Starting currents of modes in cylindrical cavities with mode-converting corrugations for second-harmonic gyrotrons

Abstract

A self-consistent system of equations (known as single-mode gyrotron equations) is extended to describe the beam-wave interaction in a cylindrical gyrotron cavity with mode-converting longitudinal corrugations, which produce coupling of azimuthal basis modes. The system of equations is applied to investigate the effect of corrugations on starting currents of the cavity modes. For these modes, eigenvalues, ohmic losses, field structure and beam-wave coupling coefficients are investigated with respect to the corrugation parameters. It is shown that properly-sized mode-converting corrugations are capable of improving the selectivity properties of cylindrical cavities for second-harmonic gyrotrons.

Mode-Converting Corrugations for Cavities of Second-Harmonic Gyrotrons with Improved Performance

“…V z of the TE mode and electron beam dynamic can be found from (1), initial conditions for beam electrons and outgoing-wave boundary conditions at both ends of the cavity (for more detail, see [14]). Hence one can determine the transverse electronic efficiency One of the main factors affecting the interaction efficiency is the beam coupling with s -th harmonic TE mode.…”

“…In a cavity with longitudinal wall corrugations, each TE mode has the form of multiple Bloch harmonics (see ( 3)), which have their own beam-wave coupling coefficients. For the n -th Bloch harmonic with amplitude n A , such coefficient reads as [14]:…”

“…for the operating TE 13,2 mode. Under this condition, the effect of wall corrugations on the operating mode is generally weak [13,14].…”

“…Mode-converting wall corrugations can be applied to further improve the selectivity properties of advanced cavities for second-harmonic gyrotrons [13,14]. Contrary to impedance corrugations [15][16][17][18][19], such corrugations induce coupling between normal modes (azimuthal Bloch harmonics) of the cavity and thereby affect frequencies of cavity modes, their ohmic losses and coupling with an electron beam [20][21][22].…”

“…Contrary to impedance corrugations [15][16][17][18][19], such corrugations induce coupling between normal modes (azimuthal Bloch harmonics) of the cavity and thereby affect frequencies of cavity modes, their ohmic losses and coupling with an electron beam [20][21][22]. According to [13,14], in a cavity of a secondharmonic gyrotron, the depth of mode-converting corrugations should be selected close to half wavelength of the operating mode. In this case, the operating mode is generally weakly affected by corrugations of the cavity wall, while characteristics of the first-harmonic competing modes undergo a material change.…”