Analytical Model for Galactic and Solar Cosmic Ray Ionization in the Planetary Ionospheres and Atmospheres

An analytical model for cosmic ray (CR) ionization in the terrestrial lower ionosphere and middle atmosphere is developed in this work. For this purpose the ionization losses (dE/dh) according the Bohr-Bethe-Bloch formula for the energetic charged particles are approximated in five different energy intervals similarly to Dorman (Cosmic Rays in the Earth’s Atmosphere and Underground. Dordrecht, Kluwer Acad. Publ. 2004), but a few precision corrections are involved. More accurate expressions for energy decrease of particles E(h) and electron production rate profiles q(h) in the ionosphere and atmosphere are derived. The obtained formulas allow comparatively easy computer programming. The integrand in q(h) gives the possibility for application of adequate numerical methods – such as Romberg method, or Gauss quadrature, for the solution of the mathematical problem. On this way the process of interaction of cosmic ray particles with the upper, middle and lower atmosphere will be described much more realistically. Here we enlarge significantly the energetic interval (5- 5000 GeV) of the penetrating cosmic rays at their interaction with the atmospheres and ionospheres of the planets, satellites and comets. We introduce new approximation formula for the ionization losses (dE/dh) of the energetic charged particles i