Ion flux energy distributions in a hydrogen-filled drift tube at high E/N

Ion flux energy distributions are calculated for H$^+$, H$_2^+$, and H$_3^+$ ions in H$_2$ for low-current, uniform-electric-field drift tubes at 1 kTd $< E/N < 10$ kTd and $5\times10^{20} \leq N d \leq 3\times10^{21}$ m$^2$, where E is the electric field, N is the gas density, and $d$ is the electrode separation. We use updated cross sections in a multi-beam model of the spatial and energy dependent particle fluxes. Calculated distributions at the cathode are compared with experiments by Rao et al.\footnote{M. V. V. S. Rao, R. J. Van Brunt, and J. K. Olthoff, ESCAMPIG '96.} and detailed theory by Bretagne et al.\footnote{J. Bretagne, G. Gousset, T. \v{S}imko, M.V.V.S. Rao, R. J. Van Brunt, Y. Wang, J. K. Olthoff, B. L. Peko and R. L. Champion, ESCAMPIG '96.} Hypothetical large increases in the total momentum transfer cross sections for H$^+$ and H$_3^+$ at 100 to 1000 eV yield approximate fits to the relative experimental distributions at high energies at moderate $E/N$. However, these fitted distributions are much too small at low ion energies. Similar discrepancies occur for analytic solutions of the Boltzmann equations using simplified reaction cross sections and the almost free-fall conditions for H$^+$ at 10 kTd.