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A simple but reasonable approach to the cold dispersion analysis of a coaxial arbitrary-shaped groove cylindrical waveguide is presented in the fast-wave regime for potential application in wideband gyro-traveling-wave tubes (gyro-TWTs). The unified dispersion equation of this structure is obtained by using an approximate field-theory analysis, in which the profile of the groove is approximately replaced by a series of rectangular steps, and the continued relation of the fields between two adjacent steps and the matching conditions at the interface between the groove region and central region are investigated. The dispersion characteristics of the disk-loaded structure obtained by modifying above results have been validated against those reported by Kesari et al. Meanwhile, the dispersion characteristics of arbitrary-shaped groove, such as the triangle-groove-loaded one are proved to agree well with computer simulation technology (CST) microwave studio simulation. The results of numerical calculations of the dispersion relation shows that the adjustment of structure parameters led to the possibility of widening the straight-line portion of omega-beta dispersion characteristics, which is required for wideband TWT performance in view of widening the bandwidth of resonance between the beam-mode and the waveguide-mode. Comparison of several different shape groove-loaded structures shows that the coaxial inverted trapezoid groove one shows the most potential application in wideband gyro-TWT because its transverse electric field is the greatest so that can interact effectively with the electron beam.