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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.
Orzechowski et al. (1987) studied this question.