Scattering from bodies of revolution

The problem of scattering of a plane electromagnetic wave from an arbitrary metallic body of revolution is solved by a theoretical method for arbitrary incidence and polarization. The method permits numerical computations by high-speed digital computers, and examples are given. The incident wave is expanded in cylindrical modes, and an integral equation is solved for the induced current distribution of each mode. The scattering cross section, including the back-scattering or radar cross section, is found by summation of the mode scattered fields. The method is limited to a maximum perimeter length of twenty wavelengths. While the cases discussed in the paper pertain to perfectly conducting bodies, other surface boundary conditions, an arbitrary surface impedance or coatings by lossy dielectrics, can also be treated with equal precision.     

Scattering from partial bodies of revolution

The electromagnetic scattering from classes of partial bodies of revolution formed by the presence of perfectly electrically or magnetically conducting (PEC or PMC) planes is investigated. It is found that when the Galerkin technique is used with a harmonic circumferential expansion, there is a modal decoupling of the integral operators. The choice of these expansions is determined by the angle subtended by the intersecting planes and by whether these planes are PEC, PMC, or a combination of the two. In this analysis, the partial bodies can be either PEC or penetrable. Examples illustrating this formulation are given for conducting and dielectric hemispherical geometries and for a modified corner reflector. Measured and calculated data are compared for the case of a half-cylinder on a finite ground plane     

Surface currents on impedance bodies of revolution

The surface currents induced by a plane wave axially incident on a rotationally symmetric body are determined by solving numerically extended form of Maue's integral equation. The relative surface impedance is independent of the azimuthal angle but may vary along the profile of the scatterer in any plane containing the axis of symmetry. Numerical results are shown for a sphere and a cone-sphere that are either perfectly conducting or perfectly absorbing. Apart from internal resonances, the computer code is found to provide accurate results well into the high-frequency region. A simple line-integral representation of the far field is given, and internal resonances are discussed for the backscattering radar cross section of a perfectly conducting and a perfectly absorbing sphere     

Scattering from inhomogeneous penetrable bodies of revolution

A systematic procedure for studying scattering from inhomogeneous penetrable bodies in which the inhomogeneity is modeled by piecewise homogeneous layers, is presented. The procedure utilizes the block tridiagonal property of the system matrix to simplify the computations and is applied to examples of dielectric bodies of revolution. An extension of the technique permits the solution of a composite missile/plume scattering problem.     

Scattering cross section of composite conducting and lossydielectric bodies

An E-field integral equation for the computation of the radar cross section of finite composite conducting and lossy inhomogeneous dielectric bodies is presented. The equivalence principle is used to replace all conducting bodies by an equivalent surface electric current, and the dielectric is replaced by an equivalent volume polarization current. The respective boundary conditions on the dielectric and the conductor are utilized to solve for the electric current on the entire structure. Also the augmented conjugate gradient method is presented for the solution of extremely large systems of equations that arise in the present problem. Finally, typical results are presented to illustrate the potential of this method     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

Scattering theorems with anisotropic surface boundary conditionsfor bodies of revolution

Two theorems relating the scattered fields when a special anisotropic boundary condition is imposed on the scattering surface are proven. The results of the theorems should serve as useful checks in numerical electromagnetic calculations. The authors have also verified the theorems numerically, based on the computations of a numerical method of moment code     

Generalized network parameters, radiation and scattering by conducting bodies of revolution

Introduces computer programs (FORTRAN IV) designed for field calculation from conducting bodies of revolution. A set of four programs which calculate the generalised impedance matrix and admittance matrix for triangular expansion functions, bistatic radar scattering for an axially incident plane wave, radiation from rotationally symmetric aperture antennas, and radar backscattering for an obliquely incident plane wave, are presented. Results for a number of examples are summarised and discussed. The accuracy of computation depends on the smoothness of the body and of the excitation     

一种旋转对称涂覆导体电磁散射高效分析方法

为改善传统方法分析旋转对称涂覆导体电磁散射问题的效率,提出了一种高效分析方法.该方法在介质表面建立电磁流混合场积分方程(Electric and Magnetic Current Combined Field Integral Equation,JMCFIE),在导体表面建立混合场积分方程(Combined Field Integral Equation,CFIE),利用了旋转对称体在空间上的旋转周期性,只需要对表面的母线进行剖分,具有未知量少且阻抗矩阵条件数好的特点.根据等效原理与边界条件推导了JMCFIE-CFIE方程,并与传统的PMCHW-CFIE方法对比了求解效率.数值算例表明该方法能明显改善方程的收敛性.     

A comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods: Application to horns with symmetry of revolution

A system of integral equations (SIE) based on the unique-hess theorem that uses only electric equivalent currents (EEC) is formulated to analyze conducting bodies with apertures. This SIE is compared with an SIE that uses both electric and magnetic equivalent currents (EMEC). In general, to solve both SIE's numerically difficult computations of Cauchy principal-value integrals with highly singular kernels are required. These integrals appear when computing electric (magnetic) fields created by magnetic (electric) currents. Their evaluation can be avoided using the EEC approach in many practical cases when the main interest is in the radiation patterns of aperture antennas. The two SIE's are compared by carrying out an analysis of rotationally symmetric horns using the moment method (MM) in its formulation for bodies of revolution. Numerical results of electric currents and radiation patterns are presented for small horns of various geometries. These results compare quite well with measurements for both SIE's. However, the central processing unit (CPU) time for the EEC formulation is an order of magnitude smaller than for the EMEC formulation.     

Scattering by imperfectly conducting wires

An integral equation is developed for the current induced in a slender, imperfectly conducting wire of finite length by an incident plane wave. A system of linear equations is generated by enforcing the integral equation at a discrete set of points on the axis of the wire, and these equations are solved to determine the current distribution. The scattered fields and the echo area are then calculated in a straightforward manner. Numerical results are presented for the backscatter echo area of copper, platinum, and bismuth wires at the broadside aspect with lengths up to1.8lambda. These calculations show good agreement with experimental measurements. In addition, graphs are included to show the current distributions on these wires at the second resonance, the echo-area patterns for oblique incidence, and the broadside echo-area curves for perfectly conducting wires and copper wires with lengths up to3.54lambda.     

Aperture coupling in bodies of revolution

A method for predicting the field penetrating a circumferential opening in a body of revolution is described here. This method employs the method of moments and an aperture equivalence theorem. The former permits rotationally symmetric cavities with otherwise arbitrary contours. The latter improves the sensitivity of field computation when the aperture height is tiny and/or points deep within the cavity are sought. This method is evaluated with comparison to classical theory and experiment via application to spherical and cylindrical cavities. Results for a missile-like cavity irradiated by an obliquely incident plane wave are given. A computer program and user manual is available.     

Surface currents on conducting triangular prisms

A simple and accurate method for evaluation of the singular currents on a conducting cylinder of arbitrary cross-section is briefly discussed, and the computed results for the induced currents on a conducting triangular prism are presented.     

Radiation and scattering from isorefractive bodies of revolution

The radiation from an electric or magnetic dipole located on the symmetry axis of an isorefractive body of revolution (BOR) and axially oriented is considered. The boundary-value problem is solved exactly for three BORs: the isorefractive prolate and oblate spheroids and the isorefractive paraboloid. Furthermore, for the isorefractive circular cone, the radiation from an arbitrarily located and radially oriented dipole, and the scattering from an obliquely incident plane wave are determined exactly     

Scattering from a perfectly conducting cube

The cube epitomizes the complex, three-dimensional scatterer with its multiple interactions and vertex diffraction playing a critical part in the far-field patterns of some bistatic planes. the results presented are for a cube on the order of 1.5-3 wavelengths on edge which is illuminated by a plane wave at broadside incidence. The method employed is the hybrid iterative method (HIM) which utilizes an initial approximation of the surface currents on the cube faces. These currents are inserted into the magnetic-field integral equation (MFIE) to produce improved or updated approximations to these surface currents. This process is repeated to convergence by the method of successive approximations. These currents are then used to find the bistatic radar cross section (RCS) for an arbitrary plane of measurement (emphasis has been placed upon the H-plane and the E-plane). Of particular interest is the development of cross-polarized currents, which are initially approximated by zero. As the iteration process progresses, it is seen that all physical scattering processes present in this body are introduced by enforcing the MFIE     

Scattering from the perfectly conducting cube

The scattering cross sections in the E-plane, H-plane, and 45°-plane of the perfectly conducting cube illuminated broadside by an incident plane wave are computed using both a uniform high-frequency diffraction solution and magnetic-field integral equations. The computed cross sections are compared with measured cross sections for cube perimeters of 3, 6, 12, and 20 wavelengths. The total scattering cross section versus the perimeter of the cube is also computed and compared to that of the sphere     

Scattering by parallel conducting circular cylinders

The multiple scattering by two parallel conducting circular cylinders is considered. The total scattered field is divided into two components, namely a noninteraction term and a term due to all interactions between the cylinders. The noninteraction term is expressed exactly, whereas the interaction field is evaluated using the method of moments. It is found that this technique leads to an efficient solution for both the monostatic and bistatic scattering by cylinders of large radii. The computational advantages of this technique over classical boundary value and numerical solutions are presented.     

Scattering by a ferrite-coated conducting sphere

The theory for scattering by a perfectly conducting sphere with a coating of lossy, homogeneous, isotropic ferrite material is presented. In addition to the rigorous eigenfunction formulation, the physical optics (PO) and geometrical optics (GO) approximations are also included. Numerical results are shown in graphical form to illustrate the backscatter echo area versus the radius of the sphere, as well as the bistatic scattering patterns.     

Scattering by a rotating conducting sphere

The scattering of a plane wave by a rotating sphere with finite conductivity is investigated. The problem is solved by means of the "instantaneous rest-frame" hypothesis. It is shown that a surface current must be taken into account to calculate the jump in the tangential magnetic field at the surface of the sphere, even in the case of finite conductivity. The analytical solution shows that the influence of the rotation becomes negligible in the limit of a perfectly conducting sphere.