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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.
Fawley et al. (1984) studied this question.