The use of a novel hybrid scheme of a two-mirror Bragg resonator consisting of one-dimensional (1D) and two-dimensional (2D) reflectors is suggested for generation of powerful spatially coherent radiation in a coaxial free-electron laser driven by a large-size (102–103 wavelengths) high-current annular relativistic electron beam. The 2D Bragg reflector is positioned at the cathode side of the oscillator to provide synchronization of radiation from the oversized electron beam via transverse energy fluxes, which arise due to scattering on the 2D Bragg structure. The conventional 1D Bragg reflector is positioned at the collector side to complete the feedback.

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