Global nature of zonal flow due to the finite band width

The spectral effects of both micro-scale electron temperature gradient driven turbulence and zonal flow on the zonal flow generation are investigated theoretically and computationally based on the Hasegawa-Mima turbulence equation. As the minimum model describing the most primary spectral feature, we have developed an eight-wave interaction model which includes two sets of the conventional four-wave coupling systems with adjacent radial spectral difference of dk. It is found that the zonal flow is characterized by a global nature with an enhancement of growth rate γ, namely, global zonal flow eigen-mode, which is attributed to the appearance of new cross mode couplings due to the finite band width of zonal flow. This is qualitatively different from the monochromatic character of zonal flow described in the conventional four-wave coupling model. Direct numerical simulations of the Hasegawa-Mima equation with a zonal flow spectral structure have clearly proven the analytical results by employing a rigorous spectral code. The calculations further show that the global zonal mode is not only governed by the spectral structure of pump waves, but also their phase relation. © 2008 IOP Publishing Ltd.