Azimuthal selection of modes in free-electron masers with coaxial Bragg resonators

Abstract

A comparative analysis of the selective characteristics of Bragg resonators with various types of periodic corrugation is performed. In the simplest case of the azimuthal symmetric corrugation in a highly overmoded resonator (a large ratio of the perimeter to the wavelength), the Q factors of modes with different numbers of azimuthal variations are almost equal and the mode frequencies are close on the scale of the gain band of electron flow. A certain rarefaction of the mode spectrum can be attained using the helical corrugation when the traveling wave is coupled with the whispering-gallery modes and the frequency interval between the high-Q modes of the resonator with different azimuthal indices is determined by the interval between the critical frequencies of the whispering-gallery modes. The doubly periodic corrugation employed in the 2D Bragg resonators at the same (as in the case of the helical corrugation) intermode distance allows the Q-factor selection of a single azimuthal symmetric mode. The analysis is based on the method of coupled waves and the direct numerical simulation using standard codes.