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The strong-signal regime of a free-electron laser is analyzed in terms of a set of "generalized Bloch equations. " We show that for current free-electron-laser configurations the saturation will be reached for a field on the order of 10^7 V/m, with an efficiency at saturation of 510^-3. However, a strong reshaping of the electron distribution may alter the efficiency of free-electron lasers in cases where the electron beam is recycled from one shot to the next.
Hopf et al. (1976) studied this question.