Nonlinear saturation of collisionless trapped electron mode turbulence: Zonal flows and zonal density

Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter-sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear, and electron temperature gradient. For parameters where zonal flow is found to be unimportant, zonal density (purely radial density perturbations) is generated and expected to be the dominant saturation mechanism. A toroidal mode-coupling theory is presented that agrees with simulation in the initial nonlinear saturation phase. The mode-coupling theory predicts the nonlinear generation of the zonal density and the feedback and saturation of the linearly most unstable mode. Inverse energy cascade is also observed in CTEM turbulence simulations and is reported here