Multispecies hybrid model applied to ICF pre-heat mixing

The assumptions behind hydrodynamic models can break down in certain regimes (e.g. shocks). Alternatively, kinetic models provide more accurate solutions, but require many more degrees of freedom. A hybrid model combines both hydro and kinetic models into a single system of equations and applies kinetic models where needed. We present a new hybrid model for multispecies plasmas which generalizes Degond et al.’s work [1] from a single species to a multi-species model and includes electric fields. Specifically, it combines multispecies Euler with Haack, Hauck, Murillo’s [2] recently formulated model. We apply this method to study species mixing in inertial confinement fusion experiments [3]. Simulation results indicate that more than one momentum transport equation is required to capture mixing. We determine which physical regions require multiple momentum equations using the Chapman-Enskog closure of the kinetic model in conjunction with numerical estimates of the Knudsen number.

[1] Degond, P., Jin S., Mieussens L., 2005, ‘A smooth transition model between kinetic and hydrodynamic equations’, Journal of Computational Physics, 209, 665-694, Elsevier

[2] Haack, J., Hauck, C., Murillo, M., 2017, ‘A Conservative, Entropic Multispecies BGK Model’, Journal of Statistical Physics, 168, 826-856, Springer

[3] Murphey, T., et al. 2021, ‘Results from single-shock Marble experiments studying thermonuclear burn in the presence of heterogeneous mix on the National Ignition Facility’, Journal of High Energy Density Physics, 38, Page, Elsevier