Transverse Instabilities in the FERMILAB Recycler
  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. 
L. R. Prost, A. Burov, A. Shemyakin, C. M. Bhat, J. Crisp, N. Eddy
physics.acc-ph