used has been covered extensively in previous papers [@a11], [@a15]- [@a21]. In this paper the effects on the zonal flow growth rate and real frequency of toroidicity and the coupling to the acoustic modes will be investigated. There are some limitations to this derivation of the zonal flow generation namely the non-linear terms in the equation for temperature ($[\phi, T_i] = 0$) and in the parallel ion momentum equation are neglected ($[\phi, v_{i ||}] = 0$). The procedure is to start with a monochromatic pump wave (defined above) that drives the zonal flow through a modulational coupling via the sidebands. The fields for the zonal flow and the sidebands are expanded as follows, $$\begin{aligned}
\tilde{\xi}_{ZF}(x,y,t) & = & \xi_{ZF} e^{i(q_x x - \Omega t)} + c.c. \\
\tilde{\xi}_\pm(x,y,t) & = & \xi_{\pm}e^{i((q_x \pm k_x)x \pm k_y y \pm k_{\parallel} z - \omega_{\pm }t)} + c.c.\end{aligned}$$ The secondary generated zonal flow is defined as $\tilde{\xi}_{ZF}$ ($\tilde{\phi}, \tilde{T}_i$ remembering that the zonal flow does not have a density component), $\tilde{\xi}_\pm$ are the possible sidebands ($\tilde{n}_i, \tilde{\phi}, \tilde{T}_i$). The radial, poloidal and parallel wave numbers are $(k_x,k_y,k_{\parallel})$, $\omega$ is the complex frequency of the drift wave, $q_x$ is the radial wave number, $\Omega$ 