Hilbert expansion based fluid models for kinetic equations describing neutral particles in the plasma edge of a fusion device

TL;DR

This paper develops and analyzes fluid models derived from kinetic equations for neutral particles in the plasma edge of fusion devices, using Hilbert expansion and different scalings, validated against numerical benchmarks.

Contribution

It introduces a systematic derivation of transient fluid models from kinetic equations via Hilbert expansion, considering different scalings and validating with numerical experiments.

Findings

Fluid models accurately approximate kinetic equations in charge-exchange dominated regimes.

Hydrodynamic and diffusive scalings lead to different fluid model formulations.

Numerical validation shows good agreement with Monte Carlo and discrete velocity models.

Abstract

Neutral particles in the plasma edge of fusion devices based on magnetic confinement are described by a transient kinetic equation incorporating ionization, recombination, and charge-exchange collisions. In charge-exchange dominated regimes, the neutral particle velocity distribution approaches the drifting Maxwellian defined by the mean velocity and temperature of the plasma. This enables model order reduction from the kinetic equation to approximate fluid models. We derive transient fluid models consistent with the kinetic equation by exploring a splitting based approach. We split the kinetic equation in sources and sinks on the one hand, and transport combined with charge-exchange on the other hand. Combining transport with charge-exchange collisions allows for deriving Hilbert expansion based fluid models. The retrieved fluid models depend on the assumed importance (scaling) of the different terms in the split equation describing transport and charge-exchange. We explore two scalings: the hydrodynamic scaling and the diffusive scaling. The performance of the fluid models with respect to a discrete velocity model and a Monte Carlo reference solver is assessed in numerical experiments. The code used to perform the numerical experiments is openly available.