Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H₂

A model of the collisional kinetics of energetic hydrogen atoms, molecules and ions in pure H 2 discharges is used to predict H α 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 0.002–5 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 α emission is consistent with reactions among H + , H 2 + , H 3 + and H − ions, fast H atoms and fast H 2 molecules, and with reflection, excitation and attachment to fast H atoms at surfaces. The H α 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 α 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.