High-order moment closure for nonmagnetized electrons in partially ionized plasmas

Linearized moment equations are often used to derive closure models for the hydrodynamic equations of multicomponent plasmas near thermodynamic equilibrium. However, the linearized transport equations lose their validity in rarefied conditions or in the presence of strong electric fields, when the velocity distribution functions (VDFs) of the different species are non-Maxwellian and the drift between the species, i.e., the Mach number of the relative motion, becomes large. In this paper, we develop a nonlinear, high-order moment model for nonmagnetized electrons in partially ionized plasmas. We present a fourteen-moment model using a Hermitian expansion of the VDF that considers density, momentum, anisotropic pressure tensor, contracted heat flux vector, and contracted scalar kurtosis. We consider the relevant collisional processes in partially ionized plasmas, such as elastic and inelastic electron-neutral, electron-impact ionization, electron-electron Coulomb, and electron-ion Coulomb collisions. The collisional terms in the electron moment equations are integrated analytically for finite Mach numbers and accounting for the nonlinear terms in the Boltzmann operator, which are often neglected in linearized closure models. The proposed closure presents novel cross-coupling effects between moments of different tensorial nature within the collisional terms. The present nonlinear fourteen-moment model is benchmarked against a Monte Carlo simulation under a spatially homogeneous configuration, showing good agreement for a wide range of reduced electric field (e.g., up to 1000 Td) before runaway electrons occur, improving the results of a linear fourteen-moment model.