Collisional closures for high-order moment partially-ionized plasma models with the electron inertial terms

A high-fidelity characterization of the transport of mass, momentum, and energy between different particle species is fundamental in understanding reacting, partially-ionized non-equilibrium plasmas. We consider the electron kinetic equation including Coulomb, elastic, inelastic, and ionization collisions. Our model solves for the first five moments of the Boltzmann equation (density, momentum, pressure tensor, heat-flux vector, and contracted fourth moment), which results in 14 scalar variables (14-M). We compare our moment model to a Monte-Carlo collision (MCC) code that includes the Nanbu method for the Coulomb collisions. The moment model is able to quantitatively capture the evolution of the moments similar to the MCC results. In addition, velocity and energy distribution functions can be reconstructed in the moment models. The 14-M model is able to capture the depletion of the energy distribution function at the tail and the asymmetries in the velocity distribution function. In this talk we discuss the validity of the two-term spherical harmonic approach and provide new models for closure of plasma fluid models.