We investigate the dynamics of intense space-charge-dominated heavy-io
n beams. Our main interest lies in the various processes causing emitt
ance changes. We extend the well-known envelope equations for periodic
quadrupole channels by introducing a dynamics for the emittances. The
additional equations account for intrabeam scattering. The parameter
of the model, a relaxation rate, is discussed over a wide range of bea
m parameters. A generalization of the envelope equations to the case o
f storage rings, where bending magnets and thus dispersion are present
, is also given. Finally, we present first results concerning intrabea
m scattering effects in space-charge-dominated beams in storage rings.