Studies of frequency spectrum oscillating phenomenon of free electron laser amplifier

In this paper, on the basis of a single-particle model, the dispersion equation is obtained after considering the first perturbation term of a relativistic energy factor. The resuls show that the frequency spectrum of a free electron laser amplifier exhibits an oscillation phenomenon when the injected electron energy is large enough. The origin of this phenomenon is attributed to the perturbing effect of the relativistic energy factor. A detailed discussion is given.