Zm. Dai et al., SPACE-CHARGE EFFECTS IN A FREE-ELECTRON LASER WITH A 2-FREQUENCY UNDULATOR, Journal of physics. D, Applied physics, 27(12), 1994, pp. 2461-2465
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
.