One dimensional high-order moment models with realistic collisions for nonequilibrium ion transport in weakly ionized plasmas

Abstract

Ion-neutral collisions are fundamental in the transport of partially ionized plasmas. When collisional scales are comparable to the system scales or the electric field is strong, nonequilibrium conditions for the ions arise that are beyond classical transport models due to large drifts, strong heat flux, and temperature anisotropy. In this paper, we propose the resolution of non-linear high-order moment closures for simulating nonequilibrium ion dynamics in one-dimensional weakly ionized plasmas. We compare a four-moment anisotropic Maxwellian model (mass, axial momentum, and axial and perpendicular energies), a five-moment hyperbolic quadrature-based model (first five axial moments), and a novel six-moment hyperbolic quadrature-based model (first five axial moments + perpendicular energy). We derive analytical collision source terms from the Boltzmann operator for ion-neutral scattering with arbitrary differential cross sections. This formulation generalizes the Chapman-Cowling theory for arbitrary drift velocities, temperature anisotropies, and heat flux, ensuring strictly realizable distributions. The models are validated via non-linear simulations benchmarked against kinetic solutions for argon plasmas with realistic cross sections (0.05-500 mTorr). We test a bounded plasma between floating walls and a direct-current discharge. The six-moment model robustly captures ion dynamics, particularly under strong nonequilibrium, where anisotropy and heat flux are non-local. It reconstructs the distribution function with high fidelity, without noise, and at a cost comparable to fluid models in a self-consistent manner.