Solar modulation of galactic cosmic rays, 1

The equations governing cosmic-ray modulation allowing for convection, diffusion, and energy changes are approximated with simpler, more manageable equations that describe the particle behavior in a limited energy range. One of these equations determines an excellent approximation to the particle number density in the limit when the particles undergo relatively little modulation or equivalently when , where are characteristic values of the solar wind speed, the heliocentric distance, and the diffusion coefficient, respectively. This equation describes the behavior of particles with energies above a few hundred Mev/nucleon. Other approximate equations describe the behavior of the number density and radial streaming when , a condition which should be satisfied at energies below about 50–75 Mev/nucleon. Analytic solutions to the exact equations for the number density and streaming are given for cases in which the diffusion coefficient has the form κ = κoTarb, (b > 1), where r is heliocentric distance and T is particle kinetic energy. These solutions are used to demonstrate that the approximate equations accurately describe the particle behavior in their respective limits.