Modeling cosmic ray ionization in an oblate planetary ionosphere

Abstract

Considering cosmic ray ionization in the lower ionosphere in an oblate planetary body, we have derived a modified Chapman function for an ellipsoid. Velinov (1968) introduced the “classic” Chapman function for a spherical planet in considering cosmic ray ionization. In this case the particle trajectory azimuth angle is the independent variable instead of the declination used for ionization by solar electromagnetic radiation. Calculation of ionization by all particles from different directions requires integration over azimuth angle, instead of only over zenith angle as in the spherical planet case when the Chapman function is used. For an oblate planetary body (ellipsoid), the atmospheric parameters (density and optical depth) depend on particle trajectory azimuth angle, so even for cosmic rays with isotropic distributions, integration over azimuth angle, zenith angle and energy is necessary. We have calculated the maximum zenith angle of a cosmic ray particle trajectory in an ellipsoidal atmosphere and have developed a software package for calculating the maximum zenith angle for different planets. Profiles of the electron production rates produced by mono-energetic solar proton fluxes in spherical and oblate atmospheres are computed. Different types of solar and galactic cosmic ray particles must be considered for calculating the ionization by all particles of all energies and directions in an oblate planetary ionosphere.