Astrophysical magnetic field reconstruction and spectroscopy with ultra high energy cosmic rays

The next generation of ultra high energy cosmic ray experiments will probably detect several dozens of events clustered around the direction towards each of the most powerful extragalactic sources. We develop a method which could make possible to reconstruct, from the arrival directions and energies of the clustered events, the strength and coherence properties of the magnetic field along the line of sight towards the sources. The method exploits peculiar signatures arising from magnetic lensing effects, such as the strong flux magnification of multiple images around caustics. We also discuss how to obtain information about the cosmic ray composition, and apply this method to samples of simulated data.