Models of H$_{\alpha}$ Doppler emission profiles from low-pressure, hollow-cathode discharges in hydrogen

Calculated Doppler profiles are compared with experiment for the H$_{\alpha}$ line excited in collisions of fast atoms, ions, molecules, and electrons with H$_2$ in low-pressure, high-voltage hollow-cathode hydrogen discharges. We test the proposal of Lavrov and Mel'nikov\footnote{B. P. Lavrov and A. S. Mel'nikov, Optics and Spectrosc. {\bf 79}, 842 (1995).} that their observation of fast H(n=3) moving away from the cathode is the result of acceleration of H$^-$ and its subsequent collisions with H$_2$. Our recent model\footnote{A. V. Phelps, Phys. Rev. E {\bf 79}, 066401 (2009).} is extended to include the kinetics of H$^-$. Because the cathode fall is mostly outside the cylindrical cathode, the cathode is approximated as a nearly transparent planar electrode with an unknown area for reflection of fast H atoms and for production of H$^-$. Calculated Doppler profiles are compared with emission measurements parallel to the tube axis for their wide range of pressures. Using experimental H$^-$ yields, the calculated H$^-$ contribution to the H$_{\alpha}$ wing is significantly smaller than that caused by H atoms reflected by the cathode and comparable with the noise in the measured data.