Linear theory of frequency pulling in gyrotrons

Abstract

The effect of the electron beam on the gyrotron operating frequency (the frequency pulling) is studied analytically in the framework of the linear (or small-signal) theory. The theory is applicable for gyrotrons operating at any cyclotron harmonics and in modes with arbitrary axial structures. The present consideration is limited to cases of operation at the fundamental cyclotron resonance and the second harmonic; also two specific axial profiles of the resonator modes are analyzed: the constant and the sinusoidal distributions. In the case of the sinusoidal distribution, we considered the operation in modes with one, two, and three axial variations. It is shown how to use the theory developed for analyzing the frequency tunability due to the frequency pulling effect in a gyrotron with specified parameters of the electron beam.