Knowledge of the density distribution of a bunched beam is important for co
ntrolling and damping instabilities which often depend on the distribution
function (A.W. Chao, in Physics of Collective Beam Instabilities in High En
ergy Accelerators, Wiley, New York, 1993). In this paper, experimental stud
ies of the longitudinal bunch shapes and temperatures of laser-cooled bunch
ed beams are presented. These studies are combined with measurements of the
transverse density distribution of the beam using a novel technique (Madse
n et al., Proceedings of the Sixth European Particle Accelerator Conference
, EPAC'98, Stockholm, IOP Publishing, Bristol 1998, p. 1046). The bunch sha
pes for various temperatures comply with a model where the transverse tempe
rature is assumed to be high. However, in the longitudinally space-charge l
imited case, it is observed that the maximum attainable density is much low
er than it would be in a completely space-charge limited beam. Furthermore,
it is observed that this maximum density decreases with increasing current
. These observations might be important for the beam quality obtainable wit
h laser-cooling. (C) 2000 Elsevier Science B.V. All rights reserved.