Abstract:
The quantum kinetic equation method is used outside the framework of the theory of perturbations of the amplitude of an external field to calculate the gain and saturation of a freeelectron laser with a collinear low-current relativistic beam and two circularly polarized electromagnetic waves in vacuum. An analysis is made of the mechanism of saturation of the useful signal in an undulator free-electron laser. The saturation amplitude of the signal is found by direct quantum-kinetic calculations and also on the basis of the Klein–Gordon equation. The two sets of results are shown to agree apart from a constant factor. An exact allowance for the external field cannot be reduced to a simple replacement of the real mass of an electron with its effective mass. This is manifested by a difference between the formula for the wavelength of the useful signal emitted by a free-electron laser and the wavelength formula known from the published literature, as well as by the presence of an additional contribution to the saturation coefficient.
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