Analyzing Non-Maxwellian Plasma Velocity Distributions from Thomson Scattering Measurements Using Automatic Differentiation

Thomson scattering is a powerful diagnostic for probing plasma parameters. Current PlasmaPy algorithms for fitting Thomson Scattering spectra are based on the assumption that the plasma follows a Maxwellian velocity distribution. However, many plasma phenomena such as collisionless shocks occur under non-equilibrium conditions where the particle velocity distribution functions (VDFs) are non-Maxwellian. Current standard fitting methods, including differential evolution (DE) and Markov Chain Monte-Carlos (MCMCs), struggle to return accurate fits for the large number of free parameters required to describe these VDFs. We introduce a new optimization method for fitting Thomson Scattering spectra based on automatic differentiation, a gradient-descent based fitting method used to train neural networks that is constructed to optimize larger sets of parameters. This method is shown to be effective in fitting both Maxwellian and super-Gaussian (non-Maxwellian) VDFs based on numerical techniques for calculating scattered spectra from arbitrary VDFs [1]. To further test the efficacy of this method, we compare its performance with the existing methods of DE and MCMC. Specifically, we examine aspects such as run-time efficiency, its ability to handle more complex VDFs with an increase in the fit parameter space, evaluate the effect of noise on the fits, and conduct a detailed analysis of the fit uncertainty.