Threshold power transfer for the gyrotron and peniotron oscillators operating at the harmonic cyclotron frequencies using coaxial electron beam-circuit configurations

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Abstract
Recently we have solved for the linearized displacement in a thin beam in a constant axial magnetic field inside a cylindrical waveguide propagating TEsn or TMsn waveguide mode [Shrivastava and Grow (1984)]. The displacement vector indicates the existence of two modes at the s harmonic and one mode each at (s + 1) and (s − 1) harmonics of the cyclotron frequency. This paper extends the analysis for the start oscillation conditions for the monotrons based on these interactions. Using the polarization variable approach, the RF surface current density is evaluated in terms of the RF displacement. Then the RF beam power transfer in terms of TEsnl or TMsnl mode, is evaluated for each of these interactions. The power transfer is also evaluated for a magnetron resonator supporting TE-mode RF fields. A method to evaluate threshold DC beam power in terms of the RF beam power transfer, Q factor, and the stored energy in the resonator is suggested. Good agreements between this theory with other published results and large signal simulations for the TE-mode grytoron interaction threshold calculations in cylindrical and magnetron type cavities are reported. A method to evaluate the effect of velocity spread on the RF beam power transfer is given. If the effects of RF displacement are neglected in the phase variation seen by the electron, infinite power transfer is obtained. A correction to the small signal peniotron theory to include this effect is suggested.

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