The Effect of ETG Transport on the Electron Temperature Pedestal

ETG turbulence likely constrains the electron temperature profile in the pedestal in many scenarios. We present simple formulas for ETG pedestal transport extracted from a database of nonlinear gyrokinetic simulations. These formulas are surprisingly simple and accurate when taking into account a few physically-motivated parameters and accounting for certain geometric factors. They are accurate in the steep gradient region for both spherical and standard aspect ratio tokamaks. The strongest parameter dependences are the normalized inverse electron temperature gradient (a/LTe) (to the second power) and eta=Ln/LTe (to the third power). These dependences result in strong sensitivity to both the electron temperature and density gradients. The dependence on Zeff and temperature ratio can also be important. We apply these models to predicting electron temperature profiles in various pedestal scenarios. In scenarios where ETG transport is insufficient to account for the electron thermal transport (i.e. it over predicts the temperature), we posit that MTM is also active and formulate reduced models for its contribution. This work represents an initial step toward more comprehensive (i.e., accounting for transport in addition to MHD limits) modeling of pedestal structure.