A method and apparatus for suppressing lower order cyclotron harmonics in order to permit resonance within a quasi-optical gyrotron/gyroklystron configuration of a desired higher order harmonic. In the gyrotron/gyroklystron configuration at least one open resonator defined by at least two mirrors is positioned downstream from an electron beam source for receiving therethrough the beam of electrons and for exchanging energy therewith. This method includes the steps of choosing a mirror radius size .rho. for the mirrors forming the at least one open resonator which is large enough relative to the spot size of a desired radiation cyclotron harmonic .omega..sub.n so that the harmonic .omega..sub.n oscillates within the at least one resonator, but small enough so that the spot size for the next lower cyclotron harmonic .omega..sub.m is larger than the mirror so that the harmonic .omega..sub.m does not oscillate due to diffraction losses. This method further includes the step of generating an electron beam via the electron beam source with a beam current which is greater than or equal to the starting current I.sub.n for the desired nth cyclotron harmonic, but less than the starting current I.sub.m for the mth cyclotron harmonic. The method also includes the step of extracting radiation energy at the nth cyclotron harmonic from the at least one open resonator. The desired mirror radius size .rho. for a given cyclotron harmonic frequency .omega..sub.n, for a desired diffraction loss Y.sub.n for that harmonic n, a given half length separation L.sub.y between the mirrors, and a given radius of curvature R.sub.M, can be determined by the equation ##EQU1## wherein r.sub.on is the spot size at the mirror for radiation at the nth cyclotron harmonic.