TRANSVERSE MODE STRUCTURE OF A TAPERED-WIGGLER FEL OSCILLATOR

Abstract
An axisymmetric physical optics code is used to study the transverse mode structure of tapered-wiggler free-electron laser (FEL) oscillators. This approach accounts for the effects of diffraction, nonuniform gain media, refraction, and arbitrary mirror and aperture configurations. Figure 1 shows the evolution of TEM₀₀ and TEM₁₀ mode content as a plane polarized optical beam is circulated in symmetric, stable resonators of various lengths. In each case, the wiggler length is equal to two Rayleigh ranges of the optical beam, this geometry approximately optimizes the FEL interaction strength. The presence of the wiggler magnets is accounted for by including apertures of radius 1.8w at each end of the wiggler, where w is the 1/e amplitude point of the initial TEM₀₀ pump beam. A partially reflecting mirror provides output coupling of ~10 percent, equal to the FEL gain for the full saturation intensity at which the initial beam is injected. The FEL interaction is based on the synchronous particle approximation, with all trapped electrons located at the stable phase point. The unusual features of the FEL geometry, such as the narrow gain medium, the tendency of the interaction to locally focus the wave front, and the lack of gain on return passes, combine to produce a steady-state mode structure different from the fundamental cavity mode. As shown in Figure 1, higher-order cavity modes are supported in both confocal and near-concentric cavities, but are relatively suppressed in cavities of intermediate length. While confocal cavities have the desirable characteristic of compactness, practical FEL's operating at substantial power levels will likely be more nearly concentric to reduce mirror loading. Higher-order modes are supported in concentric and confocal geometries because the round-trip axial phase shift between modes is an integer multiple of 2π. This allows constructive addition of modes produced on successive round trips. Besides enhancing diffraction losses, the presence of higher-order modes has unusual effects on the intensity distribution within the wiggler. In a concentric cavity, for example, the optical beam, when compared to the fundamental cavity mode, is relatively broad and low intensity where it enters the wiggler. Before exiting the wiggler, the beam then focuses to a relatively narrow, intense waist. If not accounted for in the wiggler taper, such mode structure could result in unexpected electron detrapping. The unusual intracavity intensity stucture is exhibited because the wave front curvature is mismatched to the cavity mirrors. The wave front projects into a combination of cavity modes due to this curvature mismatch. Nevertheless, the beam has nearly diffraction limited quality.