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The coupling between betatron and synchrotron oscillations in a tapered wiggler free-electron laser (FEL) is investigated analytically and numerically. The resonance between the oscillations, first investigated by Rosenbluth, is shown to be important only for a very limited range of parameters. In general, the resonance is not a serious detrapping mechanism for high-power FEL amplifiers.

The phase change of an electromagnetic wave propagating through a free-electron laser (FEL) amplifier has been measured. The FEL operated at 34.6 GHz, with both a uniform and a tapered wiggler. The results of the experiment show a nearly constant phase derivative with increasing wiggler length through the exponential gain region and are in good agreement with analytical theory. For the tapered-wiggler amplifier, the phase derivative decreases at a point approximately one third of a synchrotron period past saturation; the decrease is in good agreement with numerical simulation. For the untapered-wiggler amplifier, however, numerical simulations predict an increase in phase derivative past saturation, whereas in the experiment the phase derivative abruptly vanishes. Several explanations for the discrepancy are discussed.