Nonlinear theory of the slow-wave cyclotron amplifier

We have developed a three-dimensional nonlinear theory for the slow-wave cyclotron instability in a dielectrically loaded waveguide. The efficiency, gain, and bandwidth of the amplifier are calculated from a self-consistent solution of a set of coupled nonlinear differential equations describing the growth of the electromagnetic field and the evolution of the electron trajectories. Calculations show that very broadband amplification with high efficiency is possible in the slow-wave region of the propagating waves. The instantaneous bandwidth (full width at half maximum) near saturation depends on the efficiency (η) of the amplifier. For a cold beam, the bandwidth Δω/ω≊6% at η≊40%, but Δω/ω increases to 30% if the amplifier is operated at an efficiency of 20%. The efficiency is very sensitive to the axial velocity spread of the beam since interaction occurs with waves having large propagation constants. The maximum efficiency drops from 48% to 10% as the velocity spread increases from 0% to 5% but the bandwidth shows a small increase.