Zonal instability and wave trapping

This paper presents a model for zonal flow generation based on a wave kinetic equation coupled to a poloidal momentum equation in a regime where wave trapping matters. Several models of the wave collision operator have been tested: Krook, diffusion and diffusion plus an instability growth rate. Conditions for zonal instability have been identified. It is found that a zonal instability is possible in all cases. However the force is a power law of the zonal velocity, so different from the quasi-linear case of random phases that produces a force that is linear in velocity. Also the zonal force may change sign, leading to flow radial profiles that are not sinusoidal.