Extragalactic cosmic rays diffusing from two populations of sources

We consider the possibility of explaining the observed spectrum and composition of the cosmic rays with energies above 10(17) eV in terms of two different extragalactic populations of sources in the presence of a turbulent intergalactic magnetic field (including also a fading galactic cosmic-ray component). The populations are considered to be the superposition of different nuclear species having rigidity-dependent spectra. The first extragalactic population is dominant in the energy range 10(17) - 10(18) eV and consists of sources having a relatively large density (> 10(-3) Mpc(-3)) and a steep spectrum. The second extragalactic population dominates the cosmic-ray flux above a few EeV; it has a harder spectral slope and has a high-energy cutoff at a few Z EeV (where eZ is the associated cosmic-ray charge). This population has a lower density of sources (< 10(-4) Mpc(-3)), so that the typical intersource separation is larger than few tens of Mpc, being significantly affected by a magnetic horizon effect that strongly suppresses its flux for energies below similar to Z EeV. We discuss how this scenario could be reconciled with the values of the cosmic-ray source spectral indices that are expected to result from the diffusive shock acceleration mechanism.