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

Collisionless shocks are an important plasma phenomenon that often occur under non-equilibrium conditions, where velocity distribution functions (VDFs) deviate significantly from Maxwellian forms. When studying shocks in a laboratory setting, Thomson scattering serves as a key diagnostic for probing the important plasma parameters. Current PlasmaPy algorithms for fitting Thomson scattering spectra typically assume Maxwellian VDFs, limiting their accuracy in collisionless shock experiments. Furthermore, traditional fitting methods like differential evolution (DE) struggle with the large number of free parameters required to describe non-Maxwellian VDFs. We introduce a fitting approach based on automatic differentiation, a gradient-descent-based optimization method, that efficiently handles higher-dimensional parameter spaces. This method accurately fits both Maxwellian and non-Maxwellian spectra, including super-Gaussian, bi-Maxwellian, and tri-Maxwellian distributions. We apply this approach to Thomson Scattering data from laser-driven shock experiments.