  Beam dynamics calculations that are based on the Vlasov equation do not
permit the the treatment of stochastic phenomena such as intra-beam scattering.
If the nature of the stochastic process can be regarded as a Markov process, we
are allowed to use the Fokker-Planck equation to describe the change of the
phase space volume the beam occupies. From the Fokker-Planck equation we derive
equations of motion for the beam envelopes and for the rms-emittances. Compared
to previous approaches based on Liouville's theorem, these equations contain
additional terms that describe the temperature balancing within the beam. Our
formalism is applied to the effect of intra-beam scattering relevant for beams
circulating in storage rings near thermodynamical equilibrium. In this case,
the Fokker-Planck coefficients can be treated as adiabatic constants of motion.
Due to the simplified analysis based on `beam moments', we obtain fairly simple
equations that allow us to estimate the growth rate of the beam emittance.
