# Modeling of curvilinear filament structure in the waveguide

Автори:
Yo.A. Zakharia

Lviv Polytechnic National University

Well known current filament modeling method is frequently for electrodynamic structures analysis in free space and in waveguide used. In both cases the electrodynamic analyse principles are the same. The current filament method is often for analysis of closed waveguide exciter, or analogous passive elements in waveguide used. For sufficient small area of closed filament structure and corresponding great field point distance in analysis the dipole model is valid. The form of structure contour is then not essential. Therefore the codition of structure momentum (electrical or magnetic) we use an polygonal modeling. The contour of filament closed structure may be analytically described. But often the contour form is arbitrary and can not be mathematical expressed. In last case it is possible the considered in this paper polygonal modeling to apply.
For example in the paper the magnetic current is taken. Such example is useful in analysis of waveguide aperture exciting. It is known, that necessary Green functions are by form of waveguide cross section defined, and usually given by infinite series. The known modified Green functions often are particularly simplified. Therefore we are forced the numerical analysis method to apply. But necessary analytical expressions we must get by electrodynamic mehods. The coresponding formulas for lineare coordinate sections of polygonal model contour are the simplest. The sloped sections of filament current model in general radiate three vector-potential components. Correspondingly, the field analysis is more complicated. It is possible to use the analogous analytical method without modeling, if filament structure contour can be mathematically expressed. Algorithm for analytical expressions in last case coincide with algorithm for sloped lineare section of magnetic current filament given in the paper But mathematical difficulties can cause, that it is impossible analytically to realize. Then we may the polygonal modeling to apply. The algorithm for analytical expressions of radiated by magnetic current electrical field tension is also given in the paper.
Use the circular filament coil with magnetic current for numerical example, the comparison of radiated by various coil polygonal model field tension, is realized in this work. It is established, that in the near zone of coil area the radiated electrical field for N=4 and N=12 is practical the same. A little difference has an order of tenth part from one per cent. We should to remind, that in the quadratic model (N=4) the sloped filament sections absent, and the calculations are simplified. In order to detect of the named above differences, the electrical field is in separate points of a current coil circle radius calculated. So it is found, that only near of quadratic model current filament the result difference icrease to one percent. Such almost on ¾ of quadratic model area the accuracy of modeling is high.
In the paper is an information about simplified modeling of sloped current filament section in waveguide by his coordinate projections given. However the difference of calculated results relative to quadratic modeling increase to three percent.