Three-dimensional nonlinear analysis of free-electron-laser amplifiers with planar wigglers

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Abstract
The nonlinear evolution of the free-electron-laser (FEL) amplifier is investigated numerically for a configuration consisting of a planar wiggler with parabolically tapered pole pieces. A set of coupled nonlinear differential equations is derived in three dimensions which governs the self-consistent evolution of the TE and TM modes in a loss-free rectangular waveguide as well as the trajectories of an ensemble of electrons. The initial conditions are chosen to model the injection of a cylindrically symmetric electron beam into the wiggler by means of a region with an adiabatically tapered wiggler amplitude, and the effect of an initial beam momentum spread is included in the formulation. Both self-field and space-charge effects have been neglected, and the analysis is valid for the high-gain Compton regime. In addition, the phase stability of the FEL amplifier against fluctuations in the beam voltage, the enhancement of the efficiency by means of a tapered wiggler amplitude, and harmonic generation are also studied. Numerical simulations are conducted to model a 35-GHz amplifier with an electron beam energy of 3.5 MeV, and good agreement is found between the simulation and an experiment conducted by Orzechowski and co-workers. Significantly, the results indicate that a tapered wiggler configuration is somewhat less sensitive to the beam thermal spread than a uniform wiggler system.