Study of radiation spectrum in a free-electron laser oscillator from noise to saturation

A three-dimensional, space–frequency model for analysis and simulation of radiation excitation in a FEL oscillator is developed. The total electromagnetic field is presented in the frequency domain as an expansion in terms of transverse eigenmodes of the (cold) resonator. Coupled-mode formulation is utilized in an analytical approach and in a numerical simulation to follow linear and nonlinear processes, taking place during radiation buildup, which lead to the establishment of single-mode lasing. The evolution of the radiation spectrum is investigated in the case of ‘grazing’, when the group velocity of the radiation is equal to the axial velocity of the electrons.