  This paper presents an analysis of the emittance preservation during a heavy
ion bunching process. This analysis aims at finding the correlation between the
rms emittance of a coasting beam and that of the resulting bunches. The
emittance of a Gaussian coasting beam bunched adiabatically in synchrotrons is
investigated using theoretical considerations and particle tracking
simulations. New results are presented on the relation between the emittance
before and after the bunching process. It is found that a constant factor can
be determined to describe this relation.
  This factor can be used to avoid time-consuming simulations. If the rms
emittance is known before the bunching process, it can be calculated for the
bunched beam afterwards. This also makes it possible to determine the required
bucket area for a certain filling ratio.
