• G. Dattoli
  ENEA C.R. Frascati, Frascati (Roma)
• M. Migliorati
  INFN/LNF, Frascati (Roma)
• A. Schiavi
  Rome University La Sapienza, Roma

We develop some considerations allowing the possibility of deriving the conditions under which laser heater devices may suppress the Coherent Synchrotron Instability (CSRI) without creating any prejudice to the use of the beam for FEL SASE or FEL oscillator operation. We discuss the problem using either numerical and analytical methods. The analytical part is aimed at evaluating the amount of laser power, necessary to suppress the instability. We use methods already developed within the context of FEL-storage rings beam dynamics, with particular reference to the interplay between FEL and Saw Tooth Instability. The numerical method employs a procedure based on the integration of the Liouville equation, describing the coupled interaction between e-beam and wake-fields, producing the instability, and the laser producing the heating. Particular attention is devoted to the competition between instability and heating. The comparison between numerical and analytical results is discussed too and the agreement is found to be satisfactory.