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An improved slow-wave structure (SWS), i.e., a dielectric-lined azimuthally periodic circular waveguide (DLAP-CW) that is a modified form of a conventional dielectric-lined circular waveguide (DL-CW), is proposed. The slow-wave characteristics are studied by the spatial harmonics method. Analytical solutions for the dispersion characteristics and interaction impedance are derived. The complicated dispersion equations have numerically been solved with MATLAB, and the results agree well with simulation results obtained from a high-frequency structure simulator. The effects of the SWS parameters on the RF characteristics are investigated. SWS parameters include the dielectric constant and the thickness and location of the metal rods. It is shown that selecting the appropriate thickness and location of the metal rods increases the interaction impedance with only slight influence on the dispersion characteristics (with the dielectric constant held fixed). Furthermore, the DLAP-CW and the conventional DL-CW are compared, and the results validate that the DLAP-CW has the potential for significantly higher interaction impedance at higher frequencies, potentially resulting in a higher gain traveling-wave-tube circuit.