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Self-Excitation of a Tapered Gyrotron Oscillator

This paper consists of two parts. In the first part, the linear theory of a tapered gyrotron oscillator, which can operate either as a gyro-backward-wave oscillator or a gyromonotron, is developed. The formulation is done for the case of excitation near cutoff frequency. The self-excitation conditions are found in a cold-cavity approximation when the axial structure that is independent of the electron beam can be described by either the Airy function or the sinusoidal distribution in tapered and constant-radius waveguides, respectively. In the second part, results of this general treatment are used for estimating the start currents and operating parameters of a terahertz-range gyrotron oscillator. For making these estimates, an axial profile of an interaction circuit is specified, and for a chosen profile, the axial structures and quality factors of modes with different numbers of axial variations are calculated with the use of available codes. This information allows us to estimate the start current by using results of the general theory obtained in the cold-cavity approximation in the first part of the paper. Then, the start currents are determined with the use of a self-consistent set of equations. The results obtained also allow estimating the tolerances in circuit fabrication.