  We present a theoretical model describing recently observed collective
effects in large magneto-optically trapped atomic ensembles. Based on a kinetic
description we develop an efficient test particle method, which in addition to
the single atom light pressure accounts for other relevant effects such as
laser attenuation and forces due to multiply scattered light with position
dependent absorption cross sections. Our calculations confirm the existence of
a dynamical instability and provide deeper insights into the observed system
dynamics.
