Abstract
Development of sideband frequencies in a free electron laser is studied numerically and analytically in axisymmetric geometry. In the case of small input power the sidebands grow independently in the exponential gain regime. For large input power an instability develops whereby the carrier is coupled to the sidebands via the synchrotron oscillation of the electrons. In a tapered system, the growth rate of sidebands decreases with increasing rate of taper. However, maximum extraction and efficiency is obtained when the particle motion is marginally nonadiabatic.
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