Pitch angle distributions of solar energetic particles and the local scattering properties of the interplanetary medium

Abstract

A diffusive approximation of the Fokker-Planck equation is presented which contains adiabatic focusing and pitch angle scattering as elementary processes. The normalized anisotropic part of the distribution function, presented in closed analytical form, is uniquely determined by observable quantities and is independent of time throughout a solar event. It depends only on the local values of the ratio of the mean free path to the focusing length and on the shape of the pitch angle diffusion coefficient. The solution is not limited to weak focusing as long as the solar injection process lasts sufficiently long. Some numerical examples are given, and the application of the model to observations represented by a Legendre expansion up to the fourth order are discussed. Deviations from quasi-linear theory and the influence of helicity on the angular distributions are discussed. The method is also applied to solar particle events aboard the space probes Helios 1 and 2.