CONTRIBUTIONS TO THE COSMIC RAY FLUX ABOVE THE ANKLE: CLUSTERS OF GALAXIES

Assuming that particles can be accelerated to high energies via diffusive shock acceleration process at the accretion shocks formed by the infalling flow toward the clusters of galaxies, we have calculated the expected spectrum of high-energy protons from the cosmological ensemble of the cluster accretion shocks. The model with Jokipii diffusion limit could explain the observed cosmic ray spectrum near $10^{19}eV$ with reasonable parameters and models if about $10^{-4}$ of the infalling kinetic energy can be injected into the intergalactic space as the high energy particles.