Analytical representation of g factors for rapid, accurate calculation of excitation rates in the dayside thermosphere


  • D. J. Strickland,

  • T. Majeed,

  • J. S. Evans,

  • R. R. Meier,

  • J. M. Picone


An algorithm has been developed that rapidly and accurately calculates altitude profiles of volume excitation rates for many species of aeronomic interest. These rates may be specified as functions of solar activity (specific to the Hinteregger et al. [1981] model in this phase of the work) and solar zenith angle (SZA). The algorithm relies on an analytical expression for the g factor as a function of total vertical column density. The g factor for a given state and excitation process can be defined as the direct volume excitation rate for this process divided by the density of the species involved in the direct excitation. Modeling results from this work show that g, when expressed as a function of total vertical column density, is independent of model atmosphere within a small error illustrated in the text. The dependence within g then reduces to solar activity (characterized by F10.7) and SZA. Extensive photoelectron transport calculations have been performed that provide numerical g factors for 22 excitation processes, 3 F10.7 values (75, 150, and 250), and 8 solar zenith angles (0°, 45°, 60°, 70°, 80°, 85°, 87°, and 90°). The results have been fitted with a 10 coefficient analytical expression comprised of a function based on an analytical solution to a simplified photoelectron transport equation and two Gaussian functions needed for structure because of soft X ray energy deposition. The resulting coefficients are used to calculate g factors for user-specified pairs of F10.7 and SZA by two-dimensional interpolation. By inputting a model atmosphere the corresponding volume excitation rates may also be specified. For photoionization excitation the analytic expression for the g factor is much simpler. Results presented herein include comparisons between numerical g factors and their fits, along with examples of both g factors and corresponding volume excitation rates for the purpose of showing the effects of changing solar activity and SZA. Tables are included that identify excitation processes, identify additional processes that must be considered to derive emission rates, and provide cross-section information for the electron impact processes addressed in this work.


This work was funded by the Air Force Defense Meteorological Satellite Program office in support of algorithm development at NRL for the Special Sensor Ultraviolet Limb Imager. We would like to acknowledge Scott Bertin of CPI for development of automated algorithms and associated software for fitting g factors and Rick Link for cross-section discussions and making available to us photoelectron results from his twostream model as part of the reported validation effort and for our initial examination of g factor properties.

The editor thanks G. R. Gladstone and S. M. Bailey for their assistance in evaluating this paper.