Characteristics Study of $3\pi $ Stopbands of Folded Waveguide Slow-Wave Structures in $V$ -Band Traveling-Wave Tubes

This paper presents a characteristics study of 3π stopbands generated by three types of loading (beam tunnels, bends, and straight segments) in a V-band folded waveguide (FWG) slow-wave structure (SWS). CST Microwave Studio was used to simulate the dispersion characteristics and the instability at 3π phase shift. For loading of beam tunnels, horizontal offset and radius give rise to a negligible width of 3π stopbands, whereas vertical offset (0.01 mm) results in 3π stopband instability. Simulation results also show that the loading of both bends and straight segments generates a wide range of widths of 3π stopbands, for which it is believed that the loading of every geometrical period of the FWG SWS is responsible.