Nonlinear analysis of free-electron-laser amplifiers in three dimensions

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Abstract
The nonlinear evolution of the free-electron-laser amplifier is investigated numerically for a configuration consisting of a helical wiggler and axial guide magnetic fields. A set of coupled nonlinear differential equations is derived in three dimensions which governs the self-consistent evolution of either the TE or TM modes in a loss-free cylindrical waveguide and the trajectories of an ensemble of electrons. The initial conditions are chosen to model the adiabatic injection of a cold, cylindrically symmetric electron beam into an interaction region in which the wiggler amplitude rises slowly from zero to a constant level in ten wiggler periods. Both self-field and space-charge effects have been neglected in the formulation, and the analysis is valid for the high-gain Compton regime of operation. Numerical simulations are conducted to model an amplifier operating in the neighborhood of 35 GHz, and for electron-beam energies of 250 keV and 1 MeV. (The free-electron-laser operating at electron-beam energies less than 500 keV is called the ubitron.) The growth rate in the linear regime prior to saturation is found to be in substantial agreement with the predictions based on a linear theory of the instability, and the saturation efficiency is consistent with that expected on the basis of simple, heuristic phase-trapping arguments. Substantial enhancements in the efficiency are found to occur due to the presence of the axial guide field.