Locating an oscillating magnetic dipole in the earth

The merits of a horizontal magnetic dipole in a source-location scheme are considered. The results have possible applications in locating trapped miners following disasters.     

Transient electromagnetic fields of a vertical magnetic dipole on a two-layer earth

The transient fields of a vertical magnetic dipole on a two-layer earth model are expressed in analytical form using two different approaches. In the first, the fields in the time domain are obtained as the inverse Laplace transforms of derived full wave time-harmonic solutions, while in the second, the concept of natural frequencies of the stratified earth is utilized. Comparison with a previously obtained approximate solution reveals that the latter is the late time part of the present solution. Important features in the waveforms of the surface fields due to step and pulsed current excitations are demonstrated by a variety of numerical examples. These features provide diagnostic means of sensing the earth's stratification, overburden thickness, and the ratio of conductivities of the layers.     

磁偶极在各向异性媒质中辐射的能流密度

对各向异性媒质中辐射问题的研究,求出磁偶极在各向异性媒质中辐射的具有张量形式的能流密度的普遍公式,在直角坐标系中,通过并矢计算,得出磁偶极在各向异性媒质中辐射的平均能流密度,并对磁偶极在各向异性媒质中的辐射作出了主要集中方向的判断,为研究各向异性媒质的开发应用提供了一个理论依据.对导出的新公式进行了验证.     

Electromagnetic fields due to dipole antennas embedded in stratified anisotropic media

A method is presented for calculating the electric and magnetic fields from dipoles embedded in anisotropic stratified media. By decomposing the fields into transverse electric (TE) and transverse magnetic (TM) modes, the results are obtained more directly and are more computationally efficient than methods using the Hertz potential. The electromagnetic fields are obtained for four types of dipole sources: horizontal electric, horizontal magnetic, vertical electric, and vertical magnetic. The source is embedded within one of several anistropic layers, which are further sandwiched between two semi-infinite media.     

A spatio-temporal dipole simulation of gastrointestinal magnetic fields

We have developed a simulation of magnetic fields from gastrointestinal (GI) smooth muscle. Current sources are modeled as depolarization dipoles at the leading edge of the isopotential ring of electrical control activity (ECA) that is driven by coupled cells in the GI musculature. The dipole moment resulting from the known transmembrane potential distribution varies in frequency and phase depending on location in the GI tract. Magnetic fields in a homogeneous volume conductor are computed using the law of Biot-Savart and characterized by their spatial and temporal variation. The model predicts that the natural ECA frequency gradient may be detected by magnetic field detectors outside the abdomen. It also shows that propagation of the ECA in the gastric musculature results in propagating magnetic field patterns. Uncoupling of gastric smooth muscle cells disrupts the normal magnetic field propagation pattern. Intestinal ischemia, which has been experimentally characterized by lower-than-normal ECA frequencies, also produces external magnetic fields with lower ECA frequencies.     

VLF fields of a horizontal dipole below the polar anisotropic ionosphere

A study is made of VLF fields excited by a horizontal dipole in the waveguide formed between the ice-covered ground and the anisotropic ionosphere of Antarctica. Numerical results are presented which describe the excitation, propagation, and polarization of radiated energy for ionospheres typical during both summer (daylight) and winter (night) conditions in Antarctica. The polarization of fields observed at the ice surface is found to be a function of both azimuth and range. Ice layer characteristics have significant effects on received fields, especially those of the quasi-TM type. The possible excitation of a TM-type surface wave at the ice-air interface under special conditions is also discussed. Fields propagating with wave numbers corresponding to quasi-TE modal solutions are least attenuated in the waveguide. Summer ionospheres tend to increase modal attenuation rates. Results are applied to a real experimental situation in Antarctica involving a horizontal dipole source and trans-Antarctic propagation paths.     

Locating a horizontal magnetic dipole buried in a 2-layer earth

The possibility of applying an electromagnetic technique to locate a horizontal magnetic dipole buried in the upper layer of a 2-layer earth is studied. Results for a highly conducting substratum for various source depths and frequencies are presented.     

The field of a dipole enclosed in an elliptic anisotropic plasma cylinder

The boundary value problem for the field of an electric dipole enclosed in a thin elliptic anisotropic plasma cylinder with a vacuum cavity is considered. A solution to the problem is obtained and analyzed. The influence of a magnetic field and the cavity of variable size on the resonance electromagnetic field is studied in the case when the shape of the plasma cylinder’s cross section varies. The effect is compared to that observed in the case of a circular plasma cylinder.     

Simple estimation of equivalent magnetic dipole moment tocharacterize ELF magnetic fields generated by electric appliancesincorporating harmonics

A simple method of quantifying the ELF (extremely low frequency) magnetic field distribution around electric appliances, which takes the harmonics into account, is newly proposed. The proposed method involves: (1) a simple estimation of the position of an equivalent magnetic dipole moment inside an appliance, using two magnetic field meters; (2) identification of the amplitude of the dipole moment magnetic-field measurements at certain points; and (3) calculation of the magnetic field distribution around the appliance using the estimated dipole moment. In this method, the dipole moment vector is assumed to be a similar value by allowing an uncertainty of 6 dB in the estimated magnetic field, which enables easy estimation of the dipole moment. In addition, the frequency characteristics of the magnetic field are taken into account by considering the harmonic components in the magnetic field waveform. The proposed method was applied to 13 types of appliances, and their equivalent magnetic dipole moments and harmonic components were determined. The results revealed that the proposed method is applicable to many electric appliances. The conditions required for the adoption of the method were also clarified     

Transient magnetic fields produced by a step-function-excited loop buried in the earth

Using a previously developed formalism, we obtain explicit results for the field waveforms observed on the Earth's surface for a small horizontal loop buried in a conducting halfspace. It is shown that the shape of the waveform is diagnostic of the relative location of the buried source. The results have possible application in mine rescue operations.     

Radiation fields from an electric dipole antenna in homogeneous Antarctic terrain

The radiation fields from an electric dipole antenna in homogeneous Antarctic terrain are analyzed. The terrain is represented as a semi-infinite ice medium with a complex dielectric constant dependent upon temperature and frequency. The space and ground waves from a horizontal dipole are evaluated initially for different ice conditions. Similar evaluations arc extended to a vertical dipole to apply superposition to the general case of an inclined dipole in Antarctic ice.     

On the radiation field from an electric dipole in an anisotropic and compressible plasma medium

The radiation fields from an electric dipole in a homogeneous, anisotropic, and compressible plasma are considered. Using the Fourier transform method, the problem is formulated in terms of three scalar functions, each of which satisfies the two-dimensional inhomogeneous wave equation. Asymptotic expressions of the radiation fields are obtained for the integrals by the saddle point method of integration.     

Transient electric and magnetic fields associated with establishinga finite electrostatic dipole, revisited

The authors reexamine the analysis of M.J. Master and M.A. Uman (1983), who derived and plotted the electromagnetic field waveforms generated by a square wave of current propagating with constant speed along a finite linear path, resulting in the formation of a finite electrostatic dipole. It was concluded that such a square pulse of current had charge only at its front and rear. The authors argue that errors were made in that analysis, correct these errors, and extend the overall analysis: (1) to show that the decomposition of the electromagnetic fields into electrostatic, induction, and radiation components on the basis of distance dependence is not general; (2) to demonstrate the use of the continuity equation in finding the charge distribution along a current path when the current distribution is known; and (3) to show how a seemingly simple analytical technique, the treatment of an abrupt step of current as a linearly rising current in the limit that the risetime goes to zero, can lead to erroneous results if there is not a good physical and mathematical understanding of all the variables involved     

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

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.     

Impedance of a short horizontal dipole over a ground plane covered with an anisotropic plasma

Impedance of a short dipole antenna placed parallel over a ground plane covered with an anisotropic plasma has been studied by the quasistatic approximation with emphasis on the effects of image displacement for arbitrary inclinations of the static magnetic field. As the image location can move with the operating frequencies, the reflected characteristic conical surfaces can create oblique resonance anomalies, depending upon source dimensions and source location. While an oblique resonance occurs when the characteristic conical surface coincides with the dipole axis, another anomaly occurs when the reflected cone grazes the dipole ends.     

Far field radiation from an arbitrarily oriented Hertzian dipole in the presence of a layered anisotropic medium

Far field radiation from an arbitrarily oriented Hertzian dipole for two-layered uniaxially anisotropic medium with a tilted optic axis is treated analytically by using the dyadic Green's function of the problem when the dipole is placed over or embedded in a two-layered uniaxially anisotropic medium. The radiation fields are evaluated using the steepest descent method. Parameter studies including anisotropy, layer thickness and dipole location are performed to investigate the effects of changing different variables on the radiation fields. Results of this work can be applied in microstrip circuits and antennas.     

Radiation from a dipole near a general anisotropic layer

The radiation properties of a dipole source located near a gyrotropic layer are investigated analytically. Both electric and magnetic anisotropy of the most general form are assumed. Fourier-transform domain field representations in conjunction with matrix analysis techniques are used to facilitate the analysis. Transmission phenomena through the general anisotropic layer are investigated by examining the radiation patterns at the far-field region. The analysis is also used to derive the response of the anisotropic layer to an incident plane wave. In this case, the transmission and reflection coefficient matrices are obtained