A numerical simulation of solar energetic particle dropouts during impulsive events

This paper investigates the conditions for producing rapid variations of solar ener- getic particle (SEP) intensity commonly known as dropouts. In particular, we use numerical model simulations based on solving the focused transport equation in the 3-dimensional Parker interplanetary magnetic field to put constraints on the proper- ties of particle transport coefficients both in the direction perpendicular and parallel to the magnetic field. To simulate the effect of field lines that may alternatively connect and disconnect an observer from a compact SEP source on the solar surface, we place several smaller SEP sources that release particles impulsively and simultaneously at separate longitudes on the solar surface. We let magnetic flux tubes filled or devoid of energetic particles pass the observer. The perpendicular particle diffusion tends to smooth out the intensity variation. Our calculations of the temporal intensity profile of 0.5 and 5 MeV protons at the Earth show that the perpendicular diffusion must be small enough while the parallel mean free path should be long in order to reproduce the phenomenon of SEP dropouts. When the parallel mean free path is a fraction of 1 AU and the observer is located at 1 AU, the perpendicular to parallel diffusion ratio must be below $10^{-5}$ if we want to see the particle flux dropping by at least several times within three hours. When the observer is located at a larger solar radial distance, the perpendicular to parallel diffusion ratio for reproducing the dropouts should be even lower than that in the case of 1 AU distance. A shorter parallel mean free path or a larger radial distance from the source to observer will cause the particles to arrive later, making the effect of perpendicular diffusion more prominent and SEP dropouts disappear.