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An analytic form is given for the energy‐transfer rate from photoelectrons to thermal electrons. The expression fits the classical formulation of Itakawa tnd Aono (1966) at low energies and gives a smooth transition to fit the quantum mechanical equation of Schunk and Hays (1971) at higher energies. The corresponding loss function or stopping power has a form that is convenient in auroral and dayglow calculations.

Photoelectron energy degradation calculations have been performed with the improved analytic expression for the photoelectron to ambient electron energy transfer rate given by Swartz et al. (1971). On the basis of these calculations, two curves oeor the mean energy transferred per photoelectron to the ambient electrons are given as functions of the electronneutral density ratio. One curve is based on the primary-photoelectron production rate, and the other on the total production rate. When the electron-neutral density ratio falls between 10 -ø and 10-% these curves provide good estimates of the electron heating rates over a wide range of F region conditions. The large differences between the energy transfer rate coefficients used in these calculations and the Butler and Buckingham (1962) form ased in most previous investigations do not result in a major modification of the ambient electron heating rate. Theoretical studies of F region electron temperatures can be greatly simplified by introducing the concept of an electron heating efficiency as first defined by Hanson [1963]. Early calculations of this efficiency have generally been presented as functions of altitude and time of day [Hanson, 1963; Dalgarno et al., 1968; Hanson and Co.hen, 1968; Nagy et al., 1969]. After studying the variations of electron heating efficiencies resulting from many photoelectron energy degradation calculations covering a wide range of F region conditions, Swartz and Nisbet [1969] presented a simple description of electron heating in terms of the electron-neutral density ratio. Since then Schunk and Hays [1971] and Schunk et al. [1971] have revised the rate of energy transfer from photoelectrons to ambient electrons. A series of electron heating efficiencies has now been recalculated with this new energy transfer rate in the analytic form given by Swartz et al. [1971] and with the program described by Swartz [1972], which is a modification of the technique developed by Nisbet [1968]. The photoelectron heating rate of the ambient electrons is highest for photoelectrons with energies low enough to be below the thresholds of most of the neutral inelastic collision processes. This effect influences the electron heating Copyright ¸ 1972 by the American Geophysical Union. in two important ways. First, for energy bands with one main loss process most of the available energy is channeled into that one process, independently of the value given for the dominant rate coefficient. Thus, even though the rate of Swartz et al. is greater than that of Butler and Buckingham [1962] by 50%, the errors in calculations using the smaller Butler and Buckingham form are not large. Second, since a large fraction of the initial energy of the faster photoelectrons is lost to the neutral gas, the amount of energy given to the ambient-electron gas depends mainly on the number of electrons produced rather than on the energy spectrum of the photoelectrons. Since all fast electrons must cascade down through the lowest energy levels, each secondary electron with no...

An empirical model of the peak electron densities in the region of the northerly main trough in the ionospheric F region is presented. The model was derived from measurements made by the satellites Alouette I and II and is in the form of a multiplicative modification factor to the CCIR peak electron density model. The model is a computer program which, when provided with the location, universal time, day number, sunspot number, and Kp index, provides the modification factor, the CCIR model prediction of N,,F 2, and the new prediction including the effect of the trough. The model is expected to be of considerable use for propagation calculations in the affected region.

In the Martian ionosphere the dominant solar ionization products are O+ and CO2+. These ions are rapidly converted to O2+ by ion neutral reactions resulting in O2+ as the dominant ion. As O2+ has a lower ionization potential, each reaction results in approximately 1.2 eV of energy to be shared by the reaction products. The kinetic energy given to the O2+ will affect the ion temperatures. Calculations have been made of the ion heating rates and temperatures which result from the degradation of these energetic ions for various energy production distributions for conditions similar to those encountered by Viking 1. It is shown that the thermalization of the energetic O2+ can greatly increase the ion temperatures above 200 km compared to those calculated using only the ambient electron heating source. The effect of small horizontal magnetic fields, as predicted by current solar wind interaction models on the ion thermal balance was also investigated. These fields act to restrict the ion thermal conductivity and thus also increase the upper altitude ion temperatures. The combination of the heating by the energetic O2+ and the effect of the magnetic field provide a partial agreement with the Viking 1 measurements.