Abstract.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. , 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 . Model 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 modelled range from short-gap, parallel-plane glow discharges to beamlike, electrostatic-confinement discharges.