Mode competition and control in free electron lasers with one- and two-dimensional Bragg resonators

We present a time domain analysis of the longitudinal and azimuthal mode dynamics which occur in relativistic free electron lasers and cyclotron autoresonance masers with one-dimensional (1-D) and two-dimensional (2-D) Bragg resonators. It is shown that when the 1-D oscillator is moderately above threshold, a single longitudinal mode generation regime is established due to nonlinear mode competition. The process of longitudinal mode selection is more effective if the region of synchronous interaction between the electron beam and the forward propagating wave is extended inside the Bragg reflectors. Further above the oscillation threshold, multimode chaotic behavior occurs. In the second part of this paper, it is shown that both traditional 1-D and novel 2-D Bragg resonators can produce radiation at a single frequency with a one-mode azimuthal distribution which corresponds to spatial synchronization of the electromagnetic radiation. In 1-D systems, electronic mode selection occurs via nonlinear mode competition. In contrast, electrodynamic mode selection occurs in 2-D Bragg resonators, resulting in the production of a single azimuthally symmetric mode after the linear stage of evolution. The 2-D Bragg resonator is shown to retain its selectivity when its radius greatly exceeds the radiation wavelength.