Energetic particle events:: Efficiency of interplanetary shocks as 50keV<E<100MeV proton accelerators

We have studied the injection rate of shock-accelerated protons in long-lasting particle events by tracing back the magnetohydrodynamic conditions at the shock under which protons are accelerated. This tracing back is carried out by fitting the observed flux and anisotropy profiles at different energies, considering the magnetic connection between the shock and the observer, and modeling the propagation of the shock and of the particles along the interplanetary magnetic field. A focused-diffusion transport equation that includes the effects of adiabatic deceleration and solar wind convection has been used to model the evolution of the particle population. The mean free path and the injection rate have been derived by requiring consistency with the observed flux and anisotropy profiles for different energies, in the upstream region of the events. We have extended the energy range of previous models down to 50 keV and up to similar to 100 MeV. We have analyzed four proton events, representative of west, central meridian, and east scenarios. The spectra of the injection rate of shock-accelerated protons derived for these events show that for energies higher than 2 MeV the shock becomes a less efficient proton accelerator. We have related the derived injection rates to the evolution of the strength of the shock, particularly to the normalized downstream-upstream velocity ratio (VR), the magnetic field ratio, and the angle theta(Bn). As a result, we have derived an empirical relation of the injection rate with respect to the normalized velocity ratio (log Q proportional to VR), but we have not succeeded with the other two parameters. The Q(VR) relation allows us to determine the injection rate of shock-accelerated particles along the shock front and throughout its dynamical expansion, reproducing multispacecraft observations for one of the simulated events. This relation allows us to analyze the influence of the corotation effect on the modeled particle flux and anisotropy profiles.