Separation of solar and interplanetary diffusion in solar cosmic ray events

A study has been made of the propagation of solar cosmic rays after their release from a flare under the assumption of diffusive motion around the sun and in interplanetary space (where kappa1 is taken to be 0). For two-dimensional diffusion around the sun and for a diffusion coefficient kappa11(r) =kappa0r/sup β/in interplanetary space, approximate analytic solutions have been found for the density N(t) and the anisotropy xi (t). Both density and anisotropy are found to be prolonged at 1 AU relative to those for impulsive injection. By combining these, the diffusion coefficients at the sun and at 1 AU can be extracted separately. To check the approximate analytic solution, numerical computation over a wide range of propagation conditions indicates that mean free paths derived near 1 AU are accurate to within 13% (when they are fitted up to time of maximum, t/sub m/) or to within 25% (up to 2t/sub m/). The effect of one- or three-dimensional diffusion around the sun instead of two-dimensional diffusion is to change the derived mean free path by less than 25% (up to t/sub m/). The effect of a non-negligible loss (or escape) of particles at the sun has been evaluated; for all except the largest value of loss rate suggested, the error is small up to t/sub m/. Application of the solution to the ground level event of September 1, 1971, when the flare was approx. =400 behind the west limb, gives a solar diffusion coefficient kappa/sub s//r/sub s/2=1.5 h-1 and a mean free path at 1 AU of 0.15 AU for the case β=0