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We present the transmission equations and dispersion equations of a helically corrugated waveguide according to the coupling wave theory and the impedance perturbation method. We analyzed the field distribution of the helically corrugated waveguide according to the dispersion equations. We developed the self-consistent nonlinear equations of beam-wave interaction through studying the self-consistent nonlinear theory of beam-wave interaction in a gyrotron traveling-wave tube with a helically corrugated waveguide. We analyzed the dispersion equations and simplified, numerically calculated, and simulated the beam-wave interaction equations.