Longitudinal stabilisation of bunched beams in a FEL storage ring

Experimental observations on FEL Storage Rings (Aco, Super-Ace, VEPP3, TERAS) have shown that in a storage ring with an operating FEL there is a mutual effect between the FEL operational mode and the beam longitudinal distribution. The main effects are the birth of a macro-temporal structure of the FEL radiation and a suppression of the synchrotron sidebands, evidence of beam stabilisation against the microwave instabilities. In this paper we discuss the main features of the beam dynamics analysed with a simulation code recently developed, which includes the FEL-beam interaction. Furtherly, we propose an heuristic model which enable to describe in a simple way the overall system.