.…”

Measurements of ion cyclotron range of frequencies mode converted wave intensity with phase contrast imaging in Alcator C-Mod and comparison with full-wave simulations

“…Efficient mode conversion heating with the more reactor relevant low-field side antennas were later observed in 3 He-H plasmas on TFTR plasma performance by turbulence suppression 24 . Direct rf flow drive has been studied theoretically [25][26][27] , but the full mechanism of flow generation in the presence of rf waves is not well understood, and this is an active area of research.…”