Abstract
Recent gain calculations for waveguide free electron lasers have shown that two gain peaks at different frequencies should be observable with the peak at the highest frequency having the highest gain. It is shown here that this conclusion depends on whether one defines gain in terms of energy or power. It is possible to find experimental conditions such that the higher frequency peak is smaller than the low frequency peak using the power gain definition, while under the same conditions the higher frequency peak is largest with the energy gain definition. This obviously leads to interesting questions as to which frequency would eventually dominate in an oscillator experiment. This problem and the relationship between power and energy gains are discussed.
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