Gyrotron coaxial cylindrical resonators with corrugated inner conductor: Theory and experiment

Gyrotron coaxial resonators with a longitudinally slotted inner cylinder are examined analytically using a surface impedance model, from which expressions for the electromagnetic field, ohmic quality (Q) factor, and characteristic equation of the transverse eigenvalues χ _m,p are obtained. The major attributes of such resonators are expressed by the dependence of χ_m,p on the parameter C-defined as the ratio of the outer to inner radii of the coaxial structure. In that connection, the effect of the corrugation parameters on χ_m,p is particularly investigated on the basis of an expression derived for the slope function dχ_m,p,p/dC. It is shown that the χ_m,p(C) curve may either exhibit oscillatory behavior or present a flat portion over a wide range of C depending on the corrugation parameters chosen. The theory is checked against experiment in which resonant frequencies and total Q factors were measured for TE modes operating in the range of 8-16 GHz in a coaxial cavity with 40 slots. Good agreement is found in that the magnitude of the relative error in frequency is less than 0.5%. Corrugated coaxial resonators prove to be relevant to megawatt gyrotrons where highly selective cavities are required to ensure high conversion efficiency