Regions of azimuthal instability in gyrotrons

This paper is devoted to the analysis of the instability of operating modes in high-power gyrotrons with cylindrically symmetric resonators. This instability manifests itself in destruction of the azimuthally uniform wave envelope rotating in a gyrotron resonator having a transverse size greatly exceeding the wavelength. The appearance of azimuthally nonuniform solutions can be interpreted as simultaneous excitation of modes with different azimuthal indices. This problem is studied self-consistently, i.e., taking into account the temporal evolution of both the azimuthal and axial structures of the wave envelope. The region of gyrotron operation free from this instability is identified. The efficiency achievable in this region can be only 1%–2% lower than the maximum efficiency. It is also possible to address the difference between the theory of mode interaction developed under assumption that all modes have fixed axial structure and the self-consistent theory presented here. As known, for fixed axial mode profiles, single-mode high-efficiency oscillations remain stable no matter how dense is the spectrum of competing modes, while the self-consistent theory predicts stable high-efficiency operation only when the azimuthal index does not exceed a certain critical value. It is shown that the azimuthal instability found in the self-consistent theory is caused by excitation of modes having axial structures different from that of the desired central mode.