Overview
This study focuses on the development and validation of one-dimensional high-order moment models to describe nonequilibrium ion transport in weakly ionized plasmas. The research introduces a novel six-moment hyperbolic quadrature-based model and compares its performance against a four-moment anisotropic Maxwellian model and a five-moment hyperbolic quadrature-based model. The models are designed to address conditions where ion-neutral collisions lead to nonequilibrium states that exceed the capabilities of classical transport models, such as those characterized by large drifts, strong heat flux, and temperature anisotropy.
Research Context
Ion-neutral collisions represent a fundamental process in the transport behavior of partially ionized plasmas. Nonequilibrium conditions for ions can emerge when collisional scales are comparable to the characteristic system scales or when strong electric fields are present. These conditions result in large drifts, significant heat flux, and discernible temperature anisotropy, which are phenomena not adequately captured by classical transport models. Existing challenges in modeling such plasmas include accurately representing these nonequilibrium effects.
Approach
The research employed the resolution of non-linear high-order moment closures as its methodological approach. Three specific models were investigated and compared:
- A four-moment anisotropic Maxwellian model, which considers mass, axial momentum, and both axial and perpendicular energies.
- A five-moment hyperbolic quadrature-based model, which accounts for the first five axial moments.
- A novel six-moment hyperbolic quadrature-based model, which incorporates the first five axial moments alongside perpendicular energy.
Analytical collision source terms were derived from the Boltzmann operator. This derivation was performed for ion-neutral scattering, accommodating arbitrary differential cross sections. This formulation extends the Chapman-Cowling theory to include arbitrary drift velocities, temperature anisotropies, and heat flux, while simultaneously ensuring strictly realizable distributions. Model validation involved non-linear simulations, which were benchmarked against kinetic solutions. These simulations utilized argon plasmas with realistic cross sections across a pressure range of 0.05-500 mTorr. The tested scenarios included a bounded plasma situated between floating walls and a direct-current discharge.
Findings
The comparative analysis indicated distinct performance characteristics among the models:
- The six-moment model demonstrated robust capabilities in capturing ion dynamics, especially under conditions described as strong nonequilibrium. In these conditions, anisotropy and heat flux exhibit non-local behavior.
- This six-moment model was observed to reconstruct the distribution function with high fidelity.
- It achieved this reconstruction without introducing noise into the results.
- The computational cost associated with the six-moment model was found to be comparable to that of fluid models, operating in a self-consistent manner.
Why This Matters
The ability to robustly capture complex ion dynamics under strong nonequilibrium conditions, particularly through a computationally efficient model like the six-moment model, offers a potential advancement in understanding and simulating partially ionized plasmas. This could provide more accurate representations of phenomena where classical transport models are insufficient due to large drifts, strong heat flux, and temperature anisotropy.