Effect of beam quality on the free-electron laser

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Abstract
The effect of finite momentum spread on the free-electron-laser amplifier is investigated for a configuration of a helical wiggler and an axial guide magnetic field. A set of coupled nonlinear differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field is derived and solved numerically for several sets of parameters. The initial beam distribution is defined external to the wiggler field and the adiabatic injection of the beam into the wiggler is modeled by allowing the wiggler amplitude to increase slowly from zero to a constant amplitude over several wiggler periods. While the efficiency is found to decrease rapidly with increasing momentum spread, resonant effects between the wiggler and guide magnetic fields are found to substantially decrease the sensitivity of the saturation efficiency to the beam emittance. In addition, a relatively sharp change in the slope of the efficiency versus beam momentum spread is identified with the transition between the ‘‘cold’’ and ‘‘thermal’’ beam regimes.