Abstract
The evolution of the spectral bandwidth in free-electron-laser (FEL) oscillators is studied and found to be different for different saturation characteristics: For weakly saturated FELs in storage rings, the limiting bandwidth is given by that derived in the supermode theory; for linac-based FELs, where the gain reduction due to the high-intensity effect is significant, it is determined by the Fourier transform of the electron pulse length; for the case of a dc beam, it is given by a Schawlow-Townes formula, but the approach to the limit is very slow.
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