Drift wave driven zonal flows in plasmas

Abstract

The generation of large-scale zonal flows by small-scale electrostatic drift waves in a plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process a generalized Hasegawa–Mima equation containing both vector and scalar nonlinearities is used. The drift waves are supposed to have arbitrary wavelengths (as compared with the ion Larmor radius). A set of coupled equations describing the nonlinear interaction of drift waves and zonal flows is deduced. The generation of zonal flows turns out to be due to Reynolds stresses produced by finite amplitude drift waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the drift pump wave. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with previous results is carried out. The present theory can be used for interpretations of drift wave observations in laboratory plasmas.