This letter concerns a design of a Bragg cavity for TM modes that can be used with a free‐electron laser (FEL) or other electron beam generator. If the corrugated wall in the FEL section meets the Bragg condition, the distributed feedback mechanism can function like mirrors in the usual laser cavity; however, the Bragg cavity eliminates the dead space between the interaction region and the reflectors so that it is a preferred design where the pulse duration of the electron beam is limited. The calculations indicate that high reflection coefficients that correspond to high cavity Q factor can be obtained if we carefully choose the parameters of the corrugated wall, such as period, amplitude, and length. Finally, we discuss factors to be considered in the design of a Bragg cavity for a FEL based on an intense relativistic electron beam and an electromagnetic pump wave.

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