Influence of the angular beam width on the free-electron laser gain

An analysis is made of the dependence of the gain in a free-electron laser on the angle of intersection of the electron beam and the electromagnetic wave being amplified. It is shown that in order to maximize the gain as the angle of intersection increases, the excess of the particle energy over the synchronous particle energy must be increased. An analysis is made of the influence of the angular beam width on the gain. The angular spread results in asymmetric broadening of a spontaneous emission spectral line in the direction of propagation of the wave being amplified. The influence of this factor on the operation of a free-electron laser under amplification conditions is studied numerically. It is found that in order to maintain a fairly high gain, either the radiation wavelength or the beam energy must be tuned. It is noted that the introduction of an energy spread reduces the dependence of the gain on the angular width.