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

TL;DR

This paper develops a model for collisional kinetics in low-pressure hydrogen discharges with non-uniform electric fields, predicting emission profiles, ion distributions, and comparing results with various experimental setups.

Contribution

It extends existing uniform-field models to non-uniform fields and high current densities, providing detailed predictions of emission and ion energy distributions in hydrogen discharges.

Findings

Hα emission is linear with current density over eight orders of magnitude.

Ion energy distributions for H₂⁺ and H₃⁺ agree well with experiments.

Model successfully describes a range of discharge types from glow to electrostatic confinement.

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.