We show that Free Electron Lasers (FEL) operating with storage rings may co
unteract beam instabilities of the Saw Tooth (STI) type. We use a model bas
ed on a set of equations that couple those describing the FEL evolution to
those accounting for the STI dynamics. The analysis provides a clear pictur
e of the FEL-STI mutual feedback and clarifies the mechanisms of the instab
ility inhibition. The reliability of the results is supported by a comparis
on with fully numerical codes. (C) 1999 Elsevier Science B.V. All rights re
served.