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The cold (beam-absent) analysis of an all-metal structure consisting of a circular waveguide loaded with axially periodic annular discs was developed in the fast-wave regime for potential application in wide-band gyro-traveling-wave tubes (TWTs) in the millimeter-wave frequency range. The analysis includes the effect of higher order standing-wave modes in the disc-occupied region, as well as higher order space harmonic propagating modes in the disc-free region of the structure. The analysis also takes into account the effect of the finite disc thickness. The dispersion characteristics of the structure obtained by the analysis have been validated against those reported elsewhere using an alternative coupled-integral-equation technique and also against those obtained using commercial simulation code HFSS. The dependence of the eigenvalue and dispersion characteristics of the structure on the disc parameters, namely, the disc hole radius, periodicity, and thickness was studied. The optimum disc parameters corresponding to the widest frequency band over which the dispersion curve can be straightened were suggested for widening the bandwidth of coalescence between the waveguide-mode and beam-mode dispersion characteristics for wide-band gyro-TWT performance. The optimum disc parameters for wide device bandwidths and high device gains were also predicted with the help of the small-signal gain equation of a gyro-TWT.