Nonlinear analysis of free-electron laser amplifiers with axial guide fields

The nonlinear evolution of free-electron lasers in the presence of an axial guide-field is investigated numerically. A set of coupled nonlinear differential equations is derived which governs the self-consistent evolution of the wave fields and particle trajectories in an amplifier configuration. The nonlinear currents which mediate the interaction are computed by means of an average over particle phases, and the inclusion of fluctuating space charge fields in the formulation permits the investigation of both the stimulated Raman and Compton scattering regimes. The initial conditions are chosen to describe the injection of a cold, axially propagating electron beam into the interaction region which consists of a uniform axial guide field and a helical wiggler field which increases to a constant level adiabatically over a distance of 10 wiggler periods. After an initial transient phase, the results show a region of exponential growth of the radiation field which is in excellent agreement with the linear theory. Saturation occurs by means of particle trapping. The efficiency of the interaction has been studied for a wide range of axial guide fields, and substantial enhancements have been found relative to the zero-guide-field limit