The effect of energy spread on the gain of a dense-beam free-electron laser amplifier is analyzed. The formalism includes collective effects and allows for the use of an arbitrary distribution function. The dispersion relation is solved numerically. Besides broadening of the spectrum and decrease in gain, lowering of the central emission frequency with energy spread is observed. An initial-value problem is formulated and numerically solved, with power computed as a function of distance. The relative contributions of the different modes when temperature changes are analyzed. In particular, the competing effects of a decrease in coupling loss with temperature together with Landau damping are investigated.
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Ibanez et al. (1983) studied this question.
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