Stochastic Propagation of Solar Energetic Particles in Coronal and Interplanetary Magnetic Fields

Abstract

This paper describes a method of simulating solar energetic particle propagation through the magnetic fields of the solar corona and interplanetary medium. The simulation code is based on the focus transport equation of energetic particles in 3-d magnetic fields, which contains all the particle transport mechanisms, including streaming, convection, gradient/curvature drift, adiabatic focusing, pitch angle scattering by Alfvénic magnetic field fluctuations and perpendicular diffusion due to the random walk of field lines. In the simulation, particles are injected at their source in the corona, and their guiding center trajectories are calculated using stochastic differential equations. Because of the vastly different time scales of particle transport mechanisms included in the equation, we use the 4-th order Runge-Kutta method to integrate the particle streaming and adiabatic focusing terms, while the stochastic terms of pitch angle scattering and perpendicular diffusion are integrated with the Euler scheme. The model is applied to the 2017 September 10 solar energetic particle event. With perpendicular diffusion, we are able to explain SEP observations from Earth and STEREO-A. A pattern of SEP precipitation on the solar surface is also predicted.