Analytic Approximations in the Study of the Solar Modulation of Electrons

Numerical solutions to the transport equation of galactic cosmic rays in the interplanetary medium have been used to investigate the applicability of commonly used approximate analytic solutions for electrons (10 MeV to 10 GeV). We find that for a given cosmic-ray diffusion coefficient: (a) the "force-field" approximation is in reasonable agreement with the numerical solution at energies ≳ 200 MeV, but deviates significantly at lower energies, depending on the shape of the interstellar electron spectrum, (b) the "diffusion-convection" approximation agrees generally with the numerical solution within a factor of ~ 2 over the entire energy range.