GZK horizon and magnetic fields

We discuss some aspects of the propagation of high-energy cosmic rays (CRs) in turbulent magnetic fields, and propose a formula for the diffusion coefficient based on accurate simulations in a wide energy range. We discuss the transition between ballistic and diffusive regimes and the magnetic horizon of CR sources, showing how magnetic fields of a few nG could modify the shape of the GZK feature. Such fields would roughly be in equipartition with the extragalactic CRs, and could build through the resonant growth of waves within the lifetime of the universe.