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Telecommunications and Radio Engineering
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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v61.i5.30
pages 394-416

The Conformal Mapping Method for Analysis of High-Frequency Electro-Magnetic Fields in Slow-Wave Structures 1. The Case of Large Slow-Downs

M. V. Mil'cho
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine 12, Academician Proskura St., Kharkov 61085, Ukraine


A numerical-analytical method for the analysis of spatial distribution of high-frequency fields of eigen oscillation modes in slow-wave structures composed of metal rectangular elements is described. Gratings, combs and other similar constructions are such systems. The field distribution for a particular slow-wave structure is represented in the form of a linear combination of solutions to several problems of wave diffraction on a periodical structure composed of finite-thickness half-planes. The solution to these auxiliary diffraction problems is found from the requirements of identity of the combined functional equations obtained at the joining of the fields for the electrodynamic and electrostatic instances. An exact solution to electrostatic problems is found by means of the conformal mapping method. The formulae for calculating the electrodynamic fields are represented in a closed form (not in the forms of series). All spatial harmonics of the field are taken into account. The field peculiarities near the sharp edges of the metal elements are described correctly. In the first part of the paper a large slow-down is considered in the case when the wave lengths of all spatial harmonics are much less than the free-space wavelengths. Plots of space-time field variations are represented for a comb slow-wave structure.