The effect of the monochromaticity of relativistic electron beam's energy on the small signal gain of free electron lasers is analyzed. For a certain pumping field, there is a critical energy divergency, over which the small signal gain will become negative. The shorter the wavelength and the longer the magnification length, the higher is the requirement of energy monochromaticity of electron beam for laser amplifiers. But the requirement of monochromaticity of electron beam for laser oscillators is much lower.
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