Idealizing the ultrashort pulse electron beam modulated by radio-frequency as a delta function on time scale, we calculate the coherent synchrotron radiation emitted by the electron micropulse in a rectangular waveguide with the method of eigenmode expansion. We find that when the frequency of radiation is the integral times of the radio frequency ωrf, the radiation field pattern will appear as "pure" eigenmodes of waveguide. In addition, we analyse the frequency performance of the coherent synchrotron radiation and the slippage effect. And finally, the gain of a rectangular electron pulse amplifying the radiation is deduced.
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