Linear analysis of a three-dimensional rectangular Cerenkov maser with a sheet electron beam

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 are 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.