The corrected dispersion relation governing the linear interaction of a TE mode in a circular cylindrical wave guide with an annular beam of gyrating electrons in a gyro-TWT configuration is derived. The derivation of the correct dispersion relation no longer involves any integration with respect to the radial coordinate ro. of the electron guiding center as the relevant equilibrium distribution function turns out to be independent of ro. When the cyclotron resonance condition is satisfied by the TE mode for a positive s-number, the small-signal theory is shown to predict an initial exponential growth of the mode with interaction length over a small but finite band of frequencies around the design frequency.
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