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An analytical model for zonal flow generation by toroidalion-temperature-gradient (ITG) modes, including finite $\beta$ electromagneticeffects, is derived. The derivation is based on a fluid model for ions andelectrons and takes into account both linear and nonlinear $\beta$ effects. Theinfluence 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 stabilitywhere $\gamma_{ZF}/\gamma_{ITG}>>1$ is obtained. In this region the parameter$\gamma_{ZF}/\gamma_{ITG}$ increases with $\beta$, indicating that the ITGturbulence and associated transport would decrease with $\beta$ at a fasterrate than expected from a purely linear or quasi-linear analysis.

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