Birth-Potential Multigroup Fluid Model for Ballistic Electrons: Breakdown and Cathode Sheath Regimes
Abstract
Fluid models of discharges fail where electron runaway dominates. On the left branch of the Paschen curve and in high-voltage cathode sheaths, the electron population splits into a thermal bulk and a ballistic beam that no single electron fluid can represent. We present a multigroup fluid model that divides ballistic electrons into groups indexed by their birth potential: the electrostatic potential at which they were liberated, offset by the forward kinetic energy they carried. Because the birth potential is a constant of ballistic motion, the electric field never moves electrons between groups and only collisions do. Each group requires a single continuity equation because its velocity follows algebraically from the local potential, and the number of groups is set by the energy resolution alone independently of the mesh. A runaway criterion based on the local field assigns each newly liberated electron to the bulk or a ballistic group, so the model applies even where no sheath exists. Benchmarked against a kinetic solver in argon, it reproduces the left branch of the Paschen curve---which local-field and local-energy models miss or misplace---and tracks the current--voltage characteristic of a cathode sheath to within a few percent at reduced fields exceeding 104 Td, where the local-energy model overpredicts the current up to thirtyfold. Since as few as 10 to 30 groups suffice, depending on the field, the approach brings near-kinetic accuracy to multi-species computational fluid dynamics solvers at the cost of that many additional species, without added velocity-space dimensions or particle noise.
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BibTeX
@misc{parent2026birthpotential,
title = {{Birth-Potential Multigroup Fluid Model for Ballistic Electrons: Breakdown and Cathode Sheath Regimes}},
author = {Bernard Parent and Brendan Perry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02139},
eprint = {2610.02139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02139},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Birth-Potential Multigroup Fluid Model for Ballistic Electrons: Breakdown and Cathode Sheath Regimes
AU - Bernard Parent
AU - Brendan Perry
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02139
UR - https://arxiv.org/abs/2610.02139
AB - Fluid models of discharges fail where electron runaway dominates. On the left branch of the Paschen curve and in high-voltage cathode sheaths, the electron population splits into a thermal bulk and a ballistic beam that no single electron fluid can represent. We present a multigroup fluid model that divides ballistic electrons into groups indexed by their birth potential: the electrostatic potential at which they were liberated, offset by the forward kinetic energy they carried. Because the birth potential is a constant of ballistic motion, the electric field never moves electrons between groups and only collisions do. Each group requires a single continuity equation because its velocity follows algebraically from the local potential, and the number of groups is set by the energy resolution alone independently of the mesh. A runaway criterion based on the local field assigns each newly liberated electron to the bulk or a ballistic group, so the model applies even where no sheath exists. Benchmarked against a kinetic solver in argon, it reproduces the left branch of the Paschen curve---which local-field and local-energy models miss or misplace---and tracks the current--voltage characteristic of a cathode sheath to within a few percent at reduced fields exceeding 10^4 Td, where the local-energy model overpredicts the current up to thirtyfold. Since as few as 10 to 30 groups suffice, depending on the field, the approach brings near-kinetic accuracy to multi-species computational fluid dynamics solvers at the cost of that many additional species, without added velocity-space dimensions or particle noise.
ER -