Simplified analysis of free-electron lasers using Madey's theorem

Spontaneous and stimulated emission calculations are made for various free-electron laser (FEL) configurations by using Madey's theorem. An analogy is provided between the FEL and a phased antenna array, and it is used to simplify the calculations. Relations for the spontaneous and stimulated emission are derived for the uniform wiggler FEL, the optical klystron, the case of
N
wiggler sections cascaded through dispersive sections, and for harmonics in a planar wiggler FEL.