Two‐dimensional spatial distribution of volume emission from line integral data

A method is presented for determining the two-dimensional (2-D) spatial distribution of the volume emission intensity [E = f(r,ϑ)] in a plasma from line integral data obtained by arrays of collimated detectors looking through the plasma along different chords. Subject to the assumption that E can be represented by 𝒥m [fm(r)cos mϑ +gm(r)sin mϑ] with only a few terms m, expressions are developed that separate harmonic contributions to the line integrals, a numerical procedure is outlined for inversion of these contributions to obtain the factors fm(r) and gm(r), and the formulas that result are presented for m = 0 through m = 5. This method was developed for application to data from arrays of soft x-ray detectors on the Impurity Study Experiment (ISX-B) tokamak. One use would be comparison of the soft x-ray volume emission contours with other measures of plasma shape. Simulations of these shape determinations were performed, using as input, a pressure profile representing a calculated MHD equilibrium for a D-shaped plasma in ISX-B. The results of these simulations are shown and the determination of the poloidal structure of MHD perturbations in the plasma is also illustrated.