Anisotropic regularization for inversion of fast-ion loss detector measurements

Abstract

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.