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In this study, we investigate a new simple scheme using a planar undulator (PU) together with a properly dispersed electron beam (
beam) with a large energy spread (
) to enhance the free-electron laser (FEL) gain. For a dispersed
beam in a PU, the resonant condition is satisfied for the center electrons, while the frequency detuning increases for the off-center electrons, inhibiting the growth of the radiation. The PU can act as a filter for selecting the electrons near the beam center to achieve the radiation. Although only the center electrons contribute, the radiation can be enhanced significantly owing to the high-peak current of the beam. Theoretical analysis and simulation results indicate that this method can be used for the improvement of the radiation performance, which has great significance for short-wavelength FEL applications.
is a prime with
. A relation between the support weight distribution of a linear code
and the dual code
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