Regularized inversion of optical Thomson scattering spectra for improved determination of plasma parameter evolution

Optical Thomson scattering spectra, particularly those measured in the collective scattering regime, are difficult to interpret due to non-linearity in the forward mapping from the electron and ion velocity distributions to the Thomson-scattered spectrum. Inversion routines often fit a spectrum to plasma parameters by minimizing a simple weighted residual sum of squares (RSS), but such routines frequently converge to solutions that are consistent with the measured data but exhibit unphysical oscillations of the fitted parameters within the uncertainty bounds of the data. This study explores one possible solution to this problem by minimizing a modified objective function that includes a regularization term penalizing solutions that evolve on unphysical timescales. A procedure for determining the optimal regularization weight hyperparameter is described. The resulting optimized regularized inversion scheme is demonstrated to avoid physically improbable but weighted-RSS-degenerate solutions and converge to a better overall description of the synthetic plasma parameters. For two of the synthetic test problems that the procedure was used on, the RSS of the best-fit parameter profiles relative to the ground truth was, on average, 0.31 and 0.65 times the RSS from the corresponding unregularized fits. For the third synthetic test problem, which involved discontinuous plasma parameters, the regularization scheme can accurately fit the plasma evolution around the discontinuity but not directly on the discontinuity.