Storage ring free electron lasers and saw-tooth instability

We show that Free Electron Lasers (FEL) operating with storage rings may counteract beam instabilities of the Saw Tooth (STI) type. We use a model based on a set of equations that couple those describing the FEL evolution to those accounting for the STI dynamics. The analysis provides a clear picture of the FEL-STI mutual feedback and clarifies the mechanisms of the instability inhibition. The reliability of the results is supported by a comparison with fully numerical codes.