Resonant and Ponderomotive Pumping of Zonal Flows by Turbulence, Alfv\'en Eigenmodes, and Radiofrequency Waves

Abstract

Analytical studies of zonal-flow (ZF) excitation by fluctuating fields, such as drift-wave turbulence and Alfv\'en eigenmodes (AEs) driven by energetic particles (EPs) in tokamaks, are usually carried out via intricate gyrokinetic calculations and simulations whose results are notoriously difficult to interpret. Here, we report a transparent result that is also not limited to any particular modes or frequency range. Using oscillation-center theory that captures both ponderomotive forces and quasilinear diffusion, we derive a compact formula for the ZF drive produced by any fluctuating field in terms of the field's canonical momentum and the dissipation power density. For ZFs generated by drift waves, our model subsumes the local relation between the zonal velocity and the drift-wave energy density that was previously derived ad hoc. The simplicity and generality of our result also opens a path toward optimization of ZF excitation with external waves and bridges the physics of AE-EP interactions with that of poloidal flows driven by radiofrequency waves in fusion plasmas.