Abstract
Linear and nonlinear theory is presented for the generation of gyroharmonic radiation from spatiotemporally modulated electron beams in cylindrical waveguides. Selection rules for axisymmetric beams are derived that show coupling at the mth temporal harmonic to be absent for all TM modes, and for TE modes other than those with an azimuthal mode index of m. Estimates from linear theory are given for the effects of spreads in axial momentum and guiding-center radius. A nonlinear multimode theory is developed in order to treat mode saturation and mode competition for TE modes in a down-tapered guide magnetic field
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