Reconstructing Plasma Velocity Distribution Functions using Stochastic Gradient Descent

Collisionless shocks in plasma are a common feature in astrophysical systems such as the Earth's bow shock and supernova remnants. To improve our understanding of these fundamentally non-linear collisionless shocks, we probe the velocity distribution functions (VDFs) of these plasmas. Recent laser experiments have recreated collisionless shocks in the laboratory, where these VDFs can be measured using a Thomson scattering diagnostic. However, their non-Maxwellian nature is difficult to interpret with existing analysis techniques. We present a new technique for reconstructing particle VDFs from Thomson scattered data using stochastic gradient descent. This method is commonly used to train neural networks and scan large parameter spaces. This could also be applied to the Thomson scattering forward models where corresponding fitting algorithms can more efficiently scan the large parameter spaces associated with non-Maxwellian VDFs. We compare the results of this technique against more traditional fitting routines such as those that use brute force, differential evolution, or Monte Carlo Markov Chains, including the quality and computational time of the fits.