Impedance calculations for traveling-wave gyrotrons operating at harmonics of the cyclotron frequency in magnetron-type circuits operating in the π mode

Impedance calculations have previously been made on a gyrotron operating with a magnetron circuit in the 2π-mode and cutoff constants were determined and impedance calculations were made for values of the ratio of vane radius to the outer waveguide radius from 0.15 to 1.00. The normalized interaction impedance and the stream voltage was then calculated for each of these magnetron circuit configurations. In this paper, calculations have been made of interaction impedance and stream voltage to achieve operation in the π-mode. The π-mode has the advantage of having higher impedance values than the 2π-mode. This advantage is offset by the necessity of strapping the vanes of the magnetron. These results for the π-mode are compared with the 2π-mode and also with a smooth waveguide operating in a TEn1mode. The advantages and disadvantages of all three configurations are discussed.