# Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H$\_{2}$

Source: [Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H$\_{2}$](<https://www.sota2.com/research/paper/68fa2f821e209131ce86d001>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:37:05.208Z

Authors: A. V. Phelps

Published: 2010-11-08T06:16:51.000Z

## Abstract

A model of the collisional kinetics of energetic hydrogen atoms, molecules, and ions in pure H$\_2$ discharges is used to predict H$\_\\alpha$ emission profiles and spatial distributions of emission from the cathode regions of low-pressure, weakly-ionized discharges for comparison with a wide variety of experiments. Positive and negative ion energy distributions are also predicted. The model developed for spatially uniform electric fields and current densities less than $10^{-3}$ A/m$^2$ is extended to non-uniform electric fields, current densities of $10^{3}$ A/m$^2$, and electric field to gas density ratios $E/N = 1.3$ MTd at 0.002 to 5 Torr pressure. (1 Td = $10^{-21}$ V m$^2$ and 1 Torr = 133 Pa) The observed far-wing Doppler broadening and spatial distribution of the H$\_\\alpha$ emission is consistent with reactions among H$^+$, H$\_2^+$, H$\_3^+$, and H$^-H$ ions, fast H atoms, and fast H$\_2$ molecules, and with reflection, excitation, and attachment to fast H atoms at surfaces. The H$\_\\alpha$ excitation and H$^-$ formation occur principally by collisions of fast H, fast H$\_2$, and H$^+$ with H$\_2$. Simplifications include using a one-dimensional geometry, a multi-beam transport model, and the average cathode-fall electric field. The H$\_\\alpha$ emission is linear with current density over eight orders of magnitude. The calculated ion energy distributions agree satisfactorily with experiment for H$\_2^+$ and H$\_3^+$, but are only in qualitative agreement for H$^+$ and H$^-$. The experiments successfully modeled range from short-gap, parallel-plane glow discharges to beam-like, electrostatic-confinement discharges.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1011.1714>)

[PDF](<https://arxiv.org/pdf/1011.1714.pdf>)