Asymmetric Abel inversion by neural network for reconstruction of plasma density distribution

This paper presents a new method for asymmetric Abel inversion by a neural network. As a typical asymmetric Abel inversion problem, we consider to reconstruct a plasma density distribution in a fusion device from a dataset obtained by interferometric measurement of electromagnetic waves, and propose a new method realized by making use of the excellent feature of a neural network to approximate wide range of mapping functions. In this method, training of the network is carried out by minimizing a squared residual of integral equation along measuring paths, where density contours are also adjusted on the basis of the database of the density contours (the plasma MHD equilibrium). By this method, therefore, we can determine the contour shapes as well as the contour values of the density even in the asymmetric Abel inversion problem. We applied this method to model problems and obtained satisfactory results. This method is applicable to similar problems provided series of contour geometries defined in a one- or a few-dimensional subspace of a multi-dimensional parameter space are given as a numerical database.