Abstract
Recent analyses of the self-consistent nonlinear interaction of the gain medium and the optical field in free-electron lasers (FELs) are reviewed. A unique longitudinal feature of the FEL stems from the closed synchrotron orbits of electrons trapped in the ponderomotive potential well. Such oscillations result in the generation of optical sidebands. Sideband buildup enhances extraction efficiency in untapered systems but leads to electron detrapping in FEL oscillators with long, highly tapered undulators. Fortunately, full extraction may be recovered with use of intracavity wavelength selectivity. Analysis of the transverse mode structure in FEL oscillators shows that typical geometries produce near diffraction-limited beam quality. However, under certain conditions, namely high gain and with near-concentric resonators, effects due to the radially nonuniform gain medium may be noticed. In particular, the one-way gain medium may result in a near diffraction-limited mode which is somewhat mismatched to the cavity. Preliminary three-dimensional analysis of the sideband instability indicates that beam quality is unaffected when the instability is active.
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