Electric Current Lines Research Articles

The choice of the concept of magnetic field lines or of electric current lines: Alfvén medal lecture

Abstract. In 1967, at the Birkeland Symposium in Sandefjord, Norway, Professor Hannes Alfvén stated that the second approach (in solving unsolved problems by the standard MHD theory) to cosmic electrodynamics is to "thaw" the "frozen-in" magnetic field lines. "We can illustrate essential properties of the electromagnetic state of space either by depicting the magnetic field lines or by depicting electric current lines," he said. There has been much progress in space physics since the Birkeland Symposium more than 40 years ago, but unfortunately our scientific community has not really succeeded in thawing the frozen-in field lines. Instead, it has pursued magnetic reconnection, a concept that Alfvén had been critical of. It is shown here that we have to study many unsolved problems and problems thought to be solved in terms of both the magnetic field line concept and the current system concept. In taking Alfvén's approach, we must consider the whole system, including the power supply (dynamo process) and its transmission and distribution (electric currents) and observed phenomena (power dissipation processes). Such a consideration can provide physical insight into many of our unsolved problems and problems thought to be solved. In this paper, we consider substorm onset processes, the substorm current system, sunspots, solar flares, coronal mass ejections, the interplanetary current sheet, and the magnetic field configuration of the heliosphere in terms of the current system concept. In particular, it is shown that a study of the current system is essential in substorm studies, more than changes of the magnetic field configuration in the magnetotail.

Influence of geometric variables on the current distribution uniformity at the edge of parallel plate electrodes

In electrochemical processes, the reaction is controlled by electrodes relative placement; to many respects parallel plates seems close to the ideal configuration. However, edge effect represents a detrimental phenomenon that can compromise overall process efficiency. Cell's enclosing insulating walls can attenuate extreme current densities occurring at the electrode edge if appropriately designed to modify the current flow paths. Configurations comprising a limited counter electrode width, an enclosing normal insulating wall, an enclosing oblique insulating wall and a thin parallel mask have been studied. Potential distribution and electrical current lines of these configurations are obtained from algebra operations of complex variables owing to conformal mapping method. It was found that current distribution non-uniformity is conveniently expressed as the absolute deviation from the prescribed value. The dependence of this parameter on geometric variables can be mapped. The picture given by these maps solved the engineering problem of deducing the cell geometry complying with a given current distribution uniformity. Furthermore, optimal parameters providing the best possible performance of each configuration have been identified. Among the geometric variables, the gap between electrodes is the governing parameter of uniformity; it scales the magnitude of edge effect.

A simple forward direct problem solver for eddy current non-destructive inspection of aluminum plates using uniform field probes

In this paper we show that a simple algorithm used to model the eddy current inspection of an aluminum plate can be used to preview the acquired voltage signals. Thus, the algorithm is suitable to work as a forward problem solver to determine the expected measurement signal obtained with a uniform excitation field probe including a giant magnetoresistor sensor. The algorithm is based on a conformal transformation and is able to preview the shape of the electrical current lines when a metallic plate with a superficial straight crack is subject to a sinusoidal excitation field with constant amplitude and orientation in a bounded zone around the sensor element. Simple and fast algorithms as the one presented in this paper are of paramount importance for testing inversion algorithms used to characterize defects in metallic plates.

Constriction Resistance of Thin Film Contacts

The electrical constriction resistance of a circular a-spot in a bulk interface stems from convergence of electrical current flow lines from a distance far from the constriction, and the subsequent spreading out of the current from the constriction. The spreading resistance of an a-spot located in a thin film cannot be identical to that generated in a bulk component of the same material since current spreading is constrained by the thin film boundaries. This paper addresses the effect of film thickness on spreading resistance, and hence on constriction resistance, in a thin conducting layer. If a and L are, respectively, the constriction radius and the film thickness, the spreading resistance is found to deviate significantly from that in a bulk solid only for relatively thin film and for values of a/L greater than 0.02. This paper also compares the dc spreading resistance in a thin film to the spreading resistance for high-frequency current in a bulk solid where current flow is limited to the electromagnetic skin depth. It turns out that spreading resistance at high-signal frequencies is comparable with the dc spreading resistance in a thin film if the thickness of the equivalent thin film is identified as the skin depth at the relevant frequency.

Influence of Hall effects on characteristics of magnetohydrodynamic converging channel

Influences of Hall effects on the flow characteristics and performance of the magnetohydrodyanmic (MHD) converging channel as an MHD generator are studied numerically in the present study. The numerical algorithm used is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of the electric field. It is found that Hall effects may lead to distortions in both the flow field and electric field in the MHD converging channel. The electric current lines are distorted and induce eddy currents, which will be mitigated by Hall effects. Comparisons of parameters characterizing the performance of the MHD generator for different geometry also reveal that the Hall effects may deteriorate the performance of MHD generator, especially for converging channel.

Electric current density distribution in planar solid tumor and its surrounding healthy tissue generated by an electrode elliptic array used in electrotherapy

The knowledge of the electric current density distribution generated by an electrode array is very useful in electrotherapy for tumor treatment. We propose an innovative mathematical approach that takes into account planar solid tumor elliptic geometry, electrical differences between it and its surrounding healthy tissue, and positioning of the electrodes with respect to tumor-surrounding healthy tissue interface. We show the distributions of the electric current density in leading order and first correction terms in a heterogeneous planar medium formed by two regions (tumor and its surrounding healthy tissue) in function of these parameters. The results show that when electrodes are completely inserted in tumor and/or its conductivity is higher than that of its surrounding healthy tissue, the electric current density lines concentrate more in tumor and its tumor-surrounding healthy tissue interface. No significant differences are reported between the electric current density distributions in leading-order and first-order correction for each parameter investigated. However, norm of this physical magnitude reveals that these distributions are different when the ratio between radius of the electrodes and radius of the tumor is less than 0.8. We conclude that the analytical modeling presented in this study is of practical interest because it provides a convenient way to visualize the electric current density distributions generated by an electrode elliptic array in order to efficiently destroy the localized planar tumors with the minimum damage to organism, through an increase of the potential applied to the electrodes, the tumor conductivity with respect to its surrounding healthy tissue and insertion of all electrodes into tumor.

Interfacial wave propagation due to an interfacial line source

Abstract Interfacial wave propagation parallel to a dielectric interface has been studied by considering an electric current line source present at the interface. The first order asymptotic evaluation of field components shows a null of the electric field at the interface. An amplitude null represents an unstable structure in the phase map and a phase front discontinuity across the interface. Higher order asymptotic evaluation has been employed to gain further insight into this propagation problem. The results show that the wavefronts need not be discontinuous. The continuity of the phase fronts is preserved with the help of interesting and stable structures such as saddle points and center points in the phase map of the electric field in both half spaces.

Characterization of the three-dimensional supersonic flow for the MHD generator

A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the corner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.

Comparative evaluation of the electrical configurations for the two-dimensionalelectric potential method of damage monitoring in carbon fiber polymer–matrixcomposite

The effectiveness of the two-dimensional electric potential method of damage sensing in aquasi-isotropic carbon fiber polymer–matrix composite depends on the electricalconfiguration, i.e., the current direction relative to the surface fibers and theelectrical contact scheme. Oblique current application in any direction provideseffective damage sensing, as shown by using electrical contacts on the oppositein-plane surfaces. In-plane current application through the cross section in anydirection also provides effective damage sensing, as shown by using electricalcontacts that are either on the edge surfaces or in holes through the composite.In-plane surface current application is effective when the current is perpendicular tothe surface fibers (due to the low resistivity in the direction of the fibers) andis ineffective when the current is parallel to the surface fibers (due to the highresistivity in the direction perpendicular to the fibers). The oblique configuration isrecommended for practical implementation. In general, the potential method is reliablewhen (i) the resistance between the electric current line and the nearly parallelelectric potential gradient line is sufficiently low, as attained when these lines aresufficiently close, and (ii) the resistance between the current line and the damagelocation is sufficiently low, as attained when the distance of separation is sufficientlysmall.

Multibit MRAM using a pair of memory cells

Magnetic random access memory (MRAM) is one of the most promising candidates to provide energy-efficient and nonvolatile memory. We present a new MRAM design using a pair of cells where each cell can store two bits of information. The pair cells have a parallelogram shape to induce broken-shape magnetic anisotropy along the short axis of the cell. One important advantage of the pair cells is that they can share the same word- and bit-lines intersection in the MRAM architecture. This means that the number of electrical current lines can be reduced and lead to higher recording density. Such design is successfully demonstrated using finite-element micromagnetic simulation.

Anomalous Effect of Porosity upon Electrical Properties of Fe-Based Samples Made by Powder Metallurgy

The microstructure of an automobile gear made by the powder metallurgy process was studied using scanning electron microscopy and optical microscopy with further computer analyzing of images. The investigation of the electrical properties of the gear was done employing standard resistivity measurements and analyzed using an original method to determine the local orientation of the electric field. This last method provided us with the distribution of the electric current lines, which clearly reflects the local anisotropy and fractures in the material. We found that the electric resistivity in the specimens studied is extremely sensitive to the porosity of the material. It is shown that none of the existing theories of the electric conductivity of composite materials, including the Maxwell theory and the frequently used “brick model,” are able to explain this supersensitive dependence on porosity. A new approach is developed, taking into account the anisotropic character of the material. The results of this modeling have shown a good agreement with experimental results. The new method of electric field mapping may be recommended for investigation of the other structural materials. The model developed might be useful, in particular, for a discussion of the influence of the pores on their mechanical properties.

An efficient method to determine Green's functions of a two-dimensional photonic crystal excited by a line source - the phased-array method

A novel and efficient method to determine Green's functions in photonic crystals (PCs), i.e., the phased-array method (PAM), is presented. The PAM is a combination of the plane-wave method and the array-scanning method, which is both more flexible and computationally faster than the eigenmodes expansion method. A complete derivation of the electric- and magnetic-field Green's functions associated, respectively, with an infinite electric and magnetic current line exciting a two-dimensional PC is given. Although the developments are presented only for a line source, the PAM can be extended to a dipole source. Thus, the PAM represents a promising method for the analysis of printed-circuit elements or antennas on PC materials. Numerical results for the Green's functions are shown for different positions of the source and a discussion about radiation patterns, asymptotic behaviors, and convergence characteristics is proposed.

Analysis of an infinite current source above a semi-infinite lossy ground using fictitious current auxiliary sources in conjunction with complex image theory techniques

The canonical problem of an infinitely long electric current line radiating above a lossy infinite half space is examined. The solution is based on the method of auxiliary sources (MAS). In this method one can, in general, apply a numerical solution by introducing sets of fictitious current sources whose fields are elementary analytical solutions to the boundary value problem, in order to approximately describe the actual electromagnetic (EM) fields in each domain. In general, the convergence rate and the accuracy of the MAS solution depend on the spatial distributions of the fictitious current sources sets and their locations in regard to the singularities of the actual EM field simulated by each set. Here, both the accuracy and the convergence rate of the method are examined, investigating complex image approximations in order to optimally choose the auxiliary sources placements. It is proved that the convergence rate and the accuracy of the method are significantly improved by utilizing the complex images as locations of the auxiliary sources. The main contribution of the paper consists in the application of MAS to an open structure, which involves lossy dielectrics excited by a nonuniform EM field, as well as in the optimal choice of the locations of the fictitious current sources according to complex image techniques.

Physics of the magnetopause

A quantitative model of the magnetic field from the large-scale system I of Birkeland currents in the Earth's magnetosphere is proposed. In the near-Earth space the electric current flow lines follow the dipolar magnetic field lines, while at larger distances they enter the high-latitude magnetosheath near mid-day, the low-latitude boundary layer along the magnetospheric flanks, and the plasma sheet boundary layer at the nightside. The model takes into account the local time dependence of the latitude of Birkeland current zone at the topside ionospheric level reported by Iijima and Potemra (1976, J. geophys. Res.81, 2165.) The effects of the geodipole tilt in the overall geometry of the field-aligned current system are also incorporated; The model is sufficiently flexible; in particular, it permits an arbitrary choice of the current sheet thickness as well as of the M.L.T. distribution of the current intensity by using an appropriate combination of model coefficients in the corresponding Fourier expansion. One more possibility is to take into account the asymmetry in the net intensity and M.L.T. distribution of Birkeland currents between Northern and Southern Hemispheres which arises due to diurnal and seasonal variations of the geodipole tilt angle. The proposed analytical representation is relatively simple, which allows it to be incorporated in semi-empirical statistical magnetospheric models with parameters to be determined from spacecraft databases.Two other approaches to the modeling of warped current sheets aimed at quantitative approximation of the magnetic field of Birkeland and tail current systems are considered.

The average shape of the Magnetopause: A comparison of three‐dimensional global MHD and empirical models

We present a predictive model of the magnetopause, constructed using three‐dimensional global MHD simulations of the magnetosphere over a range in solar wind dynamic pressure and the north‐south component of the interplanetary magnetic field (IMF BZ). The magnetopause is identified in the simulations using electric current intensity, thermal pressure, and magnetic field line mapping. The magnetopause is fitted by least squares to an ellipse in each plane, and a fully three‐dimensional magnetopause surface is constructed by assuming an elliptical cross section at intermediate clock angles. There is considerable flaring of the magnetopause dependent on BZ in the noon‐midnight meridian plane due to reconnection but virtually no flaring in the equatorial plane. Despite this asymmetry, when averaged over clock angle, the model shows a general agreement with recent (axisymmetric) empirical magnetopause models and predicts observed magnetopause crossings with about the same accuracy as the empirical models. Unlike these empirical models, our model can directly investigate asymmetries between the meridian and equatorial planes. The subsolar distance, directly measured from the simulations, varies linearly with BZ for both northward and southward interplanetary magnetic field, as do distances to the magnetopause on the flanks. Magnetospheric plasma pressure causes these distances to scale with dynamic pressure by a power law whose exponent is a bit less than −1/6 on the dayside, but little deviation from this ideal Chapman‐Ferraro value is seen in the magnetotail. These uniform changes with Bz lead to approximate conservation of (1) magnetopause shape in the dayside equatorial plane, (2) projected area in the dayside meridian plane, and (3) magnetopause cross‐sectional area in the dawn‐dusk plane. The dawn‐dusk magnetopause cross section is nearly circular on average, but cross sections in the tail are elongated in the Z direction on average.

Effective area of a horizontal long‐wire antenna collecting the atmospheric electric vertical current

The effective area of an antenna collecting the vertical air‐Earth current is a coefficient of proportionality between the collected current and the air‐Earth current density. The effective area can be correctly defined only if the model behind the proportionality relation is adequate. The current collected by a horizontal long‐wire antenna is not exactly proportional to the vertical air‐Earth Maxwell current density because of the different behavior of the displacement and conduction components of the current. Thus, two different effective areas are separately defined for the displacement and nondisplacement components. First, the dynamic effective area characterizes rapid variations of the displacement current. It is calculated assuming that the air does not contain any space charges and that the electric current flow lines match the electric field lines. Second, the static effective area characterizes the nondisplacement current, and it is calculated by taking into account the facts that the conductivity close to the wire surface is unipolar, that the wind‐determined horizontal ion trajectories do not match the electric field lines, and that there are space charges due to the electrode effect of the wire and of the ground. Traditionally, the atmospheric electric vertical current density measurements have been interpreted by using the dynamic effective area as a calibration coefficient. This turns out to be a satisfactory approximation in the case of strong turbulence when the near‐ground space charge layer is high and the static effective area approaches the dynamic effective area. In the limit of low turbulence the traditional interpretation results in errors of several tens percent. A reduced height of the antenna helps to keep the static effective area close to the dynamic effective area and to suppress the errors.

Inhomogeneity and local negative magnetoresistance of aluminum

The peculiarities of potential distribution and current flow in aluminum plate conductors are investigated under an inhomogeneous action of transverse magnetic field. A magnetic field inhomogeneity is arranged along a transport direction with a method of curving of electric current lines. For relative magnetic field gradient of about 0.3 cm−1 a potential dependence on transport direction is complicated and an inversion of spatial dependence of potential takes place. That is an increase of potential along total current vector is observed on one of conductor side as a magnetic field decreases a local resistance.

Inertial effects in electromagnetically driven liquid-metal flows with a periodically wavy boundary

We treat a liquid-metal flow in a gap between two solid perfect conductors with different voltages and with an externally applied, transverse magnetic field. One conductor has a plane surface and the other has a periodically wavy surface. There is a free surface and an electrically insulating, inviscid gas on each side of the conductor with the plane surface. Most of the electric current lines between the conductors are parallel to the magnetic field lines, but, near each corner where a free surface and the plane conductor meet, current lines fringe across the magnetic field lines. This fringing creates an electromagnetic body force which drives a flow parallel to the conductor corner. The inertialess flow for large values of the interaction parameter consists of flow over the tops of the hills of the wavy surface and a recirculation which is trapped between each pair of adjacent hills. Inertial effects convect the transverse parts of these recirculations to the crests of the hills and to the bottoms of the valleys, and this convection results in more circulations in planes which are perpendicular to the magnetic field. The flow is very different from the fully developed flow for two plane perfect conductors, and inertial effects significantly alter the periodic flow. This problem models the flow in a liquid-metal sliding electrical contact with a brush insert, and the periodically wavy boundary models the surface of the brush.

Methods for quantitative modeling of the magnetic field from Birkeland currents

A quantitative model of the magnetic field from the large-scale system I of Birkeland currents in the Earth's magnetosphere is proposed. In the near-Earth space the electric current flow lines follow the dipolar magnetic field lines, while at larger distances they enter the high-latitude magnetosheath near mid-day, the low-latitude boundary layer along the magnetospheric flanks, and the plasma sheet boundary layer at the nightside. The model takes into account the local time dependence of the latitude of Birkeland current zone at the topside ionospheric level reported by Iijima and Potemra (1976, J. geophys. Res. 81, 2165.) The effects of the geodipole tilt in the overall geometry of the field-aligned current system are also incorporated; The model is sufficiently flexible; in particular, it permits an arbitrary choice of the current sheet thickness as well as of the M.L.T. distribution of the current intensity by using an appropriate combination of model coefficients in the corresponding Fourier expansion. One more possibility is to take into account the asymmetry in the net intensity and M.L.T. distribution of Birkeland currents between Northern and Southern Hemispheres which arises due to diurnal and seasonal variations of the geodipole tilt angle. The proposed analytical representation is relatively simple, which allows it to be incorporated in semi-empirical statistical magnetospheric models with parameters to be determined from spacecraft databases. Two other approaches to the modeling of warped current sheets aimed at quantitative approximation of the magnetic field of Birkeland and tail current systems are considered.

Electric fish approach stationary signal sources by following electric current lines.

African electric fish of a pulse species, Brienomyrus brachyistius (Mormyridae), housed singly in a large, circular arena, were presented with electrical stimuli which mimicked a conspecific intruder. Stimuli were produced with either dipolar or bipolar electrodes in three different geometries. We tracked the unconditioned approach response paths taken by the fish and compared tracks for each of the geometries. The results suggest that B. brachyistius can determine neither the distance nor the direction of an electric dipole from afar, but that they do manage to find the source by maintaining a precise alignment of their body axis parallel to the direction of the local electric field vector (parallel to current lines) while swimming. This behaviour ultimately leads to the current source. We propose that this behaviour may be a simple mechanism mediating the approach response of one electric fish to another.