[en] The optimization of gyroklystron efficiency is investigated by employing a two-step procedure. As a first step, the prebuncher is analyzed using a small signal approximation, since the cavity(ies) here serve mainly to modulate slightly the velocities of the electrons, which will be bunched in the field-free drift section(s). It is found that the electrons entering the energy extraction cavity can be characterized entirely by only two dimensionless parameters: a bunching parameter q and a relative phase psi. The numerical simulation of the extraction cavity, based on the nonlinear pendulum equations describing the interaction between the electrons and the rf field, supplemented by the initial conditions specified by q and psi, constitutes the second step. The final result of this two-step analysis is the efficiency, eta/sub perpendicular, opt/ optimized with respect to q, psi and the magnetic detuning parameter Δ. This efficiency depends only on the normalized cavity length μ and the normalized rf field F of the energy extraction section. The efficiency as well as the conditions required to attain this optimum (q/sub opt/, Δ/sub opt/, and psi/sub opt/) are presented as contour plots on the (F, μ ) plane and can be used efficiently to design gyroklystrons of any frequency and output power