Low-frequency scattering from perfectly conducting spheroidal bodies in a conductive medium with magnetic dipole excitation

Inductive electromagnetic means that are currently employed in the exploration of the Earth’s subsurface and embedded voluminous bodies often call for an intensive use, primary at the modeling stage and later on at the inversion stage, of analytically demanding tools of field calculation. Under the aim of modeling implementation, this contribution is concerned with some interesting aspects of the low-frequency interaction of arbitrarily orientated (i.e. three-dimensional) time-harmonic magnetic dipoles, with 3-D perfectly conducting spheroidal bodies embedded in an otherwise homogeneous conductive medium. For many practical applications involving buried obstacles such as Earth’s subsurface electromagnetic probing at low-frequency or any other physical cases (e.g. geoelectromagnetics), non-axisymmetric spheroidal geometry approximates sufficiently such kind of metallic shapes. On the other hand, our analytical approach deals with prolate spheroids, since the corresponding results for the oblate spheroidal geometry can be readily obtained through a simple transformation. The particular physical model concerns a solid impenetrable (metallic) body under a magnetic dipole excitation, where the scattering boundary value problem is attacked via rigorous low-frequency expansions for the incident, scattered and total electric and magnetic fields in terms of positive integral powers of (ik), that is (ik)ⁿ for n ? 0, where k stands for the complex wavenumber of the exterior medium. The purpose of the modeling is to contribute to a simple yet versatile tool to infer information on an unknown body from measurements of the three-component electric and magnetic fields nearby. Our goal is to obtain the most important terms of the low-frequency expansions of the electromagnetic fields, that is the static (for n = 0) and the dynamic (n = 1, 2, 3) terms. In particular, for n = 1 there are no incident fields and thus no scattered ones, while for n = 0 the Rayleigh electromagnetic expression is easily obtained in terms of infinite series. Emphasis is given on the calculation of the next two non-trivial terms (at n = 2 and at n = 3) of the aforementioned fields. Consequently, those are found in closed form from exact solutions of coupled (at n = 2, to the one at n = 0) or uncoupled (at n = 3) Laplace equations and they are given in compact fashion, as infinite series expansions for n = 2 or finite forms for n = 3. Nevertheless, the difficulty of the Poisson’s equation that has to be solved for n = 2 is presented, whereas our analytical approach demands the use of the well-known cut-off method in order to obtain an analytical closed solution. Finally, this research adds useful reference results to the already ample library of scattering by simple shapes using analytical methods.     

A note on cylindrical wave diffraction by a perfectly conducting strip in a homogeneous bi-isotropic medium

The diffraction of an electromagnetic wave by a perfectly conducting finite strip in a homogeneous bi-isotropic medium is studied in an improved form. The problem is solved by using the Wiener–Hopf technique and Fourier transform. The scattered field in the far zone is determined by the method of steepest descent.     

Natural convection of a radiating fluid in a square enclosure with perfectly conducting end walls

Combined natural convection and radiation in an asymmetrically heated square enclosure is studied numerically with both adiabatic and perfectly conducting end walls. The momentum and energy equations are solved by a control volume based finite difference algorithm which is coupled with the discrete ordinates method for radiative heat transfer calculations. The changes in the flow patterns and temperature distributions due to the presence of radiation in an enclosure with conducting end walls are compared with those for the case of an enclosure with adiabatic end walls, and significant differences are noted. The flow field is stronger, and the heat input along the hot wall and the end walls are greater for the conducting end wall case. The effects of optical thickness, scattering and wall emissivity on the flow and temperature fields and heat transfer rates are analysed.     

Magneto-thermo-elastic problem of a conducting rectangular cylinder subjected to sinusoidal change in time of magnetic field

This study is concerned with a magneto-thermo-elastic problem of a conducting rectangular cylinder in an external magnetic field which varies sinusoidally in time. Analytical solutions of eddy currents induced in the cylinder are derived on the basis of a theory of the quasi-stationary current. Two-dimensional transient temperature change produced by the eddy current loss is derived by means of the Green’s function method. The stresses in the infinitely long cylinder in a plane state are derived by making use of the Airy’s stress function. The effect of a frequency in a sinusoidal change in time of the external magnetic field on behaviors of eddy current loss, temperature change and stresses in the cylinder is examined by numerical calculation. The skin effect with an increase in a frequency of the external magnetic field on the transient response of temperature change and stresses in the cylinder is discussed.     

Low frequency electromagnetic scattering by a perfectly conducting moving sphere

The paper investigates the propagation of a plane electromagnetic waves in the exterior of a moving obstacle. Under the assumption that the obstacle moves with uniform velocity and more slowly than the incident field, we apply the Lorentz transformation. In the object’s frame, where the scatterer is stationary, we introduce the low-frequency approximation technique. For the near electromagnetic field we obtain the Rayleigh low-frequency coefficients while in the far field we derive the leading non-vanishing terms for the scattering amplitude and scattering cross-section. Finally, using the inverse transformation we express the same quantities in the observer’s frame.     

Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane

Scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane is rigorously solved. The scattered field is represented by a Fourier-integral representation. To analytically represent the fields in a general-shaped groove, the groove is divided into L number of layers. Fields are then expressed in each layer as summations of 2D spatial harmonic fields with unknown coefficients. Matching the boundary conditions between layers provides a linear set of equations connecting all the unknown harmonic coefficients. Judicious use of Fourier transform on the equations resulting from matching boundary conditions at the groove aperture provides a series representation of the scattered field in the spectral domain with unknown harmonic coefficients of the first layer in the groove. A stable solution is obtained by solving the complete system of equations with an adaptive choice for the number of modes in each layer.     

Diffraction of a plane wave by a perfectly electromagnetic conducting (PEMC) slot

Using the duality transformations introduced by Lindell and Sihvola, an analytic theory for the electromagnetic diffraction from a perfect electromagnetic conductor (PEMC) slot is developed. Transformations have been applied to the diffracted field of a plane wave from a perfect electric conductor (PEC) slot. The problem was solved by using the Sommerfeld Green’s function and Fresnel integral.     

Image reconstruction of a buried perfectly conducting cylinder illuminated by transverse electric waves

This article presents a computational approach to the image reconstruction of a perfectly conducting cylinder illuminated by transverse electric waves. A perfectly conducting cylinder of unknown shape buried in one half‐space and scatters the incident wave from another half‐space where the scattered field is recorded. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived, and the imaging problem is reformulated into an optimization problem. The steady state genetic algorithm is then employed to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient‐based methods often get trapped in a local extreme. In addition, the effect of different noise on the reconstruction is investigated. © 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 261–265, 2005     

On waves in a random micropolar conducting magneto-thermo-viscoelastic medium

Effects of random inhomogeneity on wave propagation in the interacting micropolar conducting magneto-generalized thermo-viscoelastic medium are studied. The couple stress theory relevant to micropolar solids is employed. The analysis is carried out under the smooth perturbation technique amenable to stochastic linear differential equations up to the second perturbation. The perturbing field has been assumed to be weakly conducting and weakly thermal. The generalized thermoelasticity has been used. Six different types of waves have been observed to propagate in the medium. The dispersion equations have been derived. Effects due to random variations of micropolar-elastic, conducting-electromagnetic and generalized thermo-visco-parameters have been computed. Effects of random heterogeneity of the conducting magnetic field are readily available up to first order perturbation. However effects of the generalized thermal field are discernible only in the domain of second order perturbation. Change of phase speed occurs on account of randomness. Attenuation coefficients for types of waves have been computed. A special type of generalized theromomechanical auto- and cross-correlation functions has been used to approximately measure effects of random variations of parameters. Uncoupled problem has been formulated for future investigations.     

Scattering of inhomogeneous plane waves by a slit formed with impedance and perfectly electric conducting half planes

Scattering of an inhomogeneous plane wave with an arbitrary angle of incidence travelling through a slit made of perfectly electric conducting and impedance half planes is investigated. For the investigation of the scattering phenomena evaluation of the modified theory of physical optics integrals are evaluated asymptotically. An inhomogeneous plane wave is taken into consideration by assuming the incident angle of a homogeneous plane wave as a complex parameter. Uniform asymptotic results will be employed for the correct solution of an incoming inhomogeneous plane wave scattering problem. Asymptotic evaluation is carried out for the reflected and diffracted fields. Diffracted fields are uniformly expressed in terms of the Fresnel functions. To obtain correct plots of the diffracted fields, complex detour parameter decomposition method is applied. Obtained resultant fields are plotted numerically.     

Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane: comment

We show that the problem of scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane, which was recently studied by Basha et al. [J. Opt. Soc. Am. A24, 1647 (2007)], was solved 11 years ago using the same formulation. This method was further extended to deal with a finite number of grooves and also with complex apertures including several nonlossy and lossy dielectrics, as well as real metals.     

Electromagnetic field diffracted on two cracks in a conducting medium

A three-dimensional problem of diffraction of electromagnetic waves on two cracks is reduced to a system of two-dimensional hypersingular integral equations. For the numerical solution of this system, we propose to use the method of boundary elements. The solution obtained as a result is used for the analysis of the dependence of the space distribution of the magnetic field scattered by the cracks on the distance between these cracks.     

Conservative fluctuational-electromagnetic interaction of a conducting nanoparticle with a smooth surface of condensed medium

General expressions for a conservative force of the fluctuational-electromagnetic interaction between a neutral spherical conducting nanoparticle and a smooth surface of condensed medium are obtained for the first time with allowance for both electric and magnetic components. The results of calculations performed for a copper particle interacting with a copper surface show that the contribution of the magnetic components is predominating for all distances from the surface exceeding the particle radius R. The contribution due to the near-surface modes, which is proportional to the temperature and inversely proportional to the cube of the distance, is predominating at distances above ～10 R.     

Scattering of waves by a planar junction between resistive half-screen and perfectly electric conducting wedge

The diffraction of plane waves by a planar junction between a resistive half-plane and perfectly conducting wedge is investigated. First of all, the relation between the scattered geometrical optics waves and diffracted fields by a wedge is outlined. Then the scattered GO fields of the planar junction are obtained by subtracting the initial fields from the total geometrical optics waves. The diffracted waves by the junction is derived with the aid of the scattered GO waves’ structure. The behaviour of the fields is analysed numerically.     

On the stability for a rate-type electric conducting medium

In this article we prove the existence, uniqueness and asymptotic behaviour of the solutions for an electromagnetic non-homogeneous medium, which is characterized by a rate-type equation for the electric conduction and by dissipative boundary conditions. A domain of dependence inequality is derived and the exponential decay of the solutions is proved by the methods of the semi-group theory.     

Satellite peaks in the scattering of p-polarized light from a randomly rough film on a perfectly conducting substrate

Abstract

The diffuse scattering of p-polarized light from a one-dimensional, randomly rough dielectric film deposited on a planar, perfectly conducting surface is studied by means of small-amplitude perturbation theory. The dielectric constant ε_d and the thickness d of the dielectric film are chosen in such a way that in the absence of roughness the scattering system supports N (≥ 2) guided modes whose wavenumbers are q ₁ (ω), …,q _N(ω) at the frequency ω of the light incident at an angle θ_o. We investigate the occurrence of satellite peaks, in addition to the enhanced back-scattering peak, in the angular distribution of the intensity of the diffusely scattered light, at angles θ_s(n, m) given by sin θ_s(n, m)= ? sin θ₀± (c/ω) [Q_n(ω) ? q_m(ω)] for n, m=1, …, N(n ≠ m). These satellite peaks are multiple-scattering effects due to degenerate timereversal symmetry.