G. Dattoli*, L. Giannessi*, L. Mezi*, A.Renieri*, M.E. Couprie**, G. De Ninno**, D. Garzella**, D. Nutarelli**, E. Renault**, R. Roux***
*ENEA, Frascati / ** CEA, Saclay - LURE, Orsay / ***Sincrotrone Trieste, Trieste
We develop a semianalitical model of S.R. FEL dynamics including the effects of pulse propagation and interplay with microwave instability. The model uses the low gain, small signal pulse propagation equations coupled to a set of non linear equations accounting for the evolution of instabilities of microwave and saw tooth type. We show that the model is capable of reproducing the essential features of the system dynamics and in particular reproduces experimental evidences according to which the instability is switched off at the onset of the laser. We discuss the possibility of including instabilities of transverse type.
