Parameter Identification for a Reduced Transport Model in Fusion Plasma

Abstract

Two-dimensional transport codes for the simulation of tokamak plasmas are simplified versions of full 3D fluid models, where plasma turbulence is averaged out. One of the main challenges in such reduced models is to accurately reconstruct transverse transport fluxes that arise from the averaging of stresses due to fluctuations. These transverse fluxes are typically approximated by ad-hoc diffusion coefficients (turbulent eddy viscosity), manually adjusted to align numerical solutions with experimental observations. They can vary significantly depending on the type of tokamak, the experimental conditions, and even the location within the device, severely limiting the predictive capability of these codes for new configurations. To address this issue, we recently proposed an innovative approach to fusion plasma simulations by introducing two additional transport equations for turbulence-related variables (specifically, the turbulent kinetic energy $\kappa$ and its dissipation rate $\epsilon$) into the mean-flow system to estimate the turbulent eddy viscosity. This approach also introduces new free parameters, but they are primarily governed by the underlying transport physics and thus exhibit considerably less variation across devices and plasma regions. In this article, we continue an ongoing study of data assimilation techniques to determine the free parameters of the $\kappa -\epsilon$ model for transverse turbulent plasma transport. Based on digital twin experiments within the framework of equations averaged over the magnetic surfaces of the tokamak, we provide an in-depth study of optimization strategies to improve the performance of the calibration algorithm in a complex configuration with considerable scale variation of the parameters.