The Mean Free Path of 13–64 MeV Protons Derived from Statistical Results of Solar Energetic Particle Events

A recent study by Wang et al. investigated gradual solar proton events with energies >10 MeV, as observed by STEREO-A, STEREO-B, and the Solar and Heliospheric Observatory spacecraft. For each event, the spacecraft with the best magnetic connection to the source region among the three spacecraft was identified, and energetic proton intensities observed by the spacecraft were analyzed through fitting. The fitting process produced two parameters, b and c, for four energy channels (13–16 MeV, 20–25 MeV, 32–40 MeV, and 40–64 MeV) in each event. Parameters b and c govern the rise and decay of particle intensities, respectively. Statistical analysis revealed a power-law correlation between b and c, expressed as c ∼ b−γ. In this study, in order to explain the relation between the two parameters, we investigate the model of particle diffusion coefficients in the interplanetary space. In our simulations, the radial mean free path is modeled as a power function of radial distance, successfully reproducing the b–c relation. Consequently, the observations demonstrate that the radial mean free path varies with radial distance in a power law. In future research, the model of diffusion coefficients holds promise in determining the mean free path of energetic protons.