Propagation of Solar Energetic Particles in Three-dimensional Interplanetary Magnetic Fields

This paper presents a model calculation of solar energetic particle propagation in a three-dimensional interplanetary magnetic field. The model includes essentially all the particle transport mechanisms: streaming along magnetic field lines, convection with the solar wind, pitch-angle diffusion, focusing by the inhomogeneous interplanetary magnetic field, perpendicular diffusion, and pitch-angle dependent adiabatic cooling by the expanding solar wind. We solve the Fokker–Planck transport equation with simulation of backward stochastic processes in a fixed reference frame in which any spacecraft is roughly stationary. As an example we model the propagation of those high-energy (E 10 MeV) solar energetic particles in gradual events that are accelerated by large coronal mass ejection shocks in the corona and released near the Sun into interplanetary space of a Parker spiral magnetic field. Modeled with different scenarios, the source of solar energetic particles can have a full or various limited coverages of latitude and longitude on the solar surface. We compute the long-term time profiles of particle flux and anisotropy at various locations in the heliosphere up to 3 AU, from the ecliptic to high latitudes. Features from particle perpendicular diffusion are revealed. Our simulation reproduces the observed reservoir phenomenon of solar energetic particles with constraints on either solar particle source or the magnitude of perpendicular diffusion.