Formation of density corrugations due to zonal flow in wave-kinetic framework

Abstract

The formation of density corrugation due to zonal flow, so-called zonal staircase, is investigated theoretically, based on the wave-kinetic framework. The wave-kinetic simulation is performed, considering the profile corrugation and the turbulence trapping mechanism, where the profile corrugation changes the growth rate and the dispersion relation of turbulence. The zonal density is generated by the modulation of particle transport. We obtain the analytical expression for the zonal density, which determines the staircase height. It is found that the amplitude normalized by the ambient density can be comparable to the zonal flow normalized by the diamagnetic drift velocity. The key effect that determines the turbulence profile is found to be the phenomenon of turbulence trapping by zonal flow, while the profile corrugation due to zonal density has weaker effects. Thus, turbulence is localized where the flow curvature is negative, which leads to a flattening of the density profile through the enhancement of particle transport. This fact clearly shows that the effect of turbulence trapping dominates the density gradient dependence of the local linear instability.