First-principles closure for anomalous transport in Hall thrusters: Self-consistent implementation and numerical stability

This work presents a self-consistent implementation of a first-principles closure model for anomalous electron transport in Hall thrusters, addressing numerical challenges that have thus far hindered incorporation of the authors' previously developed wave-based transport theory. The model, derived from a wave–particle interaction theory in which electron cyclotron drift instability turbulence and its transition to longer-wavelength lower-hybrid modes dominate the nonlinear saturation of the instability, provides both fluid and kinetic formulations for the anomalous momentum-transfer collision frequency and is employed together with the anomalous electron-heating closure previously developed by the authors. When implemented within the generalized Ohm's law, the original formulation leads to a degeneracy in which the electric field vanishes from the current conservation relation, precluding the determination of a unique plasma potential. In this study, a revised scaling of the ion-trapping coefficient combined with a regularization of the azimuthal electron velocity that remains inactive in regions of large drift restore numerically well-posed formulations while preserving the underlying physics of the model. The modified formulation is implemented in a one-dimensional hybrid solver (Hall1De), enabling stable steady-state solutions and systematic numerical investigations. Parametric studies reveal the sensitivity of the anomalous transport profile to key coefficients governing wave growth and saturation, while macroscopic plasma properties remain comparatively insensitive. The results establish a robust framework for embedding physics-based closures in hybrid simulations and provide guidance for further development, including extensions to account for axial ion dynamics and future validation in fully two-dimensional hybrid simulations.