Reconstruction of source and cosmic magnetic field characteristics from clusters of ultra-high energy cosmic rays

Abstract We present a detailed Monte Carlo study coupled to a likelihood analysis of the potential of next generation ultra-high energy cosmic ray experiments to reconstruct properties of the sources and the extra-galactic magnetic field. Such characteristics are encoded in the distributions of arrival time, direction, and energy of clusters of charged cosmic rays above a few 1019eV. The parameters we consider for reconstruction are the emission timescale, total fluence (or power), injection spectrum, and distance to the source, as well as the r.m.s. field strength, power spectrum, and coherence length of the magnetic field. We discuss five generic situations which can be identified relatively easily and allow a reasonable reconstruction of at least part of these parameters. Our numerical code is set up such that it can easily be applied to the data from future experiments.