The gain calculation of media and electrostatic free-electron lasers by the madey theorem

The Madey theorem has been used to calculate the small-signal gain of a planar magnetic wiggler FEL and optical klystron. The analysis in this paper shows that the Madey theorem can also be applied to media FEL's, i.e., Cerenkov and transition radiation FEL's, as well as electrostatic FEL's. Here we use the Madey theorem to calculate the small-signal gain of these two kinds of FEL's.