SPACE-CHARGE EFFECTS IN A FREE-ELECTRON LASER WITH A 2-FREQUENCY UNDULATOR

A set of single-electron equations, including the space-charge effects , is developed to describe the evolution of the radiation field in a f ree-electron laser with a two-frequency undulator. These basic equatio ns are analysed in the weak-field low-gain regime, to obtain the singl e-pass gain. It is found that the maximum gain and radiation frequency both increase with electron density. Owing to the repulsive force bet ween the electrons, the gain is saturated with decreasing growth rate for high electron density. Our numerical results show that the saturat ion gain is greatly dependent upon the parameters of the two-frequency undulator, and that it is smaller than that of the ordinary undulator .