A generalized Abel inversion method for gamma-ray imaging of thermonuclear plasmas

A method to determine the gamma-ray emissivity profile from measurements along a few multiple collimated lines of sight in thermonuclear plasmas is presented. The algorithm is based on a generalisation of the known Abel inversion and takes into account the non circular shape of the plasma flux surfaces and the limited number of data points available. The method is applied to synthetic experimental measurements originating from parabolic and non parabolic JET gamma-ray emissivity profiles, where the aim is to compare the results of the inversion with the original, known input parameters. We find that profile parameters, such as the peak value, width and centre of the emissivity, are determined with an accuracy between 1 and 20% for parabolic and 2 to 25% for non parabolic profiles, respectively, which compare to an error at the 10% level for the input data. The results presented in this paper are primarily of relevance for the reconstruction of emissivity profiles from radiation measurements in tokamaks, but the method can also be applied to measurements along a sparse set of collimated lines of sight in general applications, provided that the surfaces at constant emissivity are known to have rotational simmetry.