Cosmic-ray propagation through the disturbed heliosphere

The stationary, source-free, one-dimensional solution to the cosmic-ray heliospheric transport equation was solved using Runge-Kutta methods. These calculations have been applied to the treatment of Forbush decreases and the evolution of the solar cycle through the heliosphere. Forbush decreases calculated by this method produce spectra that are in good agreement with both the theoretical heliocentric potential and the potential as determined from neutron monitor data. During solar modulation, the effect of the travelling disturbance is to flatten the gradient of the cosmic ray flux in the inner heliosphere at solar minimum and steepen the gradient at solar maximum, as the incoming cosmic rays see solar activity up to a year earlier. The resulting spectra at the earth's orbit are in good agreement with the heliocentric approximation. The heliocentric approximation is an accurate and convenient method of accounting for solar modulation.