Magnetic Surface Current Densities Research Articles

Inverse Source Solutions With Huygens’ Surface Conforming Distributed Directive Spherical Harmonics Expansions

Time-harmonic inverse source solutions are commonly working with electric and magnetic surface current densities defined and discretized on appropriately chosen Huygens’ surfaces. An efficient meshless alternative are spherical harmonics expansions of low-order distributed along the chosen Huygens’ surface, which still possess pretty good spatial localization properties. Similar to expansions with electric and magnetic surface current densities, distributed expansions with Cartesian spherical harmonics (SHCs) or standard vector spherical harmonics (SHVs) are redundant when they are placed on Huygens’ surfaces. This redundancy is reduced by allowing only spherical harmonics, which can be excited by surface current density distributions in a specific plane, and by forming directive spherical harmonics. This results in a considerable reduction of the necessary number of unknowns for representing the sources and improved conditioning of the discretized integral equations. Inspired by the Huygens’ radiator concept, appropriate directive harmonics on the basis of SHCs and SHVs are derived, implemented, and compared in terms of their performances. The validity of the presented techniques is confirmed via inverse source solutions for synthetic and real measurement data.

Design and optimization of a microfluidic-based inductor used as a multifunction-sensor

A planar miniaturized inductor has been designed in order to realize some transduction functions linked to the presence of fluids. Its electrical behaviour has been studied for two liquids: Galinstan and salted water. Their presence between metallic armatures modifies the inductance value at a nominal frequency, chosen at 2GHz. By using a FEM software, the spatial distributions of magnetic field and surface current density in the entire device have been modelized for six arbitrary positions of these liquids in inductor microchannels. The geometrical aspects of the device have been studied and their influence examined for each liquid. We show that the inductor performances are influenced by the spiral width variations and the inter-turn distances of the coil. Considering the device as a sensor, we have evaluated the variations of two parameters: inductance and quality factors, which can respectively attain 664% (for gallistan) and 175% (for salted water) from their nominal values.

Broadband dynamically tunable terahertz absorber based on a Dirac semimetal.

In this paper, we propose a broadband tunable metamaterial absorber in the terahertz (THz) region. The absorber comprises a Dirac semimetal film, a dielectric layer, and a gold ground plane. Numerical results show that the absorptivity remains above 90% in the range from 5.7 THz to 8.4 THz when the Fermi level is 65 meV. By varying the Fermi energy of the Dirac semimetal film from 40 meV to 80 meV, the absorption bandwidth and absorption peaks can be dynamically tuned. To explain the mechanism of high absorption, the magnetic field, surface current, and power loss density distributions at different resonant frequencies were presented. Our work may have potential applications in various fields such as sensors, detectors, and photovoltaic devices in THz regions.

3-D BEM Formulations for Eddy-Current Problems With Multiply-Connected Domains and Circuit Coupling

Quasi-static linear problems can be solved efficiently with Boundary Element Method (BEM). This method is based on surface integral equations dealing with equivalent magnetic and electric surface current densities. Many works have shown the potentiality of BEM especially for the modeling of non-destructive testing devices. In this paper, after selecting formulations enabling the modeling of multiply-connected regions, an original coupling is proposed in order to take into account external electric circuit in the problem.

A Combined Source Integral Equation With Weak Form Combined Source Condition

A combined source integral equation (CSIE) is constructed on the basis of the electric field integral equation (EFIE) to solve electromagnetic radiation and scattering problems containing perfect electrically conducting bodies. It is discretized with Rao-Wilton-Glisson basis functions only, for both electric and magnetic surface current densities. The combined source condition, which ensures the uniqueness of the solution and circumvents the interior resonance problem, is implemented as a weak form side condition. Compared to the common combined field integral equation, the proposed CSIE shows superior accuracy for sharp edges as well as structures with the interior resonance problem. Furthermore, the iterative solver convergence of the CSIE is faster than for the EFIE, which shows about the same accuracy as the CSIE. Results of numerical scattering simulations are presented to demonstrate the accuracy of the presented CSIE.

Adaptive Adjustment of Radiation Properties for Entire Range of Axial Ratio using a Parasitic Microstrip Polarizer

This paper proposes the design of microstrip patch antennas for dual-band polarization adjustment. The antenna has a multi-layer structure for dual-band operation, and each layer contains a resonating patch with surrounding strips separated into two parts. The antenna polarization is adjusted by varying the separated positions of the strips, while fixing other design parameters. To demonstrate the feasibility, an antenna sample with right-hand circular polarization is fabricated, and its antenna characteristics are measured in a full anechoic chamber. The operating principle of polarization adjustment in the dual frequency bands is also verified by observing near electromagnetic fields and the magnetic surface current density around the antenna.

New Single-Source Surface Integral Equation for Magneto-Quasi-Static Characterization of Transmission Lines Situated in Multilayered Media

We recently proposed a novel single-source integral equation (SSIE) for accurate broadband resistance and inductance extraction and current flow modeling in 2-D conductors. The new surface integral equation is advantageous compared with the traditional volume electric field integral equation (V-EFIE) used for the inductance extraction, since the unknown function is defined on the surface of conductors as opposed to the volumetric unknown current density in V-EFIE. The new SSIE is also more suitable for the solution of inductance extraction problems than the traditional surface integral equation formulations, as it features only a single unknown surface function as opposed to having the unknown equivalent electric and magnetic surface current densities. The new equation also features only the electric field Green’s functions unlike the previously known SSIE formulations. The latter property makes the new SSIE equation particularly suitable to the inclusion of the multilayered substrate effect into the inductance extraction model. This paper describes the generalization of the new SSIE formulation to the case of transmission line models embedded into the multilayered lossy substrates. This paper also shows how the matrix sparsity in the method of moments discretization of the novel integral equation can be exploited to accelerate its numerical solution and reduce associated memory use. This sparsity arises due to the skin-effect-based attenuation of the fields in conductors’ cross sections leading to vanishing levels of the matrix elements corresponding to the distant interactions. Typical examples of inductance extraction in complex interconnects situated in lossy substrate are considered to validate the proposed techniques against traditional approaches.

Fast Inverse Equivalent Source Solutions With Directive Sources

A fast inverse equivalent source technique is presented for the fully probe-corrected transformation of measured radiation or scattering fields utilizing directive sources. The directivity of the expansion sources is either obtained by combining electric and magnetic surface current densities in a directive Huygens radiator or by shifting the source locations into complex space. The latter approach is known to generate Gaussian-beam-like directive radiators. These two techniques can be used separately or in combination to obtain three different solutions that approximately satisfy the null-field condition (also known as the Love condition) outside the solution domain, i.e., inside the volume of the original device under test. The directive sources lead to a better conditioning of the inverse problem and especially the Huygens radiator concept leads to good conditioning for a small number of unknowns. Thus, considerable reduction in computation times and better solution accuracies are achieved. Moreover, antenna diagnostics is promoted by the improved localization of the directive equivalent sources. The directive sources are implemented together with Rao–Wilton–Glisson basis functions and the new concepts are utilized within the fast irregular antenna field transformation algorithm with its hierarchical propagating plane wave-based radiation operator representation. This algorithm has recently been augmented with Gaussian beam-based translation operators which lead to considerably reduced computation times and lower memory requirements. The algorithmic capabilities are demonstrated with synthetically generated near-field data as well as with real spherical measurements of a double-ridged waveguide antenna.

Guiding Center Orbit Calculation for Evaluating the Current Density Distributions of the Electrons in Electron Cyclotron Heating on QUEST

In order to evaluate the magnetic surface current density distributions, the electron guiding center orbits were calculated with the equilibrium fitting plasma equilibrium analysis. The current density distributions in electron cyclotron-heated plasma were estimated from the orbit analyses in the equilibrium plasma shaping for the fundamental and the second-harmonic resonant electrons separately. The current density distribution profiles on the equatorial plane were obtained for the electrons with initially positive and negative velocities parallel to the magnetic field direction as well as the trapped electrons. The surface averaged current density profiles of the closed flux surfaces were also evaluated. A significant amount of the positive current density distributions appeared outside the last closed flux surface (LCFS), while all the negative current density distributions were evaluated inside the LCFS. The trapped electrons being the second-harmonic electron cyclotron resonant contributed the negative current inside the LCFS. The positive current density distributions outside the LCFS were significant for the driven current density for both the fundamental and second-harmonic resonances.

Cavity induced perfect absorption in metamaterials

We present novel resonant modes at the THz regime in a structure combining conventional metamaterial absorber (MA) with a cavity (MAC). The well-known structure consisting of three individual layers of periodic metallic dishes on the top, a dielectric layer in the middle, and a metallic film in the bottom is used, and the cavity is formed on the top layer by changing the geometry of the metallic dishes. MACs with various cavity parameters are designed and their absorption characteristics, such as magnetic field distribution, surface current, and power loss density at resonant frequencies of the designed structure, are numerically investigated. Resonant effects in this work may find applications in THz tunable and broadband MA, and our investigation on the dependence of the absorption frequency and absorption intensity on the geometric cavity of the designed structure will provide a general guideline for MAC design.

Design and Performance Evaluation of Microstrip Antenna for Ultra-Wideband Applications Using Microstrip Feed

In the modern days the development in communication systems engineering requires the development of low profile antennas that are capable of maintaining high performance over a wide spectrum of frequencies. In this review, we have designed an elementary Microstrip patch Antenna for ultra-wideband application. This technological trend has focused much effort on the basic concepts, characteristics and design of a Microstrip patch antenna. This paper explains the pattern of designs of the Microstrip patch antenna along with detailed study. A thorough analysis and observations of the problem begins with the application of the equivalence principle that introduces the unknown electric and magnetic surface current densities on the dielectric surface. Here in this technical review, our main goal is to design an elementary Microstrip antenna, which will work in the ultra-wide band range and also it should work in the desired operating frequency. Ansoft High Frequency Structured Simulations (HFSS) software is used for the elementary design of a rectangular patch Microstrip antenna and also some of the basic calculations has been done by using MATLAB. This review paper also comprises of basic parameters, types of antenna, working, fundamental concepts and characteristics as well as feeding techniques and simulation, results of Microstrip patch antenna.

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

Research on Electromagnetic Engineering and Technology with Application of EFIT Code in J-TEXT Tokamak

The Grad-Shafranov equation is solved by EFIT code in J-TEXT tokamak. In this paper, it applies EFIT code to analyze the evolution of some plasma parameters during the discharge of J-TXET tokamak. Through plasmas balance calculation, the pressure of plasmas, internal magnetic surface and plasma current density profile are given. It provides important reference data for the operation and control of the J-TXET tokamak discharge.

Determination of Surface Currents on Circular Microstrip Antennas

This work aims to present a theoretical analysis of the electric and magnetic surface current densities of a circular microstrip antenna (CMSA) as a body of revolution. The rigorous analysis of these problems begins with the application of the equivalence principle, which introduces an unknown electric current density on the conducting surface and both unknown equivalent electric and magnetic surface current densities on the dielectric surface. These current densities satisfy the integral equations (IEs) obtained by canceling the tangential components of the electric field on the conducting surface and enforcing the continuity of the tangential components of the fields across the dielectric surface. The formulation of the radiation problems is based on the combined field integral equation. This formulation is coupled with the method of moments (MoMs) as a numerical solution for this equation. The numerical results of the electric and magnetic surface current densities on the outside boundary of a CMSA excited by <TEX>$TM_{11^-}$</TEX> and <TEX>$TM_{21^-}$</TEX> modes are presented. The radiation pattern is calculated numerically in the two principle planes for a CMSA and gives a good results compared with measured results published by other research workers.

Mixed discretization schemes for electromagnetic surface integral equations

In developing accurate and stable discretization schemes for integral equations, important steps are the choices of the basis and testing functions. In the electromagnetic surface integral equations, the unknown quantities, the equivalent electric and magnetic surface current densities, are by default divergence conforming and therefore should be expanded with the divergence‐conforming basis functions. The choice of the testing functions however is less obvious and depends on the choice of the basis functions and the properties of the integral operators. We develop stable and well‐defined discretization procedures where the operators are tested either their range or on the dual of their range. This requires the use of non‐conventional finite‐elements spaces, called ‘dual spaces’, and non‐traditional testing procedures. We show with numerical examples that in most cases, testing the operators on the dual of their range leads to improved solution accuracy compared with testing the operators on their range. For the integral equations of the first kind, this agrees with the conventional Galerkin's scheme, but for the integral equations of the second kind, this requires the use of Petrov–Galerkin type discretization schemes with appropriate curl‐conforming (dual) testing functions. Copyright © 2012 John Wiley &amp; Sons, Ltd.

An Active Electromagnetic Cloak Using the Equivalence Principle

Electromagnetic cloaking refers to the ability to prevent an object from scattering an incident electromagnetic field. This has been accomplished in recent works by specially designed materials. Another way of cloaking using sources has been known in the acoustics community. In this letter, we introduce a prescription for canceling the electromagnetic scattering of an object by using an array of sources. By using the equivalence principle, we show that by superimposing magnetic and electric surface current densities at the boundary of an object, the scattered fields from that object can be canceled. These magnetic and electric surface currents can be discretized into electric and magnetic dipoles that are physically implementable by straight and loop wire antennas. Finally, we confirm our results using numerical simulations.

Cavity mode waves during terahertz radiation from rectangularBi2Sr2CaCu2O8 + δ mesas

We re-examined the angular dependence of the radiation from the intrinsic Josephson junctions in rectangularmesas of Bi2Sr2CaCu2O8 + δ, in order to determine if the cavity mode part of the radiation arises from waves across the widthw or along the length of the mesas, associated with ‘hot spots’ (Wang et al 2010 Phys. Rev. Lett. 105 057002).We derived analytical forms for the angular dependence expected in both cases for ageneral cavity mode in which the width of the mesa corresponds to an integer multiple ofone-half the wavelength of the radiation. Assuming the coherent radiation from the acJosephson current source and the cavity magnetic surface current density source combineincoherently, fits to the data of Kadowaki et al (2010 J. Phys. Soc. Japan 79 023703) on amesa with mean for both wave directions using two models for the incoherent combination were made,which correspond to standing and traveling waves, respectively. The results suggest thatthe combined output from the uniform ac Josephson current source plus a cavity waveforming along the rectangle length is equally probable as that of the combined output fromthe uniform ac Josephson current plus a cavity wave across the width. However, for mesasin which is integral, where n is theindex of the rectangular TMzn, 0 mode, it is shown that standing cavity mode waves along the length of the mesa do not radiate in thexz plane perpendicular to the length of the mesa, suggesting experiments on such mesas couldhelp to resolve the question.

Angular Dependence of the Radiation Power of a Josephson STAR-emitter

We calculate the angular dependence of the power of stimulated terahertz amplified radiation (STAR) emitted from a dc voltage applied across a stack of intrinsic Josephson junctions. During coherent emission, we assume that a spatially uniform ac Josephson current density in the stack acts as a surface electric current density antenna source, and the cavity features of the stack are contained in a magnetic surface current density source. A superconducting substrate acts as a perfect magnetic conductor with H ||,ac=0 on its surface. The combined results agree very well with recent experimental observations. Existing Bi2Sr2CaCu2O8+δ crystals atop perfect electric conductors could have Josephson STAR-emitter power in excess of 5 mW, acceptable for many device applications.

INVERSE EQUIVALENT SURFACE CURRENT METHOD WITH HIERARCHICAL HIGHER ORDER BASIS FUNCTIONS, FULL PROBE CORRECTION AND MULTILEVEL FAST MULTIPOLE ACCELERATION

An inverse equivalent surface current method working with equivalent electric and/or magnetic surface current densities on appropriately chosen Huygens surfaces is investigated. The considered model with triangular surface meshes is compatible with the models known from method of moments (MoM) solutions of surface integral equations. Divergence conforming current basis functions of order 0.5 and of order 1.5 are considered, where the order 0.5 functions are the well-known Rao-Wilton-Glisson basis functions. Known near-fleld samples typically obtained from measurements are mapped on the unknown equivalent surface current densities utilizing the radiation integrals of the currents as forward operator, where the measurement probe in∞uence is formulated in a MoM like weighting integral. The evaluation of the forward operator is accelerated by adaptation of the multilevel fast multipole method (MLFMM) to the inverse formulation, where the MLFMM representation is the key to full probe correction by employing only the far-fleld patterns of the measurement probe antennas. The resulting fully probe corrected algorithm is very ∞exible and e-cient, where it is found that the computation speed is mostly dependent on the MLFMM conflguration of the problem and not that much on the particular equivalent current expansion as long as the expansion is able to represent the currents su-ciently well. Inverse current and far-fleld pattern results are shown for a variety of problems, where near-fleld samples obtained from simulations as well as from realistic measurements are considered.

Multilevel Fast Multipole Accelerated Inverse Equivalent Current Method Employing Rao–Wilton–Glisson Discretization of Electric and Magnetic Surface Currents

The radiation of any object in a homogeneous environment can be described by a set of equivalent sources. Different types of equivalent sources are feasible and all of them have their own benefits. Equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> information about the object shall be used. Also, they can immediately provide diagnostic information about the object. In this paper, a very flexible equivalent current method is presented, which has been derived from a general purpose boundary integral equation solver. As such the method works with arbitrary triangular surface meshes and Rao-Wilton-Glisson basis functions, where electric and/or magnetic surface current densities can be assumed. High efficiency is achieved since the multilevel fast multipole method has been adapted to speed-up the inverse solution process. Results obtained from simulations and measurements are presented, where large-scale problems with dimensions up to 75 wavelengths are considered.