Coherent radiation generated by the short pulse effect of the electron beam

In this paper, basing on the given refs, a nonsteady state self-consistent equation in the linear regime of the free-electron laser in the mode space is derived. The equation contains two kinds of coherent radiations: super-radiant generated by the short pulse effect of the electron beam and stimulated emission which is the conventional free-electron laser. One can obtain from the equation that in the usual case in which the length of the electron beam is much longer than the wavelength of radiation, i.e., σzK0>>1, the stimulated emission is dominant; but when the length of the electron beam is comparable with the wavelength of radiation, i.e., σzK0 = 2πσz/λ0≤1, the super-radiant is dominant. A formula of calculating the power of the super-radiant due to the short pulse effect of the electron beam is also derived. The result of the calculation with the derived formula agrees with that of the experiment well in the order of magnitude