Infinitesimal Dipole Research Articles

Modelling cracks in finite bodies by distributed dislocation dipoles

The method of continuous distribution of dislocations is extended here to model cracks in finite geometries. The cracks themselves are still modelled by distributed dislocations, whereas the finite boundaries are represented by a continuous distribution of dislocation dipoles. The use of dislocation dipoles, instead of dislocations, provides a unified formulation to treat both simple and arbitrary boundaries in a numerical solution. The method gives a set of singular integral equations with Cauchy kernels, which can be readily solved using Gauss–Chebyshev quadratures for finite bodies of simple shapes. When applied to arbitrary geometries, the continuous distribution of infinitesimal dislocation dipoles is approximated by a discrete distribution of finite dislocation dipoles. Both the stress intensity factor and the T‐stress are evaluated for some well‐known crack problems, in an attempt to assess the performance of the methods and to provide some new engineering data.

Induced Voltage on a Communication Cable Caused by Incoming Radio Waves

AbstractWith a view to estimating the induced voltage generated in a communication cable by incoming radio waves, this paper carries out an analysis specifically for the common mode and compares the results with the measured values. In the theoretical analysis, communication cables installed in an urban area are considered. An analysis model is introduced in which both ends of the cable are sloped down to the ground surface. In the analysis, the communication cable is treated as the sum of infinitesimal dipoles. From a comparison of the theoretical and measured results, the usefulness of the proposed analysis method is discussed. First, an experiment on a conducting ground plane with a scale model is carried out. Satisfactory agreement with the theoretical values is demonstrated. Next, a field experiment is carried out by using a practical 10‐pair communication cable and terminating sets. As a result, it is found that an evaluation of the induced voltage generated in the cable is possible by paying attention to the settings of various parameters used in the analysis, although quantitative agreement is not reached. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 85(4): 10–22, 2002

An Asymptotic Solution for Boundary - Layer Fields Near a Convex Impedance Surface

—An analytic representation for fields (E, H) that, for wavenumber k, satisfies the Maxwell equations to order k -2/3 within a suitably-defined boundary-layer neighborhood is provided for the case of a general doubly-curved convex impedance surface. This solution is an ansatz construct obtained via heuristic modification of a residue-series solution to a corresponding circular-cylinder canonical problem with an infinitesimal axial magnetic dipole excitation. The field components are in the form of creeping-ray modal series written as functions of geodesic-polar and normal coordinates (s, , n) appropriate to the vicinity of a general convex surface. Adaptation of the canonical solution to the general case begins with a transformation from the native cylindrical (p, φ, z) coordinates of the canonical solution to a system ( p, c, s) defined by cylinder-surface geodesics. The transformed canonical solution is further modified by replacement of corresponding factors deriving from the metric and curl operators in the (p, c, s) and (s, , n) systems, and by pervasive application of a substitution previously employed in a more limited way by Pathak and Wang. The physical content of the substitution process is that the creeping-ray attenuation along the geodesics occurs independently of the surface normal curvature transverse to the geodesic direction.

Efficient calculation of the fields of a dipole radiating above an impedance surface

In this paper, the classic problem of field computation for an infinitesimal dipole radiating above an impedance half-space is revisited. The expressions for the traditional solution consist of integrals of the Sommerfeld type that cannot be evaluated in closed form and due to their highly oscillatory nature are difficult to evaluate numerically. A method known as exact image theory, which has previously been applied to vertical electric and magnetic dipoles, is used to derive explicit expressions for dipoles of arbitrary orientation above impedance surfaces. Starting from the spectral representation of the field, the reflection coefficients are cast in the form of exact Laplace transforms and then by changing the order of integrations field expressions in terms of rapidly converging integrals are obtained. These expressions are exact, and valid for any arbitrary source alignment or observation position. It is shown that the formulation for a horizontal dipole contains an image in the conjugate complex plane resulting in a diverging exponential term not previously addressed in the literature. It is shown through further mathematical manipulations, that the diverging term is a contribution of the mirror image which can be extracted. Comparison of numerical results from exact image theory and the original Sommerfeld-type expressions shows good agreement as well as a speedup in computation time of many orders of magnitude, which depends on the distance between the transmitter and the receiver. This formulation can effectively replace the approximate asymptotic expressions used for predicting wave propagation over a smooth planar ground (having different regions of validity). The exact image formulation is also of practical use in evaluation of the Green's function for various applications in scattering problems where approximate solutions are not sufficient.

Ray-based amplitude tomography for crosshole georadar data: a numerical assessment

Analyses of travel times and amplitudes of crosshole georadar data provide estimates of the electromagnetic velocity and attenuation of the probed media. Whereas inversions of travel times are well established and robust, ray-based inversions of amplitudes depend critically on the complex directive properties of the georadar antennae. We investigate the variations of radiation patterns in the presence of water-filled boreholes and/or changes of electrical material properties in the vicinity of the transmitters or receivers. To assess the implications of such complicating factors for ray-based georadar amplitude tomography, we generate crosshole georadar data for a suite of canonical models using a finite difference time domain (FDTD) solution of Maxwell's equations in cylindrical coordinates. The emitting dipole-type antenna is approximated by an infinitesimal vertical electric dipole, whereas a corresponding receiving antenna is emulated by recording the vertical component of the transmitted electric field. Inversions of the amplitudes of these synthetic data demonstrate that the presence of water-filled boreholes as well as changes in the material properties along the boreholes may cause substantial artifacts in the estimated attenuation structure. Furthermore, our results indicate that ray-based amplitude tomography of crosshole georadar data is unable to constrain absolute values of attenuation. Despite these inherent limitations, the method is surprisingly robust at detecting and constraining relative changes in attenuation. In particular, we find the method to be highly effective for locating conductivity contrasts that are not associated with corresponding changes in dielectric permittivity, and hence, cannot be located by travel time tomography alone.

Multicomponent georadar data: Some important implications for data acquisition and processing

Many seismic reflection processing techniques are applied routinely to ground‐penetrating radar (georadar or GPR) data. Although similarities exist between seismic (acoustic) and radar wave propagation there are some significant differences, some of the most important of which are associated with the dipole nature (1) of georadar sources and receivers and (2) of elemental sources used to represent scattering bodies. Neglecting the dipole character of electromagnetic surveys may result in incomplete or biased images of the subsurface. In an attempt to understand better the consequences of recording dipolar wavefields, we have simulated numerous multicomponent georadar data sets. These simulations are based on the weak scattering (Born) approximation, such that point heterogeneities in the subsurface can be represented by infinitesimal dipoles with moments parallel and proportional to the incident georadar wavefields. The effects of depolarization and dispersion are not included. Nevertheless, many subsurface structures can be modeled by suites of appropriately distributed infinitesimal dipoles. Georadar images of even the simplest subsurface structures are shown to depend strongly on the relative orientations and positions of the source and receiver antennas. A positive aspect of dipolar wavefields is that multicomponent georadar profiles contain information on the locations of both in‐plane and out‐of‐plane structures. Furthermore, “pseudoscalar” wavefields can be simulated from coincident georadar data sets acquired with two pairs of parallel source‐receiver antennas, one oriented perpendicular to the other. Pseudoscalar georadar data, which are characterized by low degrees of directionality, can be processed (including migration) confidently using standard seismic processing software (assuming that dispersion is not a major problem). To illustrate the advantages of multicomponent georadar data, two field examples are presented. One demonstrates the value of recording dual‐component georadar data along isolated profiles; the other shows the benefits of combining 3-D georadar data sets acquired with dual component source‐receiver antenna pairs to form pseudoscalar wavefield images.

Rectangular Conducting Waveguide Filled With Uniaxial Anisotropic Media: a Modal Analysis and Dyadic Green's Function - Abstract

Electromagnetic fields in a rectangular conducting waveguide filled with uniaxial anisotropic media are analyzed in this paper using Fourier transform. TE modes and TM modes are found to be related to the ordinary waves and extraordinary waves, respectively. The calculated dispersion curves are depicted and the effects of the material parameters on the cutoff frequencies are shown. The cutoff frequencies change considerably especially for TM modes. The field distributions are plotted to compare with the isotropic rectangular waveguide. The electric type dyadic Green's function due to electric source is derived in the form of vector wave functions expansion by applying Ohm-Rayleigh method. The final result shows that the parameters of the medium have close and intricate relationships with the properties of the Green's function, hence, influencing the propagation of the guided wave. The dyadic Green's function is reducible to that in the isotropic medium. From Maxwell equations, the magnetic dyadic Green's function due to electric source is also given. As the application of the dyadic Green's functions, numerical results of the fields inside the waveguide excited by an infinitesimal dipole are present.

Scattering By an Arbitrarily Shaped Rotationally Uniaxial Anisotropic Object: Electromagnetic Fields and Dyadic Green's Fucntions - Abstract *

The electromagnetic scattering by a three-dimensional arbitrarily shaped rotationally uniaxial anisotropic object is studied. Electromagnetic fields in a uniaxial medium are solved for first using the method of separation of variables, and then expressed in a very compact form by introducing the modified spherical vector wave functions. The equivalence theorem and the T-matrix method are applied in the analysis of the scattering problem. The scattered fields and the dyadic Green's functions both external and internal to the scatterer are derived in terms of spherical vector wave functions and matrix-form coefficients. Through making use of the dyadic Green's functions obtained, numerical results are provided for an incident field excited by an infinitesimal dipole. The scatterers are assumed to be prolate and oblate dielectric spheroids with the rotational z-axis. The angular scattering intensities in far-zone are plotted for all these cases. And some conclusions are also drawn eventually from numerical discussions.

Consideration of radiated electromagnetic waves from partial discharge based on half-wave dipole antenna model

Partial discharge (PD) may take place due to residual defects like metallic particles in SF6 gas-insulated power apparatus such as GIS. However, the signal of PD occurring in SF6 gas is very weak and susceptible to external noise in air. Moreover, because of the complicated mechanism of PD, the radiation property of electromagnetic waves from PD has not as yet been clarified. Therefore, it is hard to distinguish the PD signal in SF6 gas from external noise. From the above points of view, we have been investigating the radiation mechanism of electromagnetic waves from PD. We measured the polarization characteristics of electromagnetic waves radiated from PD in comparison with those of half-wave dipole antennas. The polarization characteristics of PD were explained by the theory of half-wave dipole antenna, rather than that of an infinitesimal dipole antenna. Moreover, we compared the power spectrum for PD measured using a biconical antenna with that received from the half-wave dipole antenna or infinitesimal dipole. It was found that the power spectrum for PD also corresponded to that for the half-wave dipole antenna with a length of 50 cm. © 1999 Scripta Technica, Electr Eng Jpn, 126(4): 40–47, 1999

Excitation of leaky modes on multilayer stripline structures

A quasi-analytical method for calculating the excitation of leaky modes on multilayer stripline structures by a finite source is presented in this paper. Simple sources such as an infinitesimal dipole near the conducting strip or a delta-gap feed on the conducting strip of the transmission line are considered. The method uses a numerically constructed Green's function for the source in the presence of the conducting strip, which is calculated from Fourier transform theory in terms of a one-dimensional Green's function for a line source in the presence of the conducting strip. The numerical Green's function involves a one-dimensional integration in the longitudinal wavenumber plane. The residue contributions from the poles of the Green's function define the excitation amplitudes of the leaky and bound modes that exist on the structure. The numerical Green's function is also used to numerically calculate the complete current on the strip excited by the source. The correlation between the leaky-mode current and the complete current is used to define the extent of the physical meaning of the leaky mode. The generalized pencil of functions (GPOF) method is used to study this correlation by resolving the complete current on the strip into exponential waves, which are then compared with the current of the leaky mode. The physical meaning of the leaky modes is also analytically examined by consideration of the branch cuts in the longitudinal wavenumber plane for the numerical Green's function integration. A path consistency is established as a necessary condition for the physical meaning of the leaky mode.

Validation of the finite-difference time-domain method for near-field bioelectromagnetic simulations

Validations of the accuracy of the FDTD method for near-field simulations are critical at this time to assess the accuracy of the FDTD method for the simulation of personal communication devices. Excellent comparisons between the FDTD method and analytical or measured results are shown for a dipole antenna next to a layered half-space, a layered box, and a sphere, and also an infinitesimal dipole near a sphere. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 341–345, 1997.

Errors and correction factors for schelkunoff's shielding effectiveness formula

AbstractThis paper presents the error of the resistive film approximation and that of Schelkunoff's equation with respect to the rigorous solution. Both of these approximate equations cause errors for the planar shield for which either an infinitesimal electric dipole or an infinitesimal magnetic dipole is the source. Hence, the four types of planar shield with different directions and types of dipole source are investigated.Next, the conditions for causing the error is studied. When Schelkunoff's equation and the resistive film approximation are rewritten, they become functions of three dimensionless parameters. However, the numerical analysis reveals that only two error‐causing parameters are sufficient if the choice is carefully made. With these two parameters, the correction factors are derived with which the rigorous value is obtained from Schelkunoff's equation or the resistive film approximation. the rigor ous solution is a complicated equation including integral calculation. On the other hand, Schelkunoff's equation is relatively simple. If this correction value is used, a solution equivalent to the rigorous solution can be obtained from Schelkunoff's equation or even simpler resistive film approximation.

Numerical consideration and some improvement of corner diffraction formulas applicable to spherical wave incidence

AbstractDiffraction by a corner is one of the canonical problems remaining unsolved. However, several practical formulas have been proposed; any one of which must be able to be incorporated in the geometrical theory of diffraction (GTD). Of these, the corner diffraction formulas that can be applied to the spherical wave incidence are Burnside‐Pathak's formula (BP formula) and Zhang's formula (Z formula). In this paper, the BP formula and the Z formula are numerically compared by means of a hypothetical model consisting of a quarter infinite plane and an infinitesimal dipole. It is found that the BP formula and the Z formula become similar as long as they are not applied near the shadow boundary. The BP formula requires the edge parameters in the numerical process despite dealing with the corner diffraction. On the other hand, the Z formula needs only the parameters related to the corner. However, this formula experiences small discontinuity when the shadow boundary is traversed. In this paper, an empirical modification function is introduced into the Z formula so that a new corner diffraction formula (MZ formula) is proposed so that the diffracted field is uniform and continuous across the boundaries.

H(curl) elements on hexahedral and vector A.B.C.'s for unbounded microwave problems

In this paper we present a 3D Engquist-Majda type Absorbing Boundary Conditions version that can preserve the symmetry of the finite element matrix. This vector ABC's is coupled with the vector wave equation. The formulation obtained uses conforming finite elements in H(curl) on hexahedral elements. The accuracy of this alternative vector ABC's is evaluated with the radiation from an infinitesimal current dipole.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Numerical studies of the radiation patterns of resistively loaded dipoles

The far field radiation patterns of finite-size resistively loaded horizontal electric dipoles lying on a low-loss dielectric half-space are computed. The patterns are a superposition of the solutions for transient infinitesimal dipole elements, where the transient waveform for each element is synthesized from the exact steady-state solution. The current excitation for each dipole element is a half cycle of a sine squared waveform that propagates along the line of elements at a speed that can be varied. No reflections from the antenna ends are assumed. The time duration of the current half cycle governs the full period of the dominant part of the transient radiated waveform. The amplitude of the dipole excitation current is determined by a cosine distribution that accurately simulates the resistive loading. The transient radiation patterns differ from those of a steady-state dipole mainly by being more narrow in the E-plane, as is true for a finite-size steady-state dipole radiating in air. In addition, the far field waveforms are slightly distorted in directions off vertical in the E-plane. Two-way power radiation patterns are presented for both conductive and non-conductive dielectric media in a footprint mode, i.e. the power response to an isotropic point scatterer on a subsurface flat plane. The radar footprint in a conductive dielectric shows very narrow beamwidth due to the added conductive attenuation along the longer paths off the vertical direction. Field tests in water and glacial ice and laboratory observations show good agreement with the E-plane model results but suggest that the H-plane directivity is strongly affected by the separation between transmit and receive antennas and by the range.

Full wave calculation method of VLF wave radiated from a dipole antenna in the ionosphere‐analysis of joint experiment by HIPAS and akebono satellite

AbstractA method has been developed for numerically calculating, by means of the full‐wave method, the electromagnetic field intensity distribution on the ground and at the satellite altitude (∼2000 km) using the electromagnetic wave radiated by an infinitesimal dipole placed in a lower ionosphere. The amplitude and polarization are analyzed for the simultaneous observation data on the ground and the Akebono satellite for the VLF wave radiated in the ionosphere heating experiment by a high‐power HF wave. The values computed by the full‐wave method agreed well with the observed data if the VLF sources by the heating experiment are at an altitude of 66 km along the east‐west direction and the current moment is 4.3 × 104 Am.

The fields from a finite electrical dipole—A new computational approach

Controlled‐source, frequency‐domain, and time‐domain electromagnetic methods require accurate, fast, and reliable methods of computing the electric and magnetic fields from the source configurations used. Except for small magnetic dipole sources, all electric and magnetic sources are composed of lengths of straight wire, which may be grounded. If the source‐receiver separation is large enough, the composite electrical dipoles may be considered to be infinitely small, and in a 1-D earth model the fields are expressed as Hankel transforms of an input function, which depends only on the model parameters. The Hankel transforms can be evaluated using the digital filter theory of fast Hankel transforms. However, the approximation of the infinitely small dipole is not always valid, and fields from a finite electrical dipole must be calculated. Traditionally, this is done by numerical integration of the fields from an infinitesimal dipole, thus increasing computation time considerably. The fields from the finite electrical dipole are expressed as Hankel transforms and as integrals of Hankel transforms. The theory of fast Hankel transforms is extended to include integrals of Hankel transforms, and a method is devised for calculating the filter coefficients. Unlike the fast Hankel transform, the computation involved in the integrated Hankel transforms is not a true convolution, and so a set of filter coefficients must be calculated for each source‐receiver configuration. Furthermore, the method is extended to include the calculation of potential differences where one more integration is involved, which is what is actually measured in the field. The computation of filter coefficients is very fast, and for standard configurations, the coefficients need be computed only once. The method is as fast, accurate, and reliable as the fast Hankel transforms method, and is up to an order of magnitude faster than the usual numerical integration.

The bi-polar planar near-field measurement technique, part II: near-field to far-field transformation and holographic imaging methods

A novel customized bi-polar planar near-field measurement technique is presented in a two-part paper. This bipolar technique offers a large scan plane size with minimal real-estate requirements and a simple mechanical implementation, requiring only rotational motions, resulting in a highly accurate and cost-effective antenna measurement and diagnostic system. Part I of this two-part paper introduced the bi-polar planar near-field measurement concept, discussed the implementation of this technique at the University of California, Los Angeles (UCLA), and provided a comparative survey of measured results. This paper examines the data processing algorithms that have been developed and customized to exploit the unique features of the bi-polar planar near-field measurement technique. Near-field to far-field transformation algorithms investigated include both interpolatory and non-interpolatory algorithms due to the a typical arrangement of the bi-polar near-field samples. The algorithms which have been tailored for the bi-polar configuration include the optimal sampling interpolation (OSI)/fast Fourier transform (FFT), Jacobi-Bessel transform, and Fourier-Bessel transform. Additionally, holographic imaging for determination of antenna aperture fields has been incorporated to facilitate antenna diagnostics. Results for a simulated measurement of an array of infinitesimal dipoles and a measured waveguide-fed slot array antenna are included. Appropriate guidelines with respect to the advantages and disadvantages of the various processing algorithms are provided. >

Three dimensional finite element analysis of high power microwave devices

A three-dimensional nodal-based finite element formulation for electric or magnetic fields is presented. The formulation includes open boundary problems and conductor interfaces. The open boundary is modeled using the Engquist-Majda absorbing boundary condition. Current sheet excitation is used to excite modes in the waveguide. A validation using an infinitesimal current dipole is shown, and an example of modeling a circular waveguide illustrates the use of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes

The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, ν, is a significant fraction of the speed of light, c, assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission‐line model with a constant v and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large ν is to increase the radiation fields by a factor of (1 ‐ β2 cos2 θ)−1, where β = ν/c and θ is measured from the vertical, and the Poynting vector by a factor of (1 ‐ β2 cos2 θ)−2. This increase is just a few percent or less at small β, but when β = 0.67, the fields are about 80% larger at small θ and 50% larger at θ = 30°, and the power that is radiated is increased by 26%. When β = 0.5 and the peak current is 30 kA, typical values for negative first strokes, the peak power that is radiated into the upper hemisphere is 1.0 × 1010 W.