A SMALL SIGNAL TIME DOMAIN ANALYSIS OF A FREE ELECTRON LASER

A evolution equation for a optical pulse in FEL is derived .Its steady solutions are studied by numerical method. The relations between the eigenvalues and the desynchronisms are given for different parameters. Some conclutions are presented. First, the eigenvalues decrease as go increase. Second, the eigenvalues are also related to detuning parameter, when it is equal to 2 .7 the eigenvalue reaches the maximum. Third, the relations between eigenvalues and coupling parameters coincide with Dattoli's scaling law. At last we present the results calculated with the parameters of the Beijing IR FEL project .The maximum steady gain coefficient G =0.39 and the FWHM of the optical pulse is about 1 ps.