Anisotropic regularization for inversion of fast-ion loss detector measurements

Abstract

We introduce an anisotropic regularization framework for the reconstruction of distribution functions from measurements, utilizing an approach that applies distinct regularization techniques such as non-negative constrained Tikhonov, total variation, and Besov-space priors, either penalizing the one-norm or the two-norm, in each dimension to reflect the anisotropic characteristics of the multidimensional data. This method, applied to fast-ion loss detector (FILD) measurements, demonstrates a significant improvement over conventional nonnegative-constrained zeroth-order Tikhonov regularization because the prior information of the form of the distribution allows better reconstructions. The validity of the approach is corroborated through FILD measurements of prompt fast-ion losses in an ASDEX Upgrade discharge, where the reconstructed distribution function agrees well with the prompt-loss distribution predicted by ASCOT simulations. Moreover, we develop a composite quality metric, Q, that combines the mean squared error and the Jaccard index for a comprehensive evaluation of reconstruction accuracy and spatial fidelity. Finally, anisotropic regularization is applied to FILD measurements at ASDEX Upgrade to study fast-ion acceleration by edge-localized modes. The refined analysis resolves fine structure in the pitch of the accelerated ions and clearly shows that some ions are accelerated to over twice the injection energy.