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To understand in detail cosmic magnetic fields and sources of Ultra-High Energy Cosmic Rays (UHECRs) we have developed a Monte Carlo simulation for galactic and extragalactic propagation. In our approach we identify three different propagation regimes for UHECRs, the Milky Way, the local universe out to 110 Mpc, and the distant universe. For deflections caused by the galactic magnetic field a lensing technique based on matrices is applied which are created from backtracking of antiparticles through galactic field models. Propagation in the local universe uses forward tracking through structured magnetic fields extracted from simulations of the large scale structure of the universe. UHECRs from distant sources are simulated using parameterized models. In this contribution we present the combination of all three simulation techniques by means of probability maps. The combined probability maps are used to generate a large number of UHECRs, and to create distributions from approximately realistic universe scenarios. Comparisons with physics analyses of UHECR measurements enable the development of new analysis techniques and help to constrain parameters of the underlying physics models like the source density and the magnetic field strength in the universe.

A Hybrid Monte Carlo Generator for Ultra-High Energy Cosmic Rays from their Sources to the Observer