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The analysis of a disc-loaded circular waveguide interaction structure of a gyro-traveling-wave-tube (gyro-TWT) considering standing and propagating mode harmonics in the disc-occupied and disc-free regions, respectively, gave the beam-absent dispersion relation of the waveguide. The axial phase propagation constant predicted by the dispersion relation was substituted into the gyro-TWT gain-equation, the latter obtainable from the beam-present dispersion relation of the device. A method of double-tapering the structure dimensions was proposed that consists in tapering the disc-hole radius to distribute the midband frequency of amplification over a wide range of frequencies, and simultaneously tapering the waveguide-wall radius to compensate for gain reduction at band edges due to disc-hole radius tapering. The method has demonstrated wide device bandwidths at relatively large gain values.