Linear and nonlinear electron cyclotron interaction in open resonators

In this work the electron cyclotron maser oscillator interaction is analyzed in an open resonator configuration. One of the salient features of this configuration for generating high power short wavelength radiation is its ability to mode select. Both the linear and nonlinear analysis are developed for an arbitrary value of the refractive index n = kc/w. Specializing to luminous waves, as n goes to 1, it is shown that the linear gain curve is symmetric about synchronism and that instability can occur even at exact synchronism, for appropriate initial beam distributions. The nonlinear integrals of the motion are obtained, indicating that the total energy is available, the nonlinear evolution is described by a single differential equation, and the nonlinear efficiency is shown to depend on only four combinations of the beam, field, and resonator parameters. Nonlinear efficiencies up to 15% can be achieved. For a relativistic beam, a substantial frequency upshift is possible, with efficiencies up to 10%. Efficiency enhancement is possible, e.g., by the introduction of a two-stage resonator. In such a configuration, efficiencies exceeding 30% are calculated. Finally, the requirements for beam temperature and mode selectivity are found not to be particularly restrictive.