Saturation Effects in Frequency Pulling of Gyrotrons Operating in High-Order Axial Modes

Spectroscopic applications have stimulated strong interest in frequency tunable gyrotrons. One of the possibilities to tune gyrotron frequency is known as frequency pulling, which is based on the effect of the electron beam on the oscillation frequency. Recently, the linear theory of this effect was developed, and the results were obtained for a sequence of modes with different axial indices. This paper is intended to analyze saturation effects in such gyrotrons. The nonlinear theory describing the frequency pulling and the efficiency in gyrotrons is developed in the cold-cavity approximation. The results are obtained for the modes with different axial indices (from 1 to 4). The frequency shift and the efficiency are calculated in a wide range of the dimensionless parameters characterizing the beam current and the external magnetic field. These results related to the frequency pulling are compared with those of the linear theory. Also, comparison is made with the results of the self-consistent theory and experiments.