The analytical expressions for the beam-wave coupling coefficients and the beamloaded conductance of Hughes-type coupled cavity with n gaps are derived. The analytical theories show that the beam-wave coupling coefficients and the beam-loaded conductance of the operating mode (2π mode) may be very sensitive to the beam voltage with the increase of the gap numbers. In addition, the stability of the circuit was discussed through calculating the quality factor of three-gap coupled cavity. And the π/3 mode may self-oscillate due to negative beam-loaded conductance.
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