Secondary instability of electromagnetic ion-temperature-gradient modes for zonal flow generation

Abstract

An analytical model for zonal flow generation by toroidal ion-temperature-gradient (ITG) modes, including finite $\beta$ electromagnetic effects, is derived. The derivation is based on a fluid model for ions and electrons and takes into account both linear and nonlinear $\beta$ effects. The influence of finite plasma $\beta$ on the zonal flow growth rate (${\gamma }_{ZF}$) scaling is investigated for typical tokamak plasma parameters. The results show the importance of the zonal flows close to marginal stability where ${\gamma }_{ZF}/{\gamma }_{ITG}>>1$ is obtained. In this region the parameter ${\gamma }_{ZF}/{\gamma }_{ITG}$ increases with $\beta$, indicating that the ITG turbulence and associated transport would decrease with $\beta$ at a faster rate than expected from a purely linear or quasi-linear analysis.

RevTex 17 pages, 4 figures, submitted to Physics of Plasmas