Energetic storm particles (ESP) of various ion species have been shown to arise from a suprathermal seed ions accelerated by traveling interplanetary shocks. The observed spectral rollovers at~0.1 to 10 MeV/nucleon can be attributed to the finite time available for shock acceleration. We construct a finite time shock acceleration model for describing ESP events at interplanetary shocks near the Earth. Using the locally measured shock strength parameters as inputs, the finite-time shock acceleration model can successfully fit the energy spectra of carbon, oxygen, and iron ions measured by the Ultra-Low-Energy lsotope Specturemeter (ULEIS) on board the Advanced Composition Explorer during 3 ESP events. The inferred scattering mean free path in the acceleration region ranges from a typical interplanetary value for the weakest ESP event down to 0.003 AU for the strongest event.This is consistent with the idea that proton-amplified waves result from the very intense particle fluxes in major events.
