Space-frequency model of amplified spontaneous emission and super-radiance in free electron laser operating in the linear and non-linear regimes

A three-dimensional, space-frequency model for the excitation of electromagnetic radiation in a free-electron laser is presented. The approach is applied in a numerical particle code WB3D, simulating the interaction of a free-electron laser operating in the linear and non-linear regimes. Solution of the electromagnetic excitation equations in the frequency domain inherently takes into account dispersive effects arising from the cavity and the gain medium. Moreover, it facilitates the consideration of statistical features of the electron beam and the excited radiation, necessary for the study of spontaneous emission, synchrotron amplified spontaneous emission (SASE), super-radiance and noise. We employ the code to study the statistical and spectral characteristics of the radiation generated in a pulsed beam free-electron laser operating in the millimeter wavelengths. The evolution of radiation spectrum, excited when a Gaussian shaped bunch with a random distribution of electrons is passing through the wiggler, was investigated.