Fine-scale zonal flow suppression of Electron Temperature Gradient turbulence

It is found in collisionless Electron Temperature Gradient (ETG) turbulence simulations that while zonal flows are weak at early times, the zonal flows continue to grow algebraically (proportional to time). These fine-scale zonal flows have a radial wave number such that k(r)rho(i) > 1 and k(r)rho(e) < 1. Eventually, the zonal flows grow to a level that suppresses the turbulence due to ExB shearing. The final electron energy flux is found to be relatively low. These conclusions are based on particle convergence studies with adiabatic ion electrostatic flux-tube gyrokinetic delta f particle simulations run for long times. The Rosenbluth-Hinton random walk mechanism is given as an explanation for the long time build up of the zonal flow in ETG turbulence and it is shown that the generation is (k perpendicular to rho(e))(2) smaller than for isomorphic Ion Temperature Gradient (ITG) problem. This mechanism for zonal flow generation here is different than the modulational instability mechanism for ITG turbulence. These results are important because previous results indicated zonal flows were unimportant for ETG turbulence. Weak collisional damping of the zonal flow is also shown to be a n important effect.