A two-dimensional distributed feedback is an effective method of producing ultra-high power spatially-coherent radiation from an active media, that is spatially extended along two coordinates, including relativistic electron beams with sheet and annular geometry. The present paper describes progress in the investigations of planar and coaxial FEMs based on the novel feedback mechanism. The effective transverse (azimuthal) mode selection has been demonstrated under the transverse size of about 20 -25 wavelengths and narrow-frequency multi-MW microwave pulses have been generated in the Ka-and W-bands.For an active media, that is spatially extended along two co-ordinates including relativistic electron beams with sheet and annular geometry as well laser media, the use of two-dimensional (2D) distributed feedback is beneficial for providing spatial coherence of the radiation and, thus, can be used to increase the total radiation power [1,2]. Such 2D feedback can be realized in planar and co-axial 2D Bragg resonators having double-periodic corrugations of side walls (either similar modulation of dielectric constant). Spatially-extension over one of the transverse coordinates interaction space allows significant increase of the total microwave power (up to GW powers) while keeping power and current densities at moderate level.Experimental studies of FEMs based on this novel feedback mechanism are performed in Ka-band (coaxial geometry) at the University of Strathclyde [3][4][5] and in W-band (planar geometry) at the Budker Institute of Nuclear Physics (Novosibirsk) [6,7] in collaboration with the Institute of Applied Physics RAS (N.Novgorod). As a result of this work narrowband microwave generators of multi-MW power level were realized. In this experiment effective mode selection over the transverse (azimuthal) index was demonstrated with oversize parameter of the resonators of about 25 wavelengths. The present paper is devoted to the results of simulations and experimental studies of above FEMs.
I. MODELING AND EXPERIMENTAL STUDIES OF PLANAR 75 GHZ FEM WITH HYBRID BRAGG RESONATORThe 2D distributed feedback is based on the mutual scattering of the four partial wave fluxes ( t i ihx ihx ihz ihz e e e e e E E B B A A Re 0 , (1) where two fluxes (A ± ) propagate in forward and backward (in respect with the electron beam propagation) ±z directions and two other fluxes (B ± ) propagating in the transverse ±x directions act to synchronize different parts of the sheet electron beam. This scattering scheme is realized at planar 2D Bragg structures having double-periodical corrugation of the metal plates 2 2 2 cos ( ) cos ( ) 4 D D D a a h z x h z x ,where 2D a is the corrugation depth The efficient scattering of partial waves (1) takes place under the Bragg resonance condition 2D h h .In this section we describe the results of investigations of a 75 GHz planar FEM. To demonstrate the operability of the novel feedback mechanism, a sheet beam with a transverse size of about 20 wavelengths was used.Fig 1 Scheme of FEM with a hybr...