Models of H$\alpha$ Doppler emission profiles from cathode fall discharges in hydrogen

Doppler profiles are calculated for the H$\alpha$ line excited in collisions of fast atoms, ions, molecules, and electrons with H$_2$ in the cathode fall of low-pressure, moderate-current hydrogen discharges. We use a multi-beam model of the particle fluxes and energy distributions, assumed angular distributions of particles approaching and reflected by the cathode, and a simplified cathode fall model. Spectral profiles are compared with measurements parallel and perpendicular to the tube axis for the conditions reported by Cvetanovi\'c et al.\footnote{N. Cvetanovi\'c, M. M. Kuraica, and N. Konjevi\'c, J. Appl. Phys. {\bf 97}, 033302 (2005).} Excitation is principally by fast H atom collisions with H$_2$ as they approach and leave the cathode and by the electrons leaving the cathode. The calculated relative magnitudes of the wings and core of the parallel and perpendicular H$\alpha$ line profiles and the sensitivity of the emission produced by reflected atoms to cathode material are in agreement with experiment.