Propagation of Ultra High Energy Cosmic Rays in Extragalactic Magnetic   Fields: A view from cosmological simulations
  We use the CRPropa code to simulate the propagation of ultra high energy cosmic rays (with energy $\geq 10^{18} \rm eV$ and pure proton composition) through extragalactic magnetic fields that have been simulated with the cosmological ENZO code.We test both primordial and astrophysical magnetogenesis scenarios in order to investigate the impact of different magnetic field strengths in clusters, filaments and voids on the deflection of cosmic rays propagating across cosmological distances. We also study the effect of different source distributions of cosmic rays around simulated Milky-Way like observers. Our analysis shows that the arrival spectra and anisotropy of events are rather insensitive to the distribution of extragalactic magnetic fields, while they are more affected by the clustering of sources within a $\sim 50$ Mpc distance to observers. Finally, we find that in order to reproduce the observed degree of isotropy of cosmic rays at $\sim $ EeV energies, the average magnetic fields in cosmic voids must be $\sim 0.1 \rm \ nG$, providing limits on the strength of primordial seed fields. 
Stefan Hackstein, Franco Vazza, Marcus Brueggen, Guenter Sigl, Andrej   Dundovic
astro-ph.CO astro-ph.HE astro-ph.IM