Abstract
We study the electron phase-space evolution and gain in free electron lasers whose short-wavelength radiation has Gaussian spherial wavefronts. Several free electron laser designs are considered: the undulator, the tapered wavelength undulator, and the optical klystron. We find that the gain spectrum is no longer proportional to the slope of the forward spontaneous emission spectrum, and we determine the design of the Gaussian mode which maximizes the energy extraction from the electron beam.
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