Wiggler Imperfections

The free-electron laser operates by the coherent axial bunching of electrons in the ponderomotive wave formed by the beating of the wiggler and radiation fields. The interaction is extremely sensitive to the axial energy spread of the electron beam, and an energy spread of a percent or less is sufficient to cause substantial reductions in the efficiency due to the detuning of the wave-particle resonance. A related effect is caused by random imperfections in the wiggler field. Planar wigglers can easily exhibit a random rms fluctuation of 0.5% from pole to pole. This yields a velocity fluctuation that causes a phase jitter that also detunes the wave-particle resonance. In this chapter, we explore the effects of wiggler imperfections on free-electron laser performance and compare the effects of wiggler imperfections with those of an axial energy spread. In contrast to these approaches, we adapt the nonlinear formalism described in Chaps. 5 and 6 to treat the effect of wiggler imperfections. No average over a wiggler period is performed in this approach, and no explicit assumption of the random walk is included. Instead, this formalism relies upon a model of the imperfections in the wiggler field, and the evolution of the electron trajectories, as well as the growth of the radiation field, is then determined self-consistently by integration of the coupled nonlinear differential equations for the electrons and the fields. Two specific examples are discussed. The first is at a relatively long wavelength of approximately 8 mm and corresponds to the 35 GHz example discussed in Sect. 5.4 . As such, the discussion makes use of the nonlinear formalism developed in Chap. 5 directly. The second example corresponds to a short wavelength free-electron laser. For this purpose, the nonlinear formalism developed in Chap. 6 is used.