Abstract-The mathematical approach for the calculation of the membrane functions of a coaxial gyrotron cavity with an arbitrary corrugated inner rod is proposed. It is utilized mainly for two aims. First, it is shown that for typical parameters of the coaxial gyrotron cavity with the corrugated inner conductor the shape of corrugations only slightly influences the eigenvalues of competing eigen-modes. However, it can significantly influence the density of ohmic losses in the inner conductor. In particular, it is shown that the density of ohmic losses can be reduced almost twice by the proper choice of the corrugation shape. Second, it is shown that the usual idealizations of the corrugated surface of the inner conductor (the surface with rectangular grooves, having rounded edges, is approximated by a surface with wedged groves that have sharp edges) are correct. The physical interpretation of the obtained results and their practical meaning are discussed.
Ohmic losses in coaxial gyrotron cavities with corrugated insert are calculated on the basis of the rigorous singular integral equation (SIE) approach. It is found that SIE predicts significantly lower losses in the corrugated insert compared with the surface impedance model (SIM) widely used before.Calculations are performed in a wide range of corrugation parameters for the cavity of the ITER relevant coaxial gyrotron operating in the TE 34,19 mode at 170 GHz. It is shown that there exist optimal corrugation parameters for which ohmic losses are minimal. They can even be less than those in the smooth insert.
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