Statistical Analyses of Gyrokinetic Microturbulence for Transport Modelling

Gyrokinetic simulation has, over the decades, become the best first-principles approach to modelling turbulent transport in fusion devices. Widely validated against experiments [White, A.E. J. Plasma Phys. (2019) 925850102], gyrokinetic simulations are now reliable enough to use in direct optimization of magnetic configurations [Kim et.\ al., J. Plasma Phys. (2024), 905900210]. Similarly, transport simulations with fluxes obtained from gyrokinetic simulations are now routinely employed [Qian, T. et. al. 2022 Bull. Am. Phys. Soc.]. However, the speed and efficiency of these processes depends on several key factors, in particular automatically determining saturation of gyrokinetic simulations and inferring smooth fluxes from noisy simulation data. These problems also arise in performing uncertainty quantification on and building surrogate models for gyrokinetic simulations, both of which can accelerate optimization and transport simulations without sacrificing accuracy.

To address these challenges, we apply statistical techniques to analyze the uncertainty in fluxes derived from plasma turbulent simulations. Key to our methodology is the development of a procedure to disregard the initial transient phase, and to identify the steady state region of the reported flux traces. After the steady-state fluxes have been identified, we estimate the mean flux value, standard deviations and confidence intervals using short-term averages with both sliding and non-overlapping window methods. Additionally, the autocorrelation time plots are analyzed to establish a robust metric for lag cut-offs. We illustrate how our approach can be used to determine the limiting distribution of turbulent transport fluxes across various configurations of plasma simulations. Finally, we illustrate how our approach enables the assessment of the confidence in gyrokinetic simulations, as well as on on-the-fly predictions of the required simulation time in order to meet a desired level of accuracy in the computed flux statistics.