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In gyrotrons, changing parameters of the electron beam, for example, the electron cyclotron fre- quency, it is possible to change the operating mode and, so, the frequency of the output radiation. In the step-tunable axisymmetric gyrotron there is a subsequence of operating T Env modes differing only in azimuthal indexes m. These modes are composed of similar systems of rays and, so, can be converted into the eigen mode of the mirror waveguide by the same mirror quasi-optical converter [1,2] (Fig.1) with close efficiencies. This report treats the problem in the frame of the geometrical optics. Let us consider a traditional quasi-optical converter calculated for a TEmp-wave. It consists of a launcher in the form of a spiral cut of waveguide and of a quasi-parabolc reflector (Fig.1). The spiral cut passing through reflection points of a chosen ray from cylindric wall (Fig.2) has the angle a = tin 111 • tan fi] where t9 = cos-1-(2) is an angle of beam reflection from the waveguide wall in the plane perpendicular to the waveguide axis, p is the eigen number of the operating mode, = k = 27r/A, A is operating wavelength. R is the waveguide radius. The length of the cut is L = r t9 • cot P. Reflecting quasi-parabolic mirror transforms the continuum of divergent rays radiated through the waveguide cut into a beam of parallel rays with plane phase front. After the converter the beam of parallel rays is guided up to the output window by means of mirror line. Efficiency of the wave-transformation into the Gaussian wave beam can be described by coefficient
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