  We study the propagation of an atom laser beam through a spatial region with
a magnetic field tuned to a Feshbach resonance. Tuning the magnetic field below
the resonance produces an effective focusing Kerr medium that causes a
modulational instability of the atomic beam. Under appropriate circumstances,
this results in beam breakup and filamentation seeded by quasi-particle
fluctuations, and in the generation of correlated atomic pairs.
