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 10**(19)
eV. The parameters we consider for reconstruction are the emission timescale,
total fluence (or power), injection spectrum, and distance of 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.Comment: 23 latex pages, 11 postscript figures included, uses (and includes)
elsart.sty and epsf.sty. Submitted to Astroparticle Physic
