Transport of solar energetic particles accelerated by ICME shocks: Reproducing the reservoir phenomenon

In this work, gradual solar energetic particle (SEP) events observed by multiple spacecraft are investigated with model simulations. Based on a numerical solution of the Fokker-Planck focused transport equation including perpendicular diffusion of particles, we obtained the fluxes of SEPs accelerated by an interplanetary coronal mass ejection driven shock as it propagates outward through the three-dimensional Parker interplanetary magnetic field. The shock is treated as a moving source of energetic particles with an assumed particle distribution function. We look at the time profiles of particle flux as they are observed simultaneously by multiple spacecraft located at different locations. The dependence of particle fluxes on different levels of perpendicular diffusion is determined. The main purpose of our simulation is to reproduce the reservoir phenomenon, during which it is frequently observed that particle fluxes are nearly the same at very different locations in the inner heliosphere, up to 5 AU, during the decay phase of gradual SEP events. The reservoir phenomenon is reproduced in our simulation under a variety of conditions of perpendicular diffusion of particles estimated from the nonlinear guiding center theory (NLGC). As the perpendicular diffusion coefficient increases, the nonuniformity of particle fluxes becomes smaller, making the reservoir phenomenon more prominent. However, if the shock acceleration strength decreases slower than r ^-2.5 with the radial distance r, the reservoir phenomenon might disappear, with limited perpendicular diffusion constrained by the NLGC theory. Therefore, observation of the reservoir phenomenon in gradual SEP events can be used to test qualitatively theories of particle diffusion and shock acceleration.