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A typical problem of weakly relativistic low-power gyrotrons (especially in the case of operation at high cyclotron harmonics) is the use of long cavities ensuring extremely high diffraction Q-factors for the operating near-cutoff waves. As a result, a great share of the rf power radiated by electrons is spent in Ohmic losses. In this paper, we propose to use a sectioned cavity with π-shifts of the wave phase between sections. In such a cavity, a far-from-cutoff axial mode of the operating cavity having a decreased diffraction Q-factor is excited by the electron beam in a gyrotron-like regime.

We propose to use of an undulator with the guiding axial magnetic field as a "kicker" forming a bunch of electron gyro-oscillators with a small spread in the axial velocity. The cyclotron emission from the bunch leads to losing oscillatory velocity of electron gyrorotation, but it does not perturb the axial electron velocity. This effect can be used for transformation of minimization of the spread in electron axial velocity in the undulator section into minimization of the spread in electron energy in the cyclotron radiation section.