Measured (circles) and simulated (asterisks) energy spectra of energetic protons. The solid and dashed lines illustrate the power-law fit to the spectra. Panel a: flux peak energy spectra, where the estimated spectrum indexes are 3.68 from the simulation and 3.38 from the measurement. Panel b: event-integrated energy spectra calculated by integrating proton fluxes from 21 August 05:00 UT to 24 August 10:00 UT and the spectrum indexes are 3.62 and 3.45, respectively.