In general, a slow-wave structure s

In general, a slow-wave structure supports several eigenmodes at a given frequen-cy, and therefore the superposition of excited fields due to these eigenmodes wouldinteract with the electron beam. If, however, only one of the modes was to interactwith the beam due to the synchronization of their phase velocities, it would be justi-fied to use the simplified single-TL model as used in Pierce model above. However,the exact form of the slow-wave structure does not play a role in the Pierce modeldue to the very general nature of such analysis. Some commonly used slow-wave structures include the helix and its variants, such as the ring-bar and the ring-loop structures, as well as coupled cavity structures and those devices are naturally mul-timodes. In light of the recent growing demand for high power efficient TWTs and BWOs, it is beneficial to explore unconventional multimodal slow-wave structures with the aim of increasing the peak power levels and the operating efficiency of the TWT.