GENERAL FORMULA OF THE ENERGY-TRANSFER RATE IN GYROTRON, CYCLOTRON-AUTORESONANCE-LASER, AND NONWIGGLER-FREE-ELECTRON-LASER OSCILLATORS

A general formula of the energy-transfer rate of the transverse-electric-mode gyrotron, cyclotron-autoresonance-maser, and nonwiggler-free-electron-laser oscillators is rigorously derived within the Vlasov framework. The present result can be used to deal simultaneously with the influences of the finite cavity length, spreads, higher harmonics, and nonresonance, and to describe the situation of a large-orbit or a polyaxial relativistic electron beam. The general formula is examined for a cold electron beam and is found to be in agreement with the result obtained by the Madey theorem for these devices.