  Transverse instabilities of the antiproton beam have been observed in the
Recycler ring soon after its commissioning. After installation of transverse
dampers, the threshold for the instability limit increased significantly but
the instability is still found to limit the brightness of the antiprotons
extracted from the Recycler for Tevatron shots. In this paper, we describe
observations of the instabilities during the extraction process as well as
during dedicated studies. The measured instability threshold phase density
agrees with the prediction of the rigid beam model within a factor of 2. Also,
we conclude that the instability threshold can be significantly lowered for a
bunch contained in a narrow and shallow potential well due to effective
exclusion of the longitudinal tails from Landau damping.
