Rigorous numerical theory of finite length periodic structure excitation

Progress in high power microwaves (HPM) connected with the appearance of microwave sources with peak power above 10 GW employing intense relativistic electron beams has created new problems in the areas of theory, mathematical description and simulation of regimes of high power microwave excitation. Electrodynamic systems (EDS) of HPM devices can include sections of retarding structures with a diameter greatly in excess of the wavelength and of the order of the longitudinal size. In the present report we restrict ourselves to the simplest model of EDS, namely a finite length lattice with a rectangular element of periodicity. The results obtained allow us to study the character and intensity of diffraction broadening of spatial harmonics, to find the structure and efficiency of diffraction radiation and to investigate the features of transformation of surface waves into volume ones on the end of EDS. We obtain the dispersion relation for eigenfrequencies of the "cold" structure, near which the efficiency of diffraction radiation is the highest.