Modeling Plasma Plumes from Rapid Target Heating with Differentiable Smoothed Particle Hydrodynamics

We present a fully differentiable Smoothed Particle Hydrodynamics (SPH) simulator for modeling the hydrodynamic expansion of plasma plumes resulting from rapid target heating. Many formulations of SPH have been developed for modeling compressible flows involving plasma, such as those seen in astrophysics and engineering applications. However, the parameters of these SPH formulations are usually adjusted by trial and error. In this work, we leverage differentiable programming to automatically fine-tune SPH parameters to experimental data. We embed Neural Networks withing the SPH framework for estimating unknown functions, such as smoothing kernels and equations of state. 

The approach is first validated and analyzed for the 1d Sod shock and 2D Taylor-Sedov blast wave problems, i.e. learn-able and parameterized compressible SPH formulations are fit to the analytical solutions using gradient-based optimization. Next, we extend the SPH formulation to model the spatio-temporal evolution of plasma plumes generated from rapid thin-target heating by 20 MeV electron beams. The generation of plasma plumes during such heating processes can significantly impact various high-energy physics experiments, making accurate prediction of their behavior crucial for experimental design and analysis. The plasma plumes of interest evolve in vacuum, making the SPH framework a natural choice for modeling at the coarse grained scales of interest. Furthermore, the complex physics involved motivates the use of machine learning to fill in the gaps with exploring new parameterized terms within SPH. We employ experimental data to fine tune the SPH models, using pulsed bunches of approximately $10^{15}$ electrons to heat a range of thin targets to temperatures above 1 eV. The shadowgraph and interferometer measurements provide spatially resolved snapshots of the expanding plume's electron density and temperature distributions at discrete time points.