Non-linear high-order fluid moment closure for nonmagnetized electrons in partially-ionized plasmas

Linearized moment equations are often used to derive transport models for the closure of the hydrodynamic equations of multi-component plasmas close to thermodynamic equilibrium. However, the linearized transport equations lose their validity in rarefied conditions or in the presence of strong electric fields, when the distribution function of the different species are non-Maxwellian and the drift between the species becomes large. We develop a non-linear high-order moment model for 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, three elements for contracted heat flux vector, and one scalar contracted fourth-order moment. We consider the dominant 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 moment equations are integrated analytically for finite drift velocity between species and accounting for the non-linear terms in the Boltzmann operator. The new collisional terms present novel cross-effects that couple moments of different tensorial nature in the collisional terms, which are not present in the linearized equations and that are beyond Curie's symmetry principle. The present moment model is compared to 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, largely improving the results of the linear fourteen-moment model.