Galactic cosmic ray modulation from 1965–1970

Numerical solutions of the cosmic-ray equation of transport within the solar cavity and including the effects of diffusion, convection, and energy losses due to adiabatic deceleration, have been used to reproduce the modulation of galactic electrons, protons and helium nuclei observed during the period 1965–1970. Kinetic energies between 10 and 10⁴ MeV/nucleon are considered. Computed and observed spectra (where data is available) are given for the years 1965, 1968, 1969 and 1970 together with the diffusion coefficients. These diffusion coefficients are assumed to be of separable form in rigidity and radial dependence, and are consistent with the available magneticfield power spectra. The force-field solutions are given for these diffusion coefficients and galactic spectra and compared with the numerical solutions. For each of the above years we have (i) determined the radial density gradients near Earth; (ii) found the mean energy losses suffered by galactic particles as they diffuse to the vicinity of the Earth's orbit; (iii) shown quantitatively the exclusion of low-energy galactic protons and helium nuclei from near Earth by convective effects; and (iv), for nuclei of a given energy near Earth, obtained their distribution in energy before entering the solar cavity. It is shown that the energy losses and convection lead to near-Earth nuclei spectra at kinetic energies ≤100 MeV/nucleon in which the differential intensity is proportional to the kinetic energy with little dependence on the form of the galactic spectrum. This dependence is in agreement with the observed spectra of all species of atomic nuclei and we argue that this provides strong observational evidence for the presence of energy losses in the propagation process; and for the exclusion of low energy galactic nuclei from near Earth.