Calculation of VLW fields in a waveguide with A 3-D local inhomogeneity

The problem of a point-source field in an irregular impedance waveguide is solved. The 3-D inhomogeneity of one of the walls of the waveguide is given by an area-inhomogeneous impedance. To obtain a solution within the framework of the method of integral equations, we develop a procedure for asymptotic transformation of the 2-D equation into an 1-D equation with allowance for the waves reflected from all the inhomogeneity boundaries. The obtained 1-D integral equation for points that belong to both the path line and boundary contour of the inhomogeneity is solved numerically using an original algorithm. The results of model calculations in a near-earth waveguide for the case of ionospheric perturbations that are large on the wavelength scale are given.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1312–1322, December, 1995.     

Depolarization of the electromagnetic field scattered by a three-dimensional large-scale irregularity of the lower ionosphere

This paper develops analytical and numerical methods for the solution of three-dimensional problems of radio wave propagation. We consider a three-dimensional vector problem for the electromagnetic field of a vertical electric dipole in a planar Earth-ionosphere waveguide with a largescale local irregularity of negative characteristics at the anisotropic ionospheric boundary. The field components at the boundary surfaces obey the Leontovich boundary conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr≫1, where r is the distance from the source or receiver to the nearest point of the irregularity, k=2π/λ, and λ is the radio wavelength) integration over the direction perpendicular to the ray path, we transform this system to one-dimensional integral equations where integration contours represent the geometric contour of the irregularity. The system is numerically solved in the diagonal approximation, combining direct inversion of the Volterra integral operator and subsequent iterations. The proposed numerical algorithm reduces the computer time required for the solution of this problem and is applicable for studying both small-scale and large-scale irregularities. We obtained novel estimates for the field components that are not excited by the source but result entirely from scattering by the sample three-dimensional ionospheric irregularity.     

Depolarization of the electromagnetic field in a locally inhomogeneous earth-ionosphere waveguide

This paper presents a further development of the numerical-analytical method for the solution of three-dimensional problems in the theory of radio wave propagation. We consider a vector problem of the electromagnetic field of a vertical electric dipole in a plane Earth-ionosphere waveguide with a local large-scale irregularity on the anisotropic ionosphere wall. The possibility of lowering (elevating) of the local region of the upper waveguide wall with respect to the regular ionosphere level is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr ≫1) integration along the direction perpendicular to the ray path, we transform this system to a system of one-dimensional integral equations. The system is solved numerically in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent iterations. The proposed method reduces the computer time required for solving the problem and is useful for the study of both small-scale and large-scale irregularities. We obtained estimates of the TE field components that are not excited by the source considered and originate entirely from field scattering by a three-dimensional irregularity disturbing the geometric regularity of the ionospheric waveguide wall. State University of St. Petersburg, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 617–629, July, 2000.     

Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity

In this paper, we develop further the analytical and numerical method of solving three-dimensional problems in the theory of radio wave propagation, including three-dimensional local inhomogeneities (ionospheric disturbances or Earth’s surface irregularities). To model the Earth-ionosphere waveguide, we use the surface impedance concept, by which the irregularity extending beyond one waveguide wall has an arbitrary smooth shape, and its surface can be described by the impedance. In the scalar approximation, this problem is reduced to a two-dimensional integral equation for the irregularity surface, which, by asymptotic (kr ≫ 1) integration over the coordinate transverse to the propagation path (with allowance for terms of the order of (kr)⁻¹), is reduced to a one-dimensional integral equation, in which the integration contour is the linear contour of the irregularity. The equation is solved numerically, combining the inversion of a Volterra integral operator and successive approximations. By reducing the computer times, this method enables one to study both small-scale and large-scale irregularities. The results of numerical simulation of radio wave propagation in the presence of a powerful three-dimensional ionospheric disturbance are presented as an example. State University, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 5, pp. 588–604, May, 1998.     

Estimation of field in plane impedance waveguide with local geometrical irregularity. II

The author investigates effect on the field of a point source in a plane impedance waveguide of an irregularity in the form of spherical surface that projects from (or is embedded into) the plane of the, ionospheric wall of the waveguide. In a scalar approximation, the problem is reduced to a two-dimensional integral equation over the surface of the irregularity. A solution is constructed by successive approximations, for which the solution of the problem for a regular impedance waveguide is used as the initial approximation. Numerical results are given for estimation of the effect of a local ionospheric irregularity on the field of an electric dipole in the earth-ionosphere waveguide.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 6/7, pp. 569–578, June–July, 1992.     

Directional properties of an array of sound receivers positioned in an impedance screen recess

Expressions for calculating the directional characteristics of an array of sound receivers positioned in a waveguide with impedance walls are obtained from the solution to the problem on the diffraction of a plane sound wave by the waveguide open end with impedance flanges. The waveguide can be of a finite length, and, in this case, it can be considered as an open cavity in an impedance screen. The solution of the integral equation for the sound pressure distribution over the opening area is reduced to the solution of an infinite system of algebraic equations for the coefficients of the field expansion in normal waveguide waves. Examples of calculated directional characteristics are presented for arrays with receivers positioned at different distances from the opening and for different values of the impedances of the waveguide walls and flanges.     

Estimation of field in plane impedance waveguide with local geometrical inhomogeneity. I

The effect of an inhomogeneity in the form of a circular cylinder the properties of whose base are described by a certain impedance and whose lateral surface is ideally conducting on the field of a point source in a plane impedance waveguide is studied. In a scalar approximation, the problem is reduced to a two-dimensional integral equation over the surface of the inhomogeneity. A solution is constructed by the method of successive approximations; the solution of the problem for a regular impedance waveguide is used as an initial approximation. The effect of a local ionospheric inhomogeneity on the field of an electrical dipole in the earth-ionosphere waveguide is estimated.Leningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 8, pp. 908–918, August, 1991.     

Diffraction of a sound wave by the open end of a flanged waveguide with impedance walls

Diffraction of a plane sound wave by the open end of an impedance-wall waveguide connected to an opening in an impedance screen is considered. The plane wave is incident on the waveguide from a free half-space. Two versions of the problem are considered: for a semi-infinite waveguide and for a finite-length waveguide with a specified bottom impedance; the impedances of the walls, screen, and waveguide bottom can be different. The finite-length waveguide can be treated as an open cavity in the impedance screen. For the cavity of zero length, the problem is reduced to the diffraction by an impedance insert in the impedance screen. The solution in the external region determines the scattered field; the solution in the internal region allows one to determine the directional pattern of an array of receivers located in the cavity. The problem is solved using the integral Helmholtz equation with a specially selected Green’s function that provides the fulfillment of the boundary conditions. Formally, the problem is reduced to an infinite system of algebraic equations. The computational results obtained for bistatic and monostatic scattering patterns are presented.     

Diffraction of Electromagnetic Waves by an Anisotropic Cylindrical Inhomogeneity in a Planar Waveguide

We consider diffraction of electromagnetic waves by an anisotropic cylindrical inhomogeneity located in a planar waveguide with perfectly conducting walls. Anisotropy is allowed for by using the uniaxial-crystal approximation. A rigorous analytical solution is represented in the form of double sums over eigenfunctions of a planar waveguide with perfectly conducting walls and azimuthal eigenfunctions of a cylinder. Different components of the intensity of the electric field scatttered by an anisotropic inhomogeneity are numerically calculated. The influence of the anisotropy and sizes of the inhomogeneity on the scattered field is analyzed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 605–615, July 2005.     

Characteristics of an Electric Dipole in a Plane Waveguide with an Inhomogeneous Filling in the Long-Line Approximation

Within the framework of the long-line approximation, we obtain the expressions for the current distribution, input impedance, and admittance of a nonsymmetric thin electric dipole whose ends are connected to perfectly conducting walls of a plane waveguide filled by an inhomogeneous dielectric. The use of this approximation allows one to qualitatively interpret the results of rigorous solution of the problem of the effect of the medium inhomogeneity on the radiation characteristics of the antenna.     

Field Structure in the Cross Section of a Ferrite Inhomogeneous Anisotropic Insert of a Rectangular Waveguide

We develop a physico-mathematical model describing excitation and distribution of electromagnetic waves in an anisotropic waveguide or resonator in the three-dimensional case. We develop a theoretical approach for discretization of the Maxwell equations in an arbitrary medium in the presence of bounding walls of a waveguide or resonator. The resulting system of linear algebraic equations for the electric-field components in an inhomogeneous anisotropic medium is solved by the method of biconjugate gradient. The results of calculating the electric field lines in the cross section of an anisotropic insert of a rectangular waveguide are presented.     

Numerical method for problems of diffraction on semi-infinite structures

We propose a method which transforms homogeneous integral equations into inhomogeneous ones for problems of diffraction by semi-infinite structures. New integral equations and the corresponding stationary functionals dependent on the desired scattering parameters are obtained. The consideration is performed for the open-end diffraction problem of a parallel-plate waveguide which has a rigorous solution, but the method has sufficient generality to use it for two-dimensional surface integral equations describing planar and nonplanar structures as well as for an arbitrary structure of waveguide transformer type, the solution for which can be sought in the finite domain. The method is based on field representation at the infinity as incident and scattered waves. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 3, pp. 235–245, March 2006.     

A linear-operator formalism for bianisotropic waveguides

A bianisotropic waveguide can be defined as a cylindrical waveguide filled with bianisotropic materials, and all the conventional waveguides are special cases of the bianisotropic waveguide. In this paper, guided wave propagation in bianisotropic waveguide is analyzed by the theory of linear operators, and two types of adjoint waveguides and inner products are introduced respectively. Based on the concept of adjoint waveguides, the functional expressions of the field equations can be obtained, and from which the eigenvalue problem of the bianisotropic waveguide can be solved. Also, bi-orthogonality relations of guided modes are derived. These biorthogonality relations reported here can be used to expand electromagnetic fields in terms of a complete set of modes in straight bianisotropic waveguide. As an example of application, mode matching formulae for a discontinuity problem are given.     

Effect of large-scale boundary irregularity on the ELF waveguide field

The effect of boundary irregularity on the ELF field in a waveguide is studied by the full-wave/ray method using the focusing-factor equation. The displacement of the normal-wave trajectories into the complex region and the field along them are estimated, and the applicability conditions of a longitudinal approximation of field phase and amplitude in a two-dimensionally irregular waveguide are determined. The transverse scale of an inhomogeneity that changes the qualitative dependence of the field on distance is found.Scientific-Research Institute, St. Petersburg University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1576–1586, December, 1994.     

Diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma

The problem of diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma is formulated and solved. The integral equations for the field are reduced to function equations, which are solved with the aid of a special function that is introduced. The properties of this function are studied. The general solution is represented as a double contour integral in the plane of a complex variable. The radiation field and surface waves for a number of special cases are analyzed: a source of cylindrical waves on an edge; at infinity; etc. Diffraction in a half-plane is studied separately.     

Eigenmodes evolution due to changing the shape of the waveguide cross-section

The problem of eigenmodes in a hollow waveguide with an arbitrary shape of cross-section is considered. To calculate this problem rigorously, the formalism of Fredholm integral equations of the second kind is developed. Basing on it, phenomena of field mode structure evolution in a system of initially circular waveguides are analysed.     

Method for solving moving boundary value problems for linear evolution equations

We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation omega(k), in the domain l(t)相似文献   

Diffraction of guided waves by the end face of a dielectric slab waveguide terminated with a finite conductive strip

The diffraction of guided waves by the end face of a dielectric slab waveguide short circuited with a finite conductive strip is analyzed. An integral equation technique is employed to formulate the corresponding boundary problem. The unknown term in this integral equations is the electric field E(x) on the terminal plane of the waveguide. The homogeneous term is determined from the incident guided wave. A method of moments technique is employed to compute approximately the electric field E(x) by using Laguerre functions as describing and testing functions. The reflection coefficients of the guided waves are computed by using the approximate expression of the E(x) field. Numerical results are given for several guide and conductor plate dimensions.     

一种可稳定计算Pekeris波导中声场的波数积分方法

提出一种可稳定计算Pekeris波导中声场的波数积分方法,并在此基础上开发出一个数值模型,可用于提供Pekeris波导中声场的精确、稳定的数值解。在这个方法中,由于与深度有关的波动方程齐次解中所有的上行波与下行波均采用了合理的归一化表示,从而得到的系统方程是无条件稳定的。在简正波方法中,割线积分一般只对近场有显著影响。因此,传统的简正波模型一般都忽略割线积分对声场的贡献。但是,如果某号简正波离割线非常近,则割线积分对非常远距离的声场仍可能有显著影响。在这种情况下,传统的简正波模型由于忽略割线积分的贡献,从而得到的声场结果是不准确的。本文通过数值算例比较本文提出的波数积分模型与传统的简正波模型。数值结果表明,本文提出的模型可以提供精确、稳定的Pekeris波导中声场的数值解,而在某些情况下传统的简正波模型得到的声场结果是不准确的。因此,本文提出的模型可以作为Pekeris波导中声传播问题的标准模型使用。