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

TL;DR

The paper addresses non-equilibrium ion dynamics in bounded, low-temperature plasmas by evaluating high-order moment closures up to the fourth moment (5M) against kinetic PIC-MCC data. It analyzes four closures—Globally Hyperbolic Regularized Grad, HyQMOM, EQMOM, and Maximum Entropy—within a 1D ion kinetics framework and uses efficient numerical schemes with analytic or interpolated closures to maintain computational costs similar to classical 3M fluids. Results show that all 5M closures improve over 3M fluids, with HyQMOM delivering the most robust performance across bulk and sheath regimes, while ME and EQMOM suffer from Junk line singularities at low pressures and Grad regularization can induce positivity issues. The study demonstrates that high-order moment methods can capture both moments and velocity distribution functions with high fidelity at a fraction of kinetic-simulation cost, enabling accurate and efficient bounded-plasma simulations. It also highlights the potential of combining HyQMOM with GQMOM for VDF reconstruction and points to future work on more realistic collision physics and self-consistent electron-ion coupling.

Abstract

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.

Figures (9)

• Figure 1: Scheme of the numerical set-up.
• Figure 2: Variation of the closing flux $s_\star$ as the heat flux $q_\star$ and the kurtosis $r_\star$. The hatched zoned represent the non-realizable region where no positive function can have such heat-flux and kurtosis, and the dashed line represents the Junk line and the purple cross the thermodynamic equilibrium.
• Figure 3: Density profiles of all the simulations for four pressures.
• Figure 4: Temperature profiles of all the simulations for four pressures. For each plot we show a zoom of the sheath next to it.
• Figure 5: Heat flux profiles of all the simulations for four pressures. We represent the Fourier heat flux of the non-isothermal Maxwellian cases in dashed lines. For each plot we show a zoom of the sheath next to it.