Free electron lasers with sheet electron beams and two-dimensional planar Bragg resonators

The use of two-dimensional Bragg resonators of planar geometry, realizing two-dimensional distributed feedback, is considered as a method of producing spatially coherent radiation from a large sheet electron beam. Selective properties of a 2-D Bragg resonator are studied when the transverse sides of the resonator are open and also when they are closed. A time-domain analysis of the excitation of an open 2-D Bragg resonator by a sheet electron beam demonstrates that a single mode steady-state oscillation regime may be obtained for a sheet electron beam of width up to 1000 wavelengths. At the same time, even in a closed 2-D Bragg resonator a steady-state regime can be realized if the beam width does not exceed 50-100 wavelengths. The project of an FEL with a 2-D Bragg resonator driven by a sheet electron beam based on the U-2 accelerator (INP RAS, Novosibirsk) is discussed