Simulation of ion temperature gradient turbulence in tokamaks

Results are presented from non-linear gyrokinetic simulations of toroidal ion temperature gradient turbulence and transport. The ion thermal fluxes are found to have an offset linear dependence on the temperature gradient and are significantly lower than gyrofluid or IFS-PPPL model predictions. A new phenomenon of non-linear effective critical gradients larger than the linear instability threshold gradients is observed and is associated with undamped flux surface averaged shear flows. The non-linear gyrokinetic codes have passed extensive tests, including comparison against independent linear calculations, a series of non-linear convergence tests and a comparison between two independent non-linear gyrokinetic codes. The most realistic simulations to date used actual reconstructed equilibria from experiments and a model for dilution by impurity and beam ions. These simulations highlight the importance of both self-generated and external E ×B flow shear as well as the need for still more physics to be included.