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Telecommunications and Radio Engineering
SJR: 0.202 SNIP: 0.2 CiteScore™: 0.23

ISSN Imprimer: 0040-2508
ISSN En ligne: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v73.i3.20
pages 203-219

AN ANALYTICAL SOLUTION TO THE PROBLEM OF DIPOLE MODE COUPLING IN RESONATORS WITH A SMALL HOLE

M.I. Ayzatsky
National Scientific Center "Kharkov Institute of Physics and Technology" 1, Akademicheskaya St., NSCKIPT, 61108 Kharkov, Ukraine
K.Yu. Kramarenko
National Scientific Center "Kharkov Physicotechnical Institute", National Academy of Sciences of Ukraine 1, Academicheskaya St., Kharkiv 61108, Ukraine

RÉSUMÉ

The problem of dipole mode coupling in resonant cavities is of great importance for practical applications since it is the basic one for describing axially-asymmetric oscillations in iris-loaded waveguides. Oscillations of the kind are responsible for the transverse displacement of the accelerated beam and, consequently, for the development of the transverse instability in the linear resonance accelerators. Until recently there has been no method capable of calculating coupling factors of the cavity dipole modes under various assumptions concerning geometries of the coupling apertures and cavities based on the rigorous electrodynamic approach. For this reason these coefficients were calculated by approximate methods which are based on the solutions of the electrostatic and magnetostatic problems. We have presented the electromagnetic fields in different regions in the form of expansions in the complete sets of eigenfunctions consisting of solenoidal and potential subsystems. The infinite sets of algebraic equations derived through applying boundary conditions were transformed into sets of paired integral equations. Analytical solutions have been obtained for these equations. Analysis of the solutions has shown that the expansion of the tangential component of the electric field on across the aperture with respect to a small parameter (~α) contains no zero-order approximation. The electric field tangential component is proportional to both the magnetic field tangential components of the TM110- and TE111-modes (~α/λ, withλ being the wavelength) and the normal (with respect to the aperture plane) electric field component of the TM110-mode (~a/b, with b being the cavity radius). Expressions have been also derived for the coupling factor of the TM110- and TE111-modes. It is shown that the coupling coefficients determined within the accuracy up to α3 are dependent on the electric field solenoidal component on the aperture alone. In contrast to the widely used heuristic approach which is based on selection of the parameters of the chain of coupled circuits, the suggested technique provides a possibility to more accurately describe the characteristics of the axially-asymmetric oscillations in slow-wave structures and process of their excitation by high-current electron beams.


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