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

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