MODE COMPETITION AND CONTROL IN FREE-ELECTRON LASERS WITH ONE-DIMENSIONAL AND 2-DIMENSIONAL BRAGG RESONATORS

We present a time domain analysis of the longitudinal and azimuthal mo de dynamics which occur in relativistic free electron lasers and cyclo tron autoresonance masers with one-dimensional (1-D) and two-dimension al (2-D) Bragg resonators. It is shown that when the 1-D oscillator is moderately above threshold, a single longitudinal mode generation reg ime is established due to nonlinear mode competition. The process of l ongitudinal mode selection is more effective if the region of synchron ous interaction between the electron beam and the forward propagating wave is extended inside the Bragg reflectors, Further above the oscill ation threshold, multimode chaotic behavior occurs. In the second part of this paper, it is shown;that both traditional 1-D and novel 2-D Br agg resonators can produce radiation at a single frequency with a one- mode azimuthal distribution, which corresponds to spatial synchronizat ion of the electromagnetic radiation, in 1-D systems, electronic mode selection occurs via nonlinear mode competition, In contrast, electrod ynamic mode selection occurs in 2-D Bragg resonators, resulting in the production of a single azimuthally, symmetric mode after the linear s tage of evolution. The 2-D Bragg resonator is shown to retain its sele ctivity when its radius greatly exceeds the radiation wavelength.