Generation of a spatially coherent field structure in free-electron masers with 2D distributed feedback

Nonlinear dynamics of free-electron masers (FEMs) is studied in the planar geometry with 2D distributed feedback (DFB). As is distinct from previous works, the field structure is not fixed with respect to the three spatial coordinates including the coordinate that is orthogonal to surfaces of the plates of the 2D Bragg resonator. Conditions on the allowed oversize parameter (ratio of the gap between the resonator plates to wavelength) under which the steady-state generation remains stable upon variation in electron-beam parameters are derived. It is demonstrated that, at a relatively large gap, variations in the mismatch lead to the jumps of oscillation frequency that correspond to the excitation of bunches of modes with different transverse indices of partial waves. The results of simulation using a particle-in-cell method are presented for a FEM prototype with 2D DFB that is created using an ELMI accelerator at the Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences. The simulated results show that narrow-band spatially coherent radiation can be generated at experimental parameters of the electron beam and electrodynamic system. The advantages of 2D Bragg structures in comparison with conventional 1D structures are demonstrated for FEMs.