  In this paper, we determine the magnitude of phase fluctuations caused by
atom-atom interaction in a one-dimensional beam of bosonic atoms. We imagine
that the beam is created with a large coherence length, and that interactions
only act in a specific section of the beam, where the atomic density is high
enough to validate a Bogoliubov treatment. The magnitude and coherence length
of the ensuing phase fluctuations in the beam after the interaction zone are
determined.
