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The coaxial ridged disk-loaded structure which is a new disk-loaded periodic system is presented and analyzed in this paper. As an all-metal slow-wave circuit, it has properties that can be used in high-power traveling wave tubes (TWT) and relativistic TWTs. The dispersion equation and coupling impedance of the structure are investigated in the first part of this paper. The results of numerical calculations of the dispersion relation and coupling impedance with different structure dimensions indicate that the interaction impedance of the ridged disk-loaded structure is higher than that of the disk-loaded structure without ridges in most frequency ranges. In the second part, the "hot" dispersion equation of this circuit with an annular electron beam is obtained according to a self-consistent linear theory. The influence of physical dimensions and beam parameters on the small signal gain is discussed.