Conformal Mapping Based Dispersion Characterization of Radial Slow Wave Structure

The design of vacuum electron devices (VEDs), such as backward wave oscillators (BWO) and traveling wave tubes (TWT), relies on correctly modeling the dispersion characteristics of their Slow Wave Structures (SWS). Traditional axial structure theories do not apply to radial-line devices due to differences in coordinate systems. This study uses conformal mapping to transform rectangular radial grating SWS into their axial counterparts, allowing modified dispersion equations to calculate dispersion curves. The radial and azimuthal components of the radial SWS are transformed, while the axial component remains unchanged. The electromagnetic field distribution in radial SWS is similar to that in a planar groove with a metal plate, enabling the use of equivalent dispersion equations on mapped SWS. The periodicity of each transformed period changes logarithmically, requiring the dispersion equation to be applied for each period, with the average dispersion curve obtained by averaging individual curves. The dispersion curve for W-band frequencies is plotted with parameters: period p = 0.71 mm, groove height h = 0.41 mm, grating width d = 0.50 mm, and beam channel height s = 0.78 mm. This methodology provides a framework for accurately predicting the dispersion characteristics of radial SWS, enhancing the design of advanced VEDs.