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.

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