Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H${}_2$

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.

arXiv commentSubmitted to Plasmas Sources Science and Technology 8/18/2010

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