Anatole Berger | Searcharxiv

arXiv2026

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

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.

physics.plasm-ph↗

arXiv2025

Comparison of high-order moment models for the ion dynamics in a bounded low-temperature plasma

Low-temperature plasmas often present non-equilibrium ion distribution functions due to the collisions with the background gas and the presence of strong electric fields. This non-equilibrium is beyond classical fluid models, often requiring computationally-intensive kinetic simulations. In our work, we study high-order moment models in order to capture the non-equilibrium state with a macroscopic set of equations, which is more computationally efficient than kinetic simulations. We compare numerical simulations of different moment closures: Grad's closure, the hyperbolic quadrature method of moments (HyQMOM), the extended quadrature method of moments, and a method based on entropy maximization. We assess the different closures for plasma applications and propose efficient numerical discretizations. The numerical solution of the high-order moment models is compared to kinetic simulations of an argon plasma between two floating walls at different pressure regimes, from nearly collisionless to collisionally-dominated. In general, all the high-order moment closures capture the ion transport with high fidelity as compared to the kinetic simulations, providing an improvement as compared to classical fluid models. Classical fluid closures such as the Fourier law for the heat flux is shown to be not suitable to capture the sheath or the low pressure regime. In addition, the ability of each moment method to reconstruct the velocity distribution function from the moments is assessed. The high-order moment models are able to capture the non-equilibrium distributions in the bulk and sheath with remarkable fidelity, dramatically improving classical fluid models while having comparable computational cost. In particular, the HyQMOM shows to be a robust method that provides an excellent comparison with the kinetic simulations of both the moments and the distribution function in the bulk and the sheath.

physics.plasm-ph↗