Excitation of Zonal Flows by ion-temperature-gradient Modes Excited by the Fluid Resonance

We apply the reductive perturbation method to the simple electrostatic ion-temperature-gradient mode in an advanced fluid description. The fluid resonance turns out to play a major role for the excitation of zonal flows. This is the mechanism recently found to lead to the low-to-high (L–H) mode transition and to the nonlinear Dimits upshift in transport code simulations. It is important that we have taken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagnetic flow. This has turned out to be the most relevant effect as found in transport simulations of the L–H transition, internal transport barriers and Dimits shift. This is the first time that an analytical method is applied to a system which numerically has been found to give the right experimental dynamics.