Gyrokinetic Secondary Stability Theory For Toroidal ETG Modes

Secondary stability theory has been invoked to explain the large disparity in the non-linear behavior of Ion Temperature Gradient (ITG) and Electron Temperature Gradient (ETG) driven turbulence. In particular, the existence of persistent ``streamer'' structures in ETG turbulence indicates a significant weakening of the secondary instabilities which tend to isotropize ITG tokamak turbulence. We use the electrostatic non-linear gyrokinetic equation to solve for the secondary stability of the local two-dimensional ``toroidal'' branch of the Electron Temperature Gradient (ETG) mode. We address the issue of stable streamer structures and relate our findings to recent ETG simulations.