High-order moment closure for partially-ionized plasmas

Fluid models for the charged species in gas discharges are often based on the drift-diffusion approximation that neglects the inertial terms and uses transport coefficients that are obtained by solving the spatially-homogeneous electron kinetic in the two-term approximation. We propose an alternative model that is based on velocity-moments of the kinetic equation. In addition to conservation of mass, momentum, and energy, the moment models consider evolution equations for higher-order moments such as the heat-flux, pressure tensor, etc., which allow for capturing stronger non-equilibrium conditions. In this work, we will determine the closure of the higher-order moments while considering the relevant collisions in low-temperature plasmas, e.g., between the electrons and the gas (both elastic and inelastic) and Coulomb collisions (collisions between charged particles). We will compare our closure to the solutions of a Monte Carlo solver and a two-term Boltzmann model. The convergence with number of models as well as the numerical difficulties of these models will be discussed.