Direct allowance for the effect of photoelectrons in ionospheric modeling

Model calculations for the ionospheric E and F1 regions yield electron densities which are much too small, if no allowance is made for the production of secondary ionization by primary photoelectrons. Full calculations of this secondary production are quite difficult, since the upward and downward photoelectron fluxes must be determined as a function of energy at each height. Early studies showed that secondary ionization increases the total production rate by about 30% in the F2 region, while more recent studies show increases of around 100% in the E and F1 regions. Use of a fixed correction factor (for a given height and zenith angle) is not satisfactory, however, since the amount of secondary production varies greatly for different radiation bands. This paper describes a new approach in which a secondary production factor is determined for each ion and each radiation band. These factors (n(s)) are defined by the initial photon energy, and the mean energy of the final secondary electrons. For each radiation band the effective production efficiencies, for each ion, are increased by the factor 1 + n(s). Modeling of the ionosphere then proceeds normally, with no other changes and no increase in computer time. All results automatically include a full allowance for secondary production, for any assumed values of zenith angle, atmospheric model, or EUV fluxes. Comparison with recent, full photoelectron calculations shows that this procedure gives reliable results, with errors which are less than those due to current uncertainties in the solar fluxes, the photoionization cross sections and the electron collision cross sections.