To rapidly and accurately investigate the performance of the dielectric loaded rectangular Cerenkov maser, a simplified nonlinear theory is proposed, in which the variations of wave amplitude and wave phase are determined by two coupled first-order differential equations. Through combining with the relativistic equation of motion and adopting the forward wave assumption, the evolutions of the forward wave power, the power growth rate, the axial wave number, the accumulated phase offset, and the information of the particle movement can be obtained in a single-pass calculation. For an illustrative example, this method is used to study the influences of the beam current, the gap distance between the beam and the dielectric surface, and the momentum spread on the forward wave. The variations of the saturated power and the saturation length with the working frequency for the beams with different momentum spreads have also been studied. The result shows that the beam wave interaction is very sensitive to the electron beam state. To further verify this simplified theory, a comparison with the result produced from a rigorous method is also provided, we find that the evolution curves of the forward wave power predicted by the two methods exhibit excellent agreement. In practical applications, the developed theory can be used for the design and analysis of the rectangular Cerenkov maser.
A linear theory of a rectangular Cerenkov maser （RCM） with a sheet electron beam is developed by using the field- match method. Based on the three-dimensional beam-wave interaction model proposed in this paper, a hybrid-mode dispersion equation and its analytical solution are derived for the RCM. Through numerical calculations, the effects of the beam-grating gap, beam thickness, current density, beam voltage and waveguide width on the linear growth rate axe analysed. Moreover, the performance difference between the RCM with the closed transverse boundary and that with the upper open boundary is compared. The results show that the closed RCM model can avoid the effect of RF radiation on beam-wave interaction, which is more rational for practical applications.
