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.     

Scattering of electromagnetic waves from dielectric coated conducting spheres

Several series of rigorous numerical calculations of the backscatter cross section of a conducting sphere with a thin lossless dielectric coating were carried out. The ratio of the radius to wavelength was varied from about 0.02 to 10.0; the dielectric constant of the coating was taken to be 2.56, 4.0, or 6.0; and the thickness of the coating was 0.1 or 0.05 times the outer radius of the coated sphere. Curves of the results are presented which indicate that the backscatter cross section of a coated sphere may be increased by as much as a factor of ten over that of an uncoated sphere of the same size, and, due to interference effects, an even greater decrease may be obtained. Further, small changes (less than one per cent) in the thickness or dielectric constant of the coating, or in the wavelength, may bring about large changes in the cross section. The numerical results are also compared with some experimental measurements, and with predictions of a "creeping-wave" type of analysis carried out by Helstrom.     

The imperfectly conducting cylindrical transmitting antenna

The properties of a cylindrical antenna with a continuous ohmic resistance along its length are of interest in the design of certain types of directive broadband antennas and in the determination of the efficiency of dipole antennas. Conventionally, the contribution by ohmic resistance to the distribution of current and the impedance is contained in a particular integral that is either ignored or treated as a higher-order correction to formulas derived for perfectly conducting antennas. An alternative and more useful form has been developed in which the integral equation for the current is rearranged to permit the introduction of a complex wave numberk. An approximate solution of this equation is then obtained in terms of the three trigonometric functions,sin k(h-|z|),cos kz-cos kh, andcos frac{1}{2}k_{0}z - cos frac{1}{2}k_{0}h, wherek_{0}is the free-space wave number. Expressions are derived for the coefficients of these functions and fork. Explicit formulas are given for the distribution of current and the admittance.     

Electromagnetic imaging for an imperfectly conducting cylinder

A computational approach to the imaging or inverse scattering of an imperfectly conducting cylinder is presented. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered field is recorded on a circle surrounding the scatterer. By properly processing the scattered data, the shape and conductivity of the scatterer can be reconstructed. The problem is formulated in the form of nonlinear integral equations, which can be solved numerically by the Newton-Kantorovitch algorithm. The pseudoinverse technique is used to overcome the ill-posedness, and the condition number of the matrix is also discussed. Numerical examples are given to illustrate the capability of the inversion algorithm using the simulated scattered fields in both near and far zones. Multiple incident directions permit good reconstruction of shape and, to a lesser extent, conductivity in the presence of noise in measured data     

An experimental study of imperfectly conducting dipoles

Input admittances of dipole antennas with moderately high internal impedance were measured in the UHF range with the antenna lengths varying from one-tenth wavelength to such a value that the antenna behaved as if infinitely long. The measured results are compared with the three-term theory of King and Wu[1] and with the theoretical values obtained by Shen and Wu[3] for an infinitely long antenna.     

Integral equation formulations for imperfectly conducting scatterers

Integral equation formulations are presented for characterizing the electromagnetic (EM) scattering interaction for nonmetallic surfaced bodies. Three different boundary conditions are considered for the surfaces: namely, the impedance (Leontovich), the resistive sheet, and its dual, the magnetically conducting sheet boundary. The integral equation formulations presented for a general geometry are specialized for bodies of revolution and solved with the method of moments (MM). The current expansion functions, which are chosen, result in a symmetric system of equations. This system is expressed in terms of two Galerkin matrix operators that have special properties. The solutions of the integral equation for the impedance boundary at internal resonances of the associated perfectly conducting scatterer are examined. The results are compared with the Mie solution for impedance-coated spheres and with the MM solutions of the electric, magnetic, and combined field formulations for impedance-coated bodies.     

On the attenuation of transient fields by imperfectly conducting spherical shells

Exact formulas for the electric and magnetic fields at any arbitrary point within a cavity region completely enclosed by a conducting spherical shell of arbitrary size are derived under the assumption that the exciting electromagnetic field is a linearly polarized, monochromatic, plane wave falling on the external surface of the shell. It is shown that the polarization of the electromagnetic field at the center of the cavity is the same as the polarization of the incident wave. From a knowledge of this steady-state solution, the time history of the electromagnetic field at the center of the cavity is calculated for the case where the incident wave is a Gaussian pulse. Numerical information on the effectiveness of the aluminum and copper shields under steady-state and transient conditions is provided for several pulse durations, shield sizes, and wall thicknesses.     

The maximum echo area of imperfectly conducting dipoles

The question has often been raised as to when the effects of imperfect conductivity must be taken into account when studying the echo area of a wire scatterer such as the dipole. The conditions under which the echo area is sensitive to the conductivity are shown.     

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 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 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.     

Propagation in rectangular tunnel with imperfectly conducting walls

An approximate formulation is presented for what is usually considered to be an intractable problem in waveguide theory. The essence is to show that a TM (transverse magnetic) class of modes will be an adequate representation even when all four walls are imperfectly conducting.     

Generation of field scattered by imperfectly conducting objects from the solution of a perfectly conducting object

Surface currents induced on imperfectly conducting objects are obtained from the surface current of a perfectly conducting object using the impedance boundary conditions on its surface. The resulting errors in computation of these surface currents are determined and are shown to depend on the excitation source.     

The imperfectly conducting cylindrical transmitting antenna: Numerical results

The complex wave number, the distribution of current, the admittance, and the radiating efficiency of cylindrical antennas made of imperfect conductors are evaluated numerically from a previously derived theory[1]. The quantity2lambda r^{i}/zeta_{0}(wherer^{i}is the resistance per unit length,lambdais the free-space wavelength, andzeta_{0} = 377ohms) is used as the parameter in a range that extends from zero to 200. Extensive graphs and tables are given.     

Scattering by a moving unidirectionally conducting screen

The problem of scattering that results when an arbitrary field is incident on a unidirectionally conducting screen undergoing translational motion is analyzed. The screen is assumed to move at a constant speed in its own plane and in a direction perpendicular to that of conduction. A relativistically exact solution is obtained in the (stationary) frame of the observer via representing the screen as a plane where boundary conditions must be met plus a field constraint to be applied everywhere. The solution is presented in integral form and applied to the case of plane wave incidence for which low velocity effects are displayed