A novel frequency domain maximum likelihood approach for estimating transport coefficients in cylindrical geometry for nuclear fusion devices

Abstract

This paper introduces a novel maximum likelihood approach to determine the local thermal transport coefficients belonging to diffusion and convection from excitation (perturbative) transport experiments. It extends previous work developed for linear (slab) geometry to cylindrical (toroidal) geometry for fusion reactors. The previous linear geometry approach is based on analytic solutions of the partial differential equation. However, for cylindrical geometries with convection the analytic solutions are confluent hypergeometric functions (CHFs) with complex valued arguments. Most numerical libraries do not support CHFs evaluation with complex valued arguments. Hence, this paper proposes the use of an ultra-fast transfer function evaluation based on sparse numerical solutions for the discretized partial differential equation. This solution is implemented in MATLAB© and incorporated in the frequency domain Maximum Likelihood Estimation framework. Consequently, transport coefficients can be estimated consistently when measurements are perturbed by coloured and spatially correlated noise.