Backward-wave interaction using step periodic structures

Periodicities introduced into hollow waveguides with step and turn symmetry are shown to have characteristics useful for backward-wave interaction in microwave electron tubes. Using Floquet's theorem, it is shown that the modes of a hollow waveguide can be shifted in phase over one period of the structure. Interaction with the shifted backward-wave mode is then possible over a range of frequencies. A gyrotron backward-wave oscillator is particularly suited to this structure; the interaction could be magnetically tuned over a range of frequencies, while a low phase constant is maintained. A lower phase constant allows the electron beam to interact coherently with the backward wave over longer distances, since any velocity spread in the electron beam forces some of the electrons to be out of step with the backward wave, thus reducing efficiency. A solid waveguide has the added advantages of being easily built for high frequencies and rugged for high temperatures.