Two-dimensional distributed feedback as a method for generation of powerful coherent radiation from spatially-extended relativistic electron beams

The purpose of the research presented in the review is to analyze a new feedback mechanism — two-dimensional (2D) distributed feedback, and to study the possibility of using this mechanism for generation of powerful spatially-coherent radiation. Such 2D distributed feedback is implemented by applying 2D Bragg structures, which represent sections of planar or coaxial waveguides with the 2D-periodical corrugation and can be considered as an analog of the 2D photonic crystals. Methods. Theoretical analysis of 2D Bragg structures and powerful relativistic masers based on them was carried out in the framework of the coupled-waves method using geometrical and quasi-optical approximations. High selectivity of 2D Bragg structures was confirmed by the simulations and «cold» electrodynamic tests. Results. Simulations of the dynamics of oscillators with 2D distributed feedback shows that the transverse (relative to the electron beam propagation) wave-fluxes that occur in 2D Bragg structures lead to synchronization of the radiation of different parts of wide electron beams and establishment of a stable single-mode generation at the transverse sizes of the systems of up to $\sim$ 0$^2$ …10$^3$ wavelengths. Operability of novel feedback mechanism has been demonstrated experimentally in planar and coaxial Free-Electron Masers realized in the 4-mm and 8-mm wavelength bands, where a stable narrow-band generation with a record output power of up to 100 MW level is achieved at the transverse sizes of the system of about 50 wavelengths. Conclusion. Theoretical and experimental studies have shown that the 2D distributed feedback is an effective method for obtaining coherent radiation of millimeter and submillimeter ranges with a power level of $\sim$10$^8$ …10$^{10}$ W from relativistic electron beams of sheet and tubular configurations formed by the high-current accelerators. From a practical point of view, it also attractive to use the 2D feedback mechanism for synchronization of a laser active media, in particular, semiconductor heterolasers.