Automodulation instability in gyrotrons operating at the second cyclotron harmonic

Abstract

Interest in gyrotron operation at cyclotron harmonics is motivated by the users' desire to reduce the magnetic fields required for operation at a given frequency. However, operation at harmonics is more complicated than at the fundamental resonance because in harmonic gyrotrons there are many parasitic modes at the fundamental, which can be prone to excitation. The present study is devoted to the analysis of automodulation instability in harmonic gyrotrons. Such instability may occur, for example, when in the vicinity of the desired second harmonic mode there is a pair of parasitic modes at the fundamental, for the frequencies and azimuthal indices of which some specific conditions are met. In this paper, the equations describing this instability are derived in the cold-cavity approximation. The study is then focused on a second harmonic gyrotron with the parameters optimal for efficient operation. For such a gyrotron, the region of instability is determined in the plane of frequency mismatches between the operating and parasitic modes. This treatment performed within the framework of the general theory is complemented by consideration of some gyrotrons operating in specific modes, which are surrounded by specific sideband modes at the fundamental.