  We extend a recently introduced mapping model, which explains the bunching
phenomenon in an ion beam resonator for two ions [Geyer, Tannor, J. Phys. B 37
(2004) 73], to describe the dynamics of the whole ion bunch. We calculate the
time delay of the ions from a model of the bunch geometry and find that the
bunch takes on a spherical form at the turning points in the electrostatic
mirrors. From this condition we derive how the observed bunch length depends on
the experimental parameters. We give an interpretation of the criteria for the
existence of the bunch, which were derived from the experimental observations
by Pedersen et al [Pedersen etal, Phys. Rev. A 65 042704].
