Zonal Flow Generation in Gyrokinetic-Ion Electron-Temperature-Gradient Turbulence Simulations

Understanding nonlinear saturation mechanisms of electron-scale turbulence is important for predicting electron heat transport in tokamak plasmas. In fluid models, the zonal flow generation by electron-temperature-gradient (ETG) turbulence is shown to be much weaker than that of similar ion-scale ITG turbulence. This leads to the expectation of a saturated state that is characterized by radially-elongated streamers at electron gyroradius scales. However, gyrokinetic electron simulations have seen that zonal flow (ZF) modes can contribute to long timescale behavior by breaking up these streamers and leading to less radially-elongated eddies. A weak-turbulence, toroidal, gyrokinetic-electron theory [Haotian Chen et al 2021 Nucl. Fusion 61 066017] has shown that as the ETG spectrum cascades downward, a stronger Navier-Stokes type nonlinearity couples ETG and ZF modes in electron-scale simulations, thus allowing for relevant ZF generation and ETG regulation. Here, we present electron-scale continuum gyrokinetic simulations with both single-mode ETG and full-spectrum ETG results showing strong support of this previous theoretical result. We specifically look at the strength of ZF generation by ETG modes at the intermediate scale between the ion and electron scales, as well as the role of collisionality in affecting the strength of the saturated ETG turbulence. We find that zonal flows driven by intermediate-scale ETG turbulence may be responsible for regulating electron heat-flux transport levels.