Line Current Source Research Articles

Interaction of a Straight Line Current with a Superconducting Sphere: Theoretical Results

The magnetic interaction of a line current source and a superconducting sphere in the Meissner state is studied theoretically. An analytic solution for the magnetostatic scalar potential Φ yielding the image system due to the induced current line positioned at x = d and y = 0 in front of a sphere of radius a is obtained by mimicking an approach utilized earlier in hydrodynamics. The method resulted in an image system consisting of edge and surface currents all located in a circle inside the superconducting sphere. The magnetic field components B x , B y , B z , B r are generated from our exact solution, revealing certain symmetries with respect to the coordinates. It is demonstrated that various non-dimensional parameters including radius-distance ratio, which can be expressed as \(\frac {a}{d}\) or \(\frac {d}{a}\), influence the magnetic field significantly. The contour plots of the radial component portray contrasting patterns along the three coordinate planes confirming the true nature of three-dimensionality. Radial and axial components are found to have extreme values indicating strong interaction between the line current and the sphere. The levitation force on the superconducting sphere is extracted directly from the analytic solution and is expressed as a quadrature. The expression for the interaction force has a logarithmic contribution and further depends on the z coordinate. It is found that when the line current is very close to the superconductor (\(\frac {a}{d} \sim 1\)), the force is singular in the limit \(\frac {z}{d} \rightarrow 0\). The singular behavior and z dependence property of the force are new and do not occur in source-sphere and dipole-sphere superconducting systems. The computed levitation force is maximum when the line current is positioned closer to the sphere and minimum when it is farther from the sphere. It is shown numerically that the order of magnitude of the increase of the force going from large to small separations is 104. The simple nature of our theoretical results can be directly applied to models for magnetic levitation and magnetic microscopy.

Effect of Air-Gap Between a Ferrite Plate and Metal Strips on Magnetic Shielding

This paper explores the effect of an air-gap between a ferrite plate and metal strips on magnetic shielding in the presence of a periodic line current source based on an analytical solution. The Fourier transform is used to represent the magnetic vector potentials in the spectral domain, and the mode-matching technique is enforced to obtain a modal solution in rapidly converging series form, leading to numerically efficient results. Magnetic shielding effectiveness is investigated in terms of the air-gap thickness between the ferrite plate and metal strips, the metal strip width, and the position of a periodic line current source.

콘크리트 수변구조물의 누수 탐지를 위한 변형된 전기비저항 탐사 연구

A modified electrical resistivity survey has been suggested and applied to a leakage detection problem of concrete barrage. We suggest the modified electrical resistivity methods using electrodes floating on the water and apply line current sources instead of conventional point current sources in order to facilitate simple analysis. In addition, the study introduced the following three variations of modified electrode array: Direct potential array, Parallel potential array and Cross potential array. These arrays were tested and investigated through numerical experiment, physical model experiment and geophysical field exploration in order to verify their applicability to the water leakage detection of a concrete barrage. When water leakage occurred, all kind of array operations demonstrated distinct changes of aspects of potential difference in graphs obtained by not only the numerical and physical model experiments but also geophysical field exploration. Therefore, this modified electrode arrays of electrical resistivity survey, which has been adapted to the concrete barrage, has been found to be a useful method to detect water leakage.

Generation of uniform three-dimensional optical chain with controllable characteristics

An approach is proposed for the construction of a uniform three-dimensional (3D) interconnected optical chain with variable length, prescribed spot number and spacing along the optical axis. This can be achieved in a 4Pi focusing system through reversing the radiation patterns from a uniform magnetic current line source in combination with an electric current line source with a cosine-squared taper. The required pupil plane illumination for generating the desired uniform 3D optical chain near the focus of high NA lens can be found analytically. It is found that the number of dark spots only depends on the parameter N related to magnetic current periodic distribution, while the length of optical chain and the interval between two adjacent spots approximately equal to the length L of line source and L/N, respectively. Numerical results demonstrate that the characteristics of the constructed optical chain can be controlled purposely through proper choices of the parameters N and L. The present work may find valuable applications in optical microscopy as well as multi-particle trapping, delivery, and manipulation.

Analytical models for electrically thin flat lenses and reflectors.

This work presents analytical models for two-dimensional (2D) and three-dimensional (3D) electrically thin lenses and reflectors. The 2D formulation is based on infinite current line sources, whereas the 3D formulation is based on electrically small dipoles. These models emulate the energy convergence of an electrically thin flat lens and reflector when illuminated by a plane wave with specific polarization. The advantages of these models are twofold: first, prediction of the performance of electrically thin flat lenses and reflectors can be made significantly faster than full-wave simulators, and second, providing insight on the performance of these electrically thin devices. The analytic models were validated by comparison with full-wave simulation for several interesting examples. The validation results show that the focal point of the electrically thin flat lenses and reflectors can be accurately predicted through a design that assumes low coupling between different layers of an inhomogeneous media.

Magnetic shielding analysis of a multiply-slotted metal plate coated with a ferrite sheet in a periodic line current source

This paper presents an analytical solution for low-frequency magnetic shielding analysis of a multiply-slotted metal plate coated with a ferrite sheet in the presence of a periodic line current source. The Fourier transform is used to represent the magnetic vector potentials in the spectral domain and the mode matching technique is enforced to obtain a modal solution in rapidly converging series form, leading to numerically efficient results. Shielding effectiveness is investigated in terms of the geometrical configuration of multiple slots, ferrite sheet, and periodic line current source. The proposed solution is verified by a commercial finite element solver with good agreement.

1/4 파장 마이크로스트립 라인을 전류원을 갖는 서브-1V 직렬공진 차동 콜피츠 전압제어 발진기

1/4 파장 마이크로스트립 라인을 전류원을 갖는 서브-1V 직렬공진 차동 콜피츠 전압제어 발진기

Comparison between ray tracing and ray launching semianalytical methods for computing the radiation characteristics of a Fabry–Perot cavity

ABSTRACTIn this work, two semianalytical methods are compared for computing the radiation characteristics of a Fabry–Perot cavity excited by an internal current line source. One method uses the ray launching and the other method uses the ray tracing. A full‐wave method is used as a reference. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:13–15, 2015

3D modeling and inversion of the electrical resistivity tomography using steel cased boreholes as long electrodes

Abstract Electrical resistivity tomography using a steel cased borehole as a long electrode is an advanced technique for geoelectrical survey based on the conventional mise-a-la-masse measurement. In most previous works, the steel casing is simplified as a transmission line current source with an infinitely small radius and constant current density. However, in practical stratified formations with different resistivity values, the current density along the casing cannot be constant. In this study, the steel casing is modeled by a conductive physical volume that the casing occupies in the finite element mesh. The current supply point is set on the center of the top surface of the physical volume. Synthetic modeling, using both a homogenous and layered formation, demonstrates reasonability of the forward modeling method proposed herein. Based on this forward modeling method, the inversion procedure can be implemented by using a freeware R3t (Lancaster University, UK). Inversion results of synthetic modeling data match fairly well with the defined target location and validate that the method works on the inversion of the casing–surface electrical resistivity data. Finally, a field example of Changqing oil field in China is carried out using the inversion method to image water flooding results and to discover wells with great potential to enhance residual oil recovery.

Modeling and analysis of extracellular potentials in multielectrode arrays.

To compare the different schemes we tested them on current sources and tissue models of increasing complexity. We calculated the extracellular potential generated at the MEA plane while varying the following: 1) We placed a point current source inside the slice, and varied its position with respect to the MEA plane. We also varied the conductivity profile of the slice to include inhomogeneity, anisotropy, and a thin layer of saline beneath the slice. 2) We used a layer 5 pyramidal cell model (Hay et al., 2011) and tracked the transmembrane currents through its compartments during a spontaneous spike. We placed these transmembrane currents as line current sources on a reconstructed cell within the slice. We then varied the conductivity of the saline bath surrounding the slice. 3) For testing a population of cells, we used a thalamo-cortical column model (Traub et al., 2005), and tracked the transmembrane currents through all its cortical neurons during an evoked response. The MEA potentials were then calculated assuming point-like current sources positioned on the mid points of the compartments in the multicompartment neuron models. We varied the conductivity of the slice to include inhomogeneity, anisotropy, and a thin layer of saline beneath the slice . In all cases we found that the MoI gave quantitatively accurate results compared to FEM. We further investigate how the changes in the extracellular potential due to the variations in the conductivity profile of the slice affect the estimates of current source density (CSD) in a MEA setup. We used MoI to extend the kernel current source density method (Potworowski et al., 2012) to include the geometry of the slice and saline slab. We found that including the saline layer does not increase the accuracy of the estimated CSD.

Determination of the Electromagnetic Field Created by Line Current and Sheet Current Source at the Earth’s Surface

The electromagnetic field that generated by line current and sheet current at the surface of the earth can be expressed in analytical form. The line current created at the earth’s surface by an infinitely long line current is given by the inverse Fourier integrals over a horizontal wave number. The sheet current can be obtained by integrating the line current expansions using a Neumann and Struve functions; these functions have known mathematical properties, including the series expansions. The series expansions are exact with neglecting the displacement currents. Assuming a uniform earth and that there is no propagation, the three nonzero field components can be expressed in terms of the Neumann and Struve functions. The integrals of line current expansions are calculated by using the numerical methods. The results represented graphically and illustrated by figures. Results can be used to evaluate numerical solutions of more complicated modeling algorithms.

Evaluating the applicability of the finite element method for modelling of geoelectric fields

Abstract. Geomagnetically induced currents in power systems are due to space weather events which create geomagnetic disturbances accompanied by electric fields at the surface of the Earth. The purpose of this paper is to evaluate the use of the finite element method (FEM) to calculate the magnetic and electric fields to which long transmission lines of power systems on the Earth are exposed. The well-known technique of FEM is used for the first time to simulate magnetic and electric fields applicable to power systems. Several test cases are modelled and compared with known solutions. It is shown that FEM is an effective modelling technique that can be applied to determine the electric fields which affect power systems. FEM enables an increased capability beyond the traditional methods for modelling electric and magnetic fields with layered earth conductivity structures, as spatially more complex structures can be considered using FEM. As an example results are presented for induction, due to a line current source, in adjacent regions with different layered conductivity structures. The results show the electric field away from the interface is the same as calculated for a single region; however near the interface the electric field is influenced by both regions.

A lattice Boltzmann model for Maxwell’s equations

In this paper, a lattice Boltzmann model for the Maxwell’s equations is proposed by taking separate sets of distribution functions for the electric and magnetic fields, and a lattice Boltzmann model for the Maxwell vorticity equations with third order truncation error is proposed by using the higher-order moment method. At the same time, the expressions of the equilibrium distribution function and the stability conditions for this model are given. As numerical examples, some classical electromagnetic phenomena, such as the electric and magnetic fields around a line current source, the electric field and equipotential lines around an electrostatic dipole, the electric and magnetic fields around oscillating dipoles are given. These numerical results agree well with classical ones.

Electron-Energy Loss Study of Nonlocal Effects in Connected Plasmonic Nanoprisms

We investigate the emergence of nonlocal effects in plasmonic nanostructures through electron-energy loss spectroscopy. To theoretically describe the spatial dispersion in the metal permittivity, we develop a full three-dimensional nonlocal hydrodynamic solution of Maxwell's equations in frequency domain that implements the electron beam as a line current source. We use our numerical approach to perform an exhaustive analysis of the impact of nonlocality in the plasmonic response of single triangular prisms and connected bowtie dimers. Our results demonstrate the complexity of the interplay between nonlocal and geometric effects taking place in these structures. We show the different sensitivities to both effects of the various plasmonic modes supported by these systems. Finally, we present an experimental electron-energy loss study on gold nanoprisms connected by bridges as narrow as 1.6 nm. The comparison with our theoretical predictions enables us to reveal in a phenomenological fashion the enhancement of absorption damping that occurs in these atomistic junctions due to quantum confinement and grain boundary electron scattering.

Lower RCS directional antenna by left-handed material

We theoretically study the radiation of a current line source with a surrounding cylindrical shell of left-handed material (LHM). The far-field radiation pattern is obtained by solving the Maxwell equation in a cylindrical coordinate, which show that this radiation system has good directional emission characteristics and can be used as a directive antenna. The directive emission is explained due to the negative refraction and the focus effect occurring at the interface of the LHM shell. Compared with the parabolic reflector antenna with the same aperture size, our antenna has lower radar cross-section (RCS) in a broadband frequency range, providing a way to realize lower RCS antenna.

Reply to the comment by D. F. Rucker ‘T. Zhu and R. Feng, Resistivity tomography with a vertical line current source and its applications to the evaluation of residual oil saturation’

Electrical resistivity tomography using a steel cased borehole as a long electrode is an advanced technique for geoelectrical survey based on the conventional mise-à-la-masse measurement. In most previous works, the steel casing is simplified as a transmission line current source with an infinitely small radius and constant current density. However, in practical stratified formations with different resistivity values, the current density along the casing cannot be constant. In this study, the steel casing is modeled by a conductive physical volume that the casing occupies in the finite element mesh. The current supply point is set on the center of the top surface of the physical volume. Synthetic modeling, using both a homogenous and layered formation, demonstrates reasonability of the forward modeling method proposed herein. Based on this forward modeling method, the inversion procedure can be implemented by using a freeware R3t (Lancaster University, UK). Inversion results of synthetic modeling data match fairly well with the defined target location and validate that the method works on the inversion of the casing–surface electrical resistivity data. Finally, a field example of Changqing oil field in China is carried out using the inversion method to image water flooding results and to discover wells with great potential to enhance residual oil recovery.

Comment on: T. Zhu and R. Feng, Resistivity tomography with a vertical line current source and its applications to the evaluation of residual oil saturation

Electrical resistivity tomography using a steel cased borehole as a long electrode is an advanced technique for geoelectrical survey based on the conventional mise-à-la-masse measurement. In most previous works, the steel casing is simplified as a transmission line current source with an infinitely small radius and constant current density. However, in practical stratified formations with different resistivity values, the current density along the casing cannot be constant. In this study, the steel casing is modeled by a conductive physical volume that the casing occupies in the finite element mesh. The current supply point is set on the center of the top surface of the physical volume. Synthetic modeling, using both a homogenous and layered formation, demonstrates reasonability of the forward modeling method proposed herein. Based on this forward modeling method, the inversion procedure can be implemented by using a freeware R3t (Lancaster University, UK). Inversion results of synthetic modeling data match fairly well with the defined target location and validate that the method works on the inversion of the casing–surface electrical resistivity data. Finally, a field example of Changqing oil field in China is carried out using the inversion method to image water flooding results and to discover wells with great potential to enhance residual oil recovery.

Conformal transformations to achieve unidirectional behavior of light

The method of optical conformal mapping is used to design two isotropic devices through which light travels in a unidirectional manner. The first device is a directional emitter. By setting a line current source in a properly tuned refractive index profile, fields can be radiated in only one direction or its opposite without using any reflector or metallic structure. The second proposal is a dual-functional device. It works not only as a directional emitter for an embedded source but also as a quasi-diode for beams, thus having potential on-chip applications. Functionalities of the two designs are verified by finite-element-based simulations. We further investigate the spatial dependence of the refractive index near singularities, and corresponding optimization is proposed in the interests of experimental consideration. Numerical results show that the one-way property is well preserved after the parameter reduction.

Collimating lenses from non-Euclidean transformation optics

Based on non-Euclidean transformation optics, we design a thin metamaterial lens that can achieve wide-beam radiation by embedding a simple source (a point source in the three-dimensional (3D) case or a line current source in the 2D case). The scheme is performed on a layer-by-layer geometry to convert curved surfaces in the virtual space into flat sheets, which pile up and form the entire lens in the physical space. Compared to previous designs, the lens does not have extreme material parameters. Simulation results confirm its functionality.

Resistivity tomography with a vertical line current source and its applications to the evaluation of residual oil saturation

The forward and inversion methods of resistivity tomography with a vertical line current source (RTVLCS) were introduced in this paper. The technique was applied to the evaluation of residual oil saturation of the reservoir studied in an old oil region. The observed water saturation during the course of the measurement of RTVLCS and subsequent drilling records proved the reliability of our result. However, our model has not included the influence of all factors such as electrical contact resistance between the metal casing and surrounding rocks and of the size of the metal cased well taken as a vertical line current source (VLCS). In addition, RTVLCS was carried out after the well had been in use for many years, while the initial resistivity values used in the inversion were obtained from the resistivity curve logged upon the completion of the well. Therefore, the residual oil saturation obtained by RTVLCS is relative and has not complete consistency with real situations, and can only be used as reference for adjusting a plan for oil production in the mid- or post-phase of an oilfield. ► Forward and inversion methods of resistivity tomography with a vertical line current source. ► Evaluation of residual oil saturation of the reservoir studied in an old oil region. ► Residual oil saturation is relative and hasn’t complete consistency with real situations. ► Reference for adjusting a plan for oil production.