Modeling the solar energetic particle events in closed structures of interplanetary magnetic field

Abstract

We undertook a numerical modeling of the solar energetic particle (SEP) event inside a loop-like magnetic cloud in the solar wind. Particles accelerated near the Sun are injected into the cloud of a previous coronal mass ejection (CME) that already has expanded through 1 AU. In the framework of focused transport, we perform Monte Carlo simulations of the SEP propagation and adiabatic deceleration caused by an overall expansion of the CME. The loop-like structure of the interplanetary magnetic field strongly modifies the intensity-time profiles of high-energy protons. At not very small values of the particle mean free path, λ > 0.1 AU, and a power-law energy spectrum of >1 MeV protons, the proton event development after the intensity maximum is significantly closer to an exponential-decay profile than would be expected based on the modeling in the standard Archimedean-spiral field. The modeling results are similar to the patterns observed with the Energetic and Relativistic Nuclei and Electron (ERNE) particle telescope on board SOHO on 2-3 May 1998. We compare the numerical modeling results with estimates based on the diffusion-convection equation of SEP transport and provide analytical formulae, which can be used for analysis of future events.