Study of frequency of a coaxial-cavity gyrotron oscillator

The eigenvalues of a coaxial cavity must be modified by the structural eccentricity (for instance, by the misalignment of the inner rod), which causes an eigenfrequency shift. In this paper the eigenfrequency shift of the higher-order modes is numerically investigated in terms of the eigenvalue equation. Taking the TE _31,17,1, TE _32,17,1,TE _33,17,1 and TE _34,17,1 modes as examples, calculations show that the eigenfrequency of a mode may have a down-shift or tip-shift, which depends on the ratio of the outer conductor radius to the inner rod radius R _out/R _in. For a higher-order mode, the greater the value of R _out/R _in, the smaller the influence of the structural eccentricity on the eigenfrequency shift. Moreover, the structural eccentricity may have a weaker influence if the azimuthal index of the mode is higher.