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We simulate the propagation of cosmic rays at ultra-high energies, $\gtrsim10^{18}$ eV, in models of extragalactic magnetic fields in constrainedsimulations of the local Universe. We use constrained initial conditions withthe cosmological magnetohydrodynamics code {\sc ENZO}. The resulting models ofthe distribution of magnetic fields in the local Universe are used in the\crpropa code to simulate the propagation of ultra-high energy cosmic rays. Weinvestigate the impact of six different magneto-genesis scenarios, bothprimordial and astrophysical, on the propagation of cosmic rays overcosmological distances. Moreover, we study the influence of different sourcedistributions around the Milky Way. Our study shows that different scenarios ofmagneto-genesis do not have a large impact on the anisotropy measurements ofultra-high energy cosmic rays. However, at high energies above the GZK-limit,there is anisotropy caused by the distribution of nearby sources, independentof the magnetic field model. This provides a chance to identify cosmic raysources with future full-sky measurements and high number statistics at thehighest energies. Finally, we compare our results to the dipole signal measuredby the Pierre Auger Observatory. All our source models and magnetic fieldmodels could reproduce the observed dipole amplitude with a pure iron injectioncomposition. Our results indicate that the dipole is observed due to clusteringof secondary nuclei in direction of nearby sources of heavy nuclei. A lightinjection composition is disfavoured by the non-observation of anisotropy atenergies of $4-8 \rm\ EeV$.

Simulations of ultra-high Energy Cosmic Rays in the local Universe and the origin of Cosmic Magnetic Fields