Solar flare particle propagation: Comparison of a new analytic solution with spacecraft measurements

A new radial solution has been obtained to the Fokker-Planck equation for solar flare particle propagation that includes the effects of convection, energy change, and anisotropic diffusion with κγ = constant. It is assumed that the particles are injected impulsively at a single point and that there is a free escape boundary. In addition, the azimuthal solution derived by Burlaga, which was based on κθ ∝ γ², has been modified to include some of the effects of solar rotation. With an outer boundary at ∼2.7 AU, a solar wind velocity of ∼400 km/sec, and κγ ≈ 2 to 8 × 1020 cm²/sec, the complete solution gives reasonable fits to the time profiles of 1- to 10-Mev protons from ‘classical’ flare-associated events observed with the Caltech solar and galactic cosmic ray experiment aboard Ogo 6. It is not necessary to invoke a scatter free region near the sun in order to reproduce the fast rise times observed for west limb events, indicating that κγ = constant is a better description of conditions inside 1 AU than is κγ ∝ γ. The radial solution also provides insight into the possible dependence of the observed decay times on various parameters and can be used as the basis for an illustrative calculation of the evolution of the vector anisotropy.