Theory of multicomponent wiggler free-electron lasers in the small-signal regime

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Abstract
A theory of the multicomponent wiggler free-electron laser is formulated in the small-signal regime. Analytical expressions for the spontaneous spectrum and the corresponding small-signal gain are derived. The expressions are valid for an arbitrary wiggler configuration consisting of any number of constant or tapered sections and drift spaces. Thus, optical klystrons are included as a particular case of the two-component devices. As a natural result of the derivation, it is proved that Madey's theorem holds for any multicomponent wiggler configuration including the optical klystron. As particular cases, several two-component wiggler schemes are discussed in detail. Based on the simple-gain expression an upper limit is obtained for the small-signal gain. It is shown that this cannot exceed the maximum gain of a constant wiggler of the same effective length by more than 25%.