Bayesian velocity-space tomography with collision- and charge-exchange-physics prior from fast-ion D-alpha measurements at TCV with uncertainty quantification

Abstract Recent years have seen much effort and progress in reconstructing the fast-ion distribution function in fusion plasmas from noisy measurements from several different tokamak devices by solving ill-posed inverse problems. The focus of this paper is two-fold: first, to demonstrate how prior information about collision physics and charge-exchange physics improve the reconstructions in the case of a limited amount of data compared to a more standard method, and secondly, to build this prior information into a Bayesian framework to facilitate uncertainty quantification in the reconstructions. In this work, we use data from a two-view fast-ion D α spectroscopy system in Tokamak á Configuration Variable (TCV) as a test case. Reconstructions of fast-ion distributions from experimental data in TCV have not previously been published. We compare the performance of non-negativity constrained Tikhonov regularisation with two recently developed inversion schemes for fast-ion tomography. First, with a modified Tikhonov regularisation incorporating collision physics and charge-exchange physics as prior, and secondly, with a hierarchical Bayesian model incorporating the same prior information, which allows both uncertainty quantification and simultaneous estimation of hyperparameters. Evaluating the quality of each method based on synthetic measurements, it is observed that the modified Tikhonov regularisation scheme and the Bayesian inference outperform non-negativity constrained Tikhonov regularisation, and these are subsequently used to infer the fast-ion distribution function from experimental data. While the Bayesian approach matches the modified Tikhonov regularisation scheme in reconstruction quality, it furthermore allows uncertainty quantification and simultaneous estimation of hyperparameters, thus avoiding the need for time-consuming parameter search conventionally needed for Tikhonov regularisation.