Abstract
The influence of electron beam energy spread on FEL gain is investigated quantitatively. The dispersion relation is derived according to Johnston's formulation. As the results of the analysis, it is found that the growth rate of the high frequency FEL instability is greater (less) than that of the low frequency instability when the beam energy spread Δγ )Δγ c . Here, Δγ c is the critical beam energy spread which depends upon the beam current and energy, the wiggler wavelength and so on.
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