Modeling and characterization of a rectangular waveguide grating structure using transmission line theory for planar Cerenkov masers

A modeling approach is proposed based on transmission line theory for the characterization of the periodic rectangular waveguide grating (RWG) structure. Using an equivalent circuit (EC) model the dispersion equation of the structure is derived with largely reduced workloads as compared to the conventional field-theory method. An EC based analysis of the RWG structure is performed. Numerical results show a good consistency between the two methods as varying structural parameters of significance. The proposed approach is also used for the taper design with the objective of minimizing wave reflection of the structure. A resulting multistage taper can deliver a low cumulative reflection coefficient on the order of 10^{-3}. Furthermore, the coherence performance of an RWG based planar Cerenkov maser (PCM) is studied on the driving electron beam interacting with the traveling harmonic wave. This includes the impacts of the grating height uniformity, due to practical machining uncertainty, on the net wave reflection as well as on the growth rate of the wave in the maser. The obtained results show, that a non-uniformity on the order of 50 micrometers in the grating height can increase the reflection level by at least one order of magnitude. The PCM coherence can be considerably degraded, in terms of a significant reduction in the wave growth rate of more than 30% with respect to its theoretical value.