Nonlinear functional relation covering near- and far-marginal stability in ion temperature gradient driven turbulence

A novel nonlinear functional relation of turbulence potential intensity, zonal flow potential intensity, and ion thermal diffusivity that accurately reproduces nonlinear gyrokinetic simulations of toroidal ion temperature gradient (ITG) driven turbulence is proposed. Applying mathematical optimization techniques to find extremal solutions in high-dimensional parameter space, the optimal regression parameters in the functional form are determined to be valid for both near- and far-marginal regime of the ITG stability including the Dimits-shift. Then, the regression error of similar to 5% is accomplished. In addition, it is clarified that the intensity ratio of the zonal flow and turbulence potential intensity is a crucial factor to determine the reproduction accuracy.

Automated summary

A novel nonlinear functional relation is proposed to accurately reproduce gyrokinetic simulations of toroidal ion temperature gradient (ITG) driven turbulence. By applying mathematical optimization techniques, the regression parameters are determined for both near- and far-marginal regime of ITG stability, achieving a regression error of approximately 5%. The intensity ratio of zonal flow and turbulence potential intensity is found to be a crucial factor for reproduction accuracy.