a monochromatic pump wave which may couple to the zonal flow through symmetric sidebands, giving a system of four coupled waves. The corresponding system may be reduced to a fifth order dispersion relation for the zonal flow.

In this study the results are also interpreted in terms of quality of zonal flows i.e. the ratio of zonal flow growth rate and real frequency ($\Omega^{IM}/\Omega^{RE}$). The important finding is that the toroidally driven zonal flows exhibit a much larger ratio of growth rate and frequency compared to the slab like driven (factor of three difference), i.e. they have a higher quality. In most cases in scalings with $\eta_i$ the zonal flow growth rate and frequency follow the same qualitative behavior as the linear growth rate and real frequency. More importantly the quality of zonal flows is therefore rather insensitive to a scaling in $\eta_i$, in contrast to the results reported using the Wave Kinetic Equation (WKE) modeling. In many aspects the results found comparing the WKE modeling and the coherent mode coupling are qualitatively similar. In the WKE modeling a strongly decreasing zonal flow quality with increasing $\eta_i$ was found, however in the present model the decrease of zonal flow quality 