Coherent Nonlinear Phenomena in High Energy Synchrotrons: Observations   and Theoretical Models
  Nonlinear waves have been observed in synchrotrons for years but have received little attention in the literature. While pathological, these phenomena are worth studying on at least two accounts. First, the formation of solitary waves may lead to droplet formation that causes significant beam halo to develop. Secondly, a variety of nonlinear processes are likely involved in the normal saturation of unstable oscillations, leading to the possibility that low-level, but potentially broadband fluctuation spectra may develop. Both features carry indirectly the signature of the machine impedance. In this work we review a number of observations of nonlinear longitudinal waves made in Fermilab accelerators, and make a first attempt to develop appropriate theoretical models to explain these observations. 
P.L. Colestock (Fermilab), L.K. Spentzouris (Fermilab) and S.I. Tzenov   (Fermilab)