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Sourcewise represented green's function of the circular waveguide
Abstract
Singular part of the Green's function of unbounded space is singled out in explicit form and contains all singularities, including a delta-shaped singularity. The problem of construction of Green's function for a field is solved, as a problem for diffraction of potential and rotational components electric field intensity of a point current source on the circular waveguide walls. The singling out of the electric field intensity singularity in an explicit form about a source enables to develop an effective algorithm of Green's function calculation at any distance between the source point and observation point in a circular waveguide.
The present work is dedicated to the study of the processes of generation and propagation of transient electromagnetic waves in transversely inhomogeneous multiconnected cylindrical and conical transmission lines. On the base of mode basis method in cylindrical and spherical coordinate systems, new advanced numerical schemes are constructed in order to analyse the transient waves in multiconnected waveguides and conical transmission lines with inhomogeneous and time-varying filling. The convergence of introduced mode expansions for electromagnetic fields is proved numerically. The developed numerical schemes have been implemented in software. These programs allow to solve the problems of generation and propagation of
transient electromagnetic waves in shielded quasi-TEM lines and asymmetrical radially inhomogeneous biconical transmission line in rigorous electromagnetic formulation and to obtain new physical results. Particularly it is shown that in arbitrary quasi-TEM transmission line a pulse with finite spectrum can propagate without any significant waveform distortion. The effect of increasing the radiated signal amplitude in a biconical transmission line due to the introduction a radially inhomogeneous dielectric filling is found out and analysed.
The approximation algorithm to the tensor Green's function calculation in the D'Alembert equation for the polarization potential in the circular waveguide is proposed. The tensor Green's function is presented in the sourcewise form as the sum of the Green's function for free space and the regular part caused by reflections from the waveguide walls. The circular waveguide is a circular cylinder with a directrix in the form of a circle. The directrix in the form of a circle is approximated by a broken line in the form of an inscribed rectilinear polygon. This approximation allows one to use the method of specular reflections and get the tensor Green's function as an infinite sum of tensor divergent spherical waves with a delta-shaped front. The resulting representation of the Green's function can be used to solve the nonstationary intrinsic boundary-value problems of electrodynamics in the case of a circular waveguide with consideration for the reflections from the walls.