Transverse and temporal characteristics of a high-gain free-electron laser in the saturation regime

The transverse and the temporal characteristics of a high-gain free-electron laser are governed by refractive guiding and sideband instability, respectively. Using the self-consistent Vlasov–Maxwell equations, we explicitly determine the effective index of refraction and the guided radiation mode for an electron beam with arbitrary transverse size. Electrons trapped by the guided radiation execute synchrotron oscillation and hence are susceptible to the sideband instability. We explain the spectral evolution and determine the sideband growth rate. These theoretical predictions agree well with GINGER simulation results.