FORMULAS FOR SMALL SIGNAL GAIN OF VARIABLE PARAMETER UNDULATOR

Two approximate analytical expressions for small signal gain (S. S.G.) of variable parameter undulator Free Electron Laser (FEL) are obtained by disturbance method. The calculated results of them are in good agreement with those by numerical simulations. Based on those expressions, S.S.G. scalling laws of FEL with tapered undulator are derived and it is concluded that the injected energy of electron beam should be lower than that for the initial resonance.