Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles

Abstract

The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20°-60°. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20°. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slablike fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances.1. INTRODUCTION Magnetic field lines are a useful construct frequently employed (Parker 1979) to help in determining the connectivity between points of observation (Owens & Forsyth 2013, and references within). Connectivity is then employed to determine the heat flux, which, in turn, helps to determine patterns of plasma flow and the propagation of energetic particles. Connectivity influences energy transport, with possible impacts on plasma composition, reconnection, and other building blocks of space plasma studies (Suess 1993;Crooker & Horbury 2006). Mappings of coronal and interplanetary field lines are employed in studies of coronal heating and accelera-