Form Of Electromagnetic Field Research Articles

Remote Sensing of Source Currents of Narrow Bipolar Events Using Measured Electric Fields

AbstractIn this work the electric field of narrow bipolar events (NBEs) measured at a remote location is used to extract the current waveform of the source discharge. All calculations correspond to a vertical linear current source above a perfectly conducting ground plane. The current study uses the well established formulation of electromagnetic fields in the frequency domain, and develops a deconvolution based technique to obtain exact reconstruction of the source current, improving upon previous modeling of NBEs, which often require tuning several inter‐dependent parameters to determine the current that best reproduces the observed electric field. Our proposed solution, although readily available in standard electromagnetic textbooks, has never been employed in the context of lightning related discharges, and offers a simple and efficient alternative to previous conventional time domain calculations.

Electric circuit element boundary conditions in the finite element method for full-wave passive electromagnetic devices

A natural coupling of a circuit with an electromagnetic device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the electromagnetic field formulation. This contribution shows how these ECE boundary conditions can be implemented into the 3D-finite element method for solving coupled full-wave electromagnetic (EM) field-circuit problems in the frequency domain. The frequency response allows the extraction of a reduced order model of the analyzed device, accounting for all the EM field effects. The implementation is based on a weak formulation that uses the electric field strength E strictly inside the domain and a scalar potential V defined solely at the boundary. Edge elements for E are used inside the three-dimensional domain and nodal elements for V are used on its two-dimensional boundary. The weak formulation is described and implemented in the free environment Open Numerical Engineering LABoratory (onelab). The validation is carried out on 3D examples.

Theoretical and NEC Calculations of Electromagnetic Fields Generated From a Multi-Phase Underground Cable

A generalized formulation of electromagnetic fields generated from a multi-phase underground cable is proposed based on a complete solution of Maxwell equations. The lateral electromagnetic field components, the shielding effect of cables and the phase currents at high frequencies of a three phase underground cable are evaluated by the newly derived formulas. The accuracies of the recently developed extended transmission line approach of underground cables are investigated based on the performance of electromagnetic field components. It is also shown that Numerical Electromagnetics Code verifies the results calculated from the new formulas presented in this article.

Design modeling, and control of multi-stage SMES integrated with PV system

Abstract Superconducting Magnetic Energy Storage (SMES) is an electrical storage device. It stores the available energy in the form of electromagnetic fields. The features of SMES include relatively high-power density, fast response time, very quick full discharge time, high cycle efficiency, and long lifetime. SMES is suitable for short-term storage in power and energy system applications so that it can play an important role in the increased use of intermittent renewable energy. This paper presents modeling and design of a high-efficiency multi-stage SMES system supplied by either a photovoltaic (PV) source or Constant Voltage Source (CVS). The multi-staging process is a new concept for extending the SMES discharging time and improving their efficiency. The system is proposed as a standalone hybrid system that stores the PV energy in the form of an electromagnetic field. At power interruptions, the system can supply the connected loads for a specified period depending on the number of stages. The proposed model is simulated in Matlab/Simulink environment. The paper presents a comparative study between single and multi-stage SMES systems supplied by either PV or CVS source. The obtained results show that: increasing the number of stages leads to an increase in the system efficiency with a high increase in discharging time. The proposed system can be used as Uninterruptable Power Supply (UPS) for isolated or grid-connected applications.

Scattering and absorption characteristics of graphene coated metamaterial cylinder

Terahertz (THz) wave interaction from graphene coated metamaterial cylinder has been investigated analytically and numerically. The analytical formulation of electromagnetic fields is being modeled in the frame work of Mie theory while the modeling of the graphene is done by random phase approximation method. The causality principle based Kramer-Kroing relations are used to simulate the DNG metamaterial, while the DPS metamaterial is modeled by the Drude relations of SiO2. The analytical formulation is developed for both parallel and perpendicular polarized waves. The impedance boundary conditions (IBC) approach is used to model the infinitely thin graphene coating on metamaterial cylinder. Further the IBC at the interface of graphene layer and metamaterial cylinder are applied to compute the unknown scattering coefficients. The efficiency factors i.e., scattering efficiency (Qsca), extinction efficiency (Qexc) & absorption efficiency (Qabs) and bistatic radar cross section (RCS) have been computed analytically as well as numerically for both micro and nano cores. The influence of graphene parameters i.e., chemical potential (μc) & scattering rate (τ1) and size of metamaterial cylinder (R) on the scattering efficiency (Qsca) and extinction efficiency (Qexc) has been analyzed for DPS and DNG cores. It is observed that the in the nano regime, for perpendicularly polarized wave, graphene coated metamaterial cylinder supports the localized surface plasmon resonance (LSPR) modes and LSPR is found sensitive to the change in the graphene parameters and core size. However, it is reported that the parallel polarized wave has same response towards the DPS and DNG cores in the nano regime. It is concluded that under suitable parameters the graphene coating may provide extraordinary degree of freedom to actively control the THz interactions i.e., scattering efficiency, extinction efficiency and bistatic RCS. The present work may have potential applications in designing and manufacturing of Electromagnetic invisibility, cloaking and target protection devices for THz region.

Validity of Ehrenfest''s theorem for generalizedfields of dyons

The validity of Ehrenfest's theorem with its classical correspondence has been justified for the manifestly covariant equations of dyons. We have also developed accordingly the Lagrangian formulation for electromagnetic fields in a minimum coupled source giving rise to conserved current of dyons. Applying the Gupta subsidiary condition we have extended the validity of the Ehrenfest's theorem for $U\left(1\right)\times U\left(1\right)$ Abelian gauge theory of dyons. It is shown that the expectation value of the quantum equation of motion reproduces the classical equation of motion, which is the generalized form of Ehrenfest's theorem in quantum field theory.

Coupled electro-magnetic field & Lorentz force effects in silicon and metal for ESD investigation in transient and harmonic regimes

The purpose of this paper is to present a fully-coupled electro-magnetic field formulation including Lorentz force corrections with the purpose of investigating ESD events in great detail in silicon (FEOL) and the metal stack (BEOL). This study is focused on ESD events in advanced CMOS technology. For specific ESD events, responses, design and topology it is important to take into account all electromagnetic phenomena in the structure. To perform such an accurate study, the first step is to build a powerful tool for the harmonic and transient regime coupling all electric and magnetic fields. Typical ESD structures are simulated to ultimately know the impact of the electro-magnetic field and Lorentz force. The harmonic regime is used for parasitic capacitance extraction and the transient regime for the ESD behaviour. We demonstrate that the simulation tool has a wide range of applicability by giving additional applications.

Sensitivity of controlled-source electromagnetic fields in planarly layered media

The study of electromagnetic (EM) field sensitivities is useful for assessing the feasibility of controlled-source electromagnetic (CSEM) surveys. Sensitivity calculations are also a principal building block of EM inversion schemes. Sensitivities are formally given by the derivatives of the EM field components with respect to conductivity. For horizontally layered media, these derivatives can be evaluated analytically, offering advantages in computational efficiency and accuracy over numerical evaluation. We present a complete set of explicit analytic expressions for the EM field sensitivities in 1-D VTI-anisotropic media for horizontal and vertical electric and magnetic dipole sources, and also for finite horizontal electric sources. Since our derivations are based on a formulation for EM fields that is quite general in allowing for sources and receivers at any depth, our sensitivity expressions exhibit the same generality. We verify our expressions by comparison to numerical solutions, and finally present application examples that demonstrate the utility and versatility of these expressions for CSEM feasibility studies.

A distributional formulation of electromagnetic fields and sources in the presence of media discontinuities

A self-contained formulation of Maxwell's theory of electromagnetic fields and sources is presented in the language of distributional forms. Properties of a fundamental double-form of bi-degree (p,p) for p ≥ 0 are reviewed in order to establish a computational framework for analysing equations involving the Hodge-de Rham operator for p–forms on space or spacetime and singular sources. A constructive approach to Dirac distributions on (moving) submanifolds embedded in R3 is developed in terms of (Leray) forms generated by the geometry of the embedding and illustrative examples presented from problems in electrostatics, magnetostatics and radiating point charges. The formulation offers a straightforward analysis of the relativistic jump conditions across static and moving interfaces where certain fields become discontinuous and provides a general methodology for electromagnetic modeling where possibly time dependent sources of certain physical attributes, such as electric charge, electric current and polarization or magnetization, are concentrated on localized regions in space or spacetime.

Effect of Ground Conductivity on Radiation Pattern of a Dipole Antenna

This paper aims firstly to develop a theoretical formulation of electromagnet ic fields above the earth surface taking into account the finite and infinite conductivity of the ground- which has the advantages of being reasonably fast to compute, secondly to investigate the effect of ground properties on the electric field intensity. For this purpose we have analyzed radiation pattern for finite and infinite ground conductivity, frequencies and different antenna lengths. The monopole is fed to its base. The current distribution along the portion below ground is the image of the current distribution along the original monopole.The image source for calculating electric field, above the infinitely conducting ground surface is just opposite to that of the original source. The image source for calculating electric field above the finitely conducting ground surface is not just opposite to that of the original source. It is affected by the ground properties. For same frequency and identical antenna length but at different ground conductivity, there exists variation in radiation field. It is observed that at small value of ground conductivity the radiation field is small also the direction of radiation field changes. Furthermore it is obtained that rise of frequency increases the radiation field sharply in a particular direction. Finally we can say that at a fixed antenna length, there exists a minimum frequency for measurable radiation field.

Educational value of the algebraic numerical methods in electromagnetism

PurposeThe aim of this paper is to highlight the educational value of algebraic numerical methods with respect to traditional numerical techniques based on differential formulation.Design/methodology/approachAlgebraic formulations of electromagnetic fields are gaining a new interest in the research community. One common characteristic of these methods is that they impose field equations, for instance charge or mass conservation, directly in algebraic form as a sum of partial contributes, without using differential operators like the divergence one. This feature leads directly to a system of linear equations without requiring any intermediate differential formulation as in finite element method. In addition, these systems of linear equations can be efficiently expressed as a product of matrices related to problem topology and material characteristics.FindingsOwing to these features, a MATLAB implementation of these theoretical frameworks is particularly efficient and simple and can be used by electrical engineering students which, even if with a basic mathematical background, have a good practice with network theory and its computer implementation. Following this way of thinking, a MATLAB based environment has been created and here it is presented and discussed.Originality/valueThe implementation of the algebraic formulation can be done by using very basic mathematical tools, therefore the algebraic method becomes also a good way to introduce the numerical field analysis to undergraduate students.

Lagrangian formulation of electromagnetic fields in nondispersive medium by means of the extended Euler–Lagrange differential equation

This work is concerned with the Lagrangian formulation of electromagnetic fields. Here, the extended Euler–Lagrange differential equation for continuous, nondispersive media is employed. The Lagrangian density for electromagnetic fields is extended to derive all four Maxwell’s equations by means of electric and magnetic potentials. For the first time, ohmic losses for time and space variant fields are included. Therefore, a dissipation density function with time dependent and gradient dependent terms is developed. Both, the Lagrangian density and the dissipation density functions obey the extended Euler–Lagrange differential equation. Finally, two examples demonstrate the advantage of describing interacting physical systems by a single Lagrangian density.

Shifted resonances in coated metamaterial cylinders: Enhanced backscattering and near-field effects

Electromagnetic wave properties in the presence of a thin or thick coating on a cylinder are investigated. The theoretical treatment starts from the formulation of electromagnetic fields in all regions where the coating and the core are allowed to rotate. The angular velocities of the core and coating can be different and even antidirectional. The present general approach can be applied to a wide range of specific cases such as rotating and stationary and left-handed and right-handed core-coating combinations. In particular, the optical resonances due to the surface plolaritons and morphology-dependent resonances are examined. Because of the rotation, the resonances are found to shift, and the effects of velocity on such phenomena are investigated. The backscattering can thus be controlled to achieve suppression or enhancement by using proper metamaterial coatings. Physical insights as well as the numerical results are presented.

Coupling of finite formulation with integral techniques

PurposeThe paper aims to describe the coupling of magnetostatic finite formulation of electromagnetic field with two integral methods.Design/methodology/approachThe first hybrid scheme is based on Green's function applied to magnetization source while the other one is based on a magnetic scalar potential boundary element method. A comparison of the two techniques is performed on a benchmark case with analytical solution, on a 2D multiply‐connected problem and on an industrial case where measurements are available.FindingsThe proposed hybrid approaches have proved to be effective techniques to solve open boundary non‐linear magnetostatic problems. Similar convergence speed with respect to the number of unknowns is found for both schemesOriginality/valueThe paper shows the effectiveness of hybrid schemes applied to the finite formulation, assessing their performances on various test cases.

Pseudo-gradient and Lagrangian boundary control system formulation of electromagnetic fields

This paper describes an electromagnetic field analogue of the classical Brayton–Moser formulation. It is shown that Maxwell's curl equations constitute a pseudo-gradient system with respect to a single electromagnetic mixed-potential functional and a metric defined by the constitutive relations of the fields. Besides its use for the generation of power-based Lyapunov functionals for stability analysis and Poynting-like flow balances, the electromagnetic mixed-potential formulation suggests a family of alternative variational principles. This yields a novel Lagrangian boundary control system formulation admitting nonzero energy flow through the boundary. The corresponding symplectic Hamiltonian system is still associated with the total electromagnetic field energy.

Magnetostatic solution by hybrid technique and fast multipole method

The use of fast multipole method (FMM) in the solution of a magnetostatic problem is presented. The magnetostatic solution strategy is based on finite formulation of electromagnetic field coupled with an integral formulation for the definition of boundary conditions on the external surface of the unstructured mesh. Due to the hypothesis of micromagnetic problem, the resulting matrix structure is sparse and integral terms are only on the RHS. Magnetic surface charge is used as source of these integral terms and is localized on the faces between tetrahedra. The computation of the integral terms can be performed by analytical formulas for the near field contributes and by FMM for far field ones.

Dynamics of an electromagnetic linear actuator operating in error actuated control system

PurposeThe paper seeks to present an algorithm for a dynamical field‐circuit coupled simulation of an electromagnetic linear actuator operating in automated control systems.Design/methodology/approachThe mathematical model includes: a transient electromagnetic field formulation for a non‐linear conducting and moving medium, equations which describe the electric circuits of the converter and the supply system, the equation of mechanical motion, the equation describing closed‐loop control and models for the sensor and the PID controller. The numerical implementation is based on the finite element method and the step‐by‐step algorithm for time discretization. In order to account for the nonlinearity of the ferromagnetic core the Newton‐Raphson procedure has been applied. The influence of the PID controller settings on the operation of the controlled actuator is shown. Dynamic disturbances, e.g. step change of the set value of mover position or change of loading force, have been analyzed.FindingsThe elaborated algorithm and the computer code can be an effective tool for field‐circuit simulation of the dynamics of an electromagnetic linear actuator operating in an automatic control system. Only tapered plunger should be used as multi‐stable actuators.Originality/valueThe study provides information of value in electromagnetic research.

Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media

We introduce a Hamiltonian formulation of electromagnetic fields in dispersive and absorptive structured media of arbitrary dimensionality; the Kramers-Kronig relations are satisfied by construction. Our method is based on an identification of the photonic component of the polariton modes of the system. Although the medium degrees of freedom are introduced in an oscillator model, only the susceptibility of the medium appears in the derived eigenvalue equation for the polaritons; the theory is applicable to both classical and quantum optics. A discrete polariton spectrum is obtained in the transparent regime below the absorption cutoff frequency, and the normalization condition contains the material dispersion in a simple way. In the absorptive regime, a continuous polariton spectrum is obtained. The expressions for the full electromagnetic field of the system can be written in terms of the modes of a limiting, nondispersive, nonabsorptive system, so the theory is well suited to studying the effect of dispersion or absorption on photonic dispersion relations and mode structure. Available codes for dispersive photonic modes can easily be leveraged to obtain polariton modes in both the transparent and absorptive regimes.

Finite formulation of nonlinear magnetostatics with Integral boundary conditions

This paper describes two hybrid methods coupling finite formulation of electromagnetic fields (FFEF) in a bounded domain to integral boundary conditions taking into account far field conditions. The two hybrid techniques use different boundary conditions: the first formulation is based on Green's function applied to magnetization source inside bounded domain while the other one is based on a boundary-element method on its external surface. Details about the coupling terms are given and handling of different magnetization sources is described, including the fictitious magnetization sources coming from nonlinear solutions. The proposed methods are validated versus different benchmark cases. Comparisons between the two techniques have been performed using different criteria (accuracy and convergence, memory requirements, etc.).

Taub-NUT/bolt black holes in Gauss-Bonnet-Maxwell gravity

We present a class of higher-dimensional solutions to Gauss-Bonnet-Maxwell equations in $2k+2$ dimensions with a $U(1)$ fibration over a $2k$-dimensional base space $\mathcal{B}$. These solutions depend on two extra parameters, other than the mass and the Newman-Unti-Tamburino charge, which are the electric charge $q$ and the electric potential at infinity $V$. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of $\mathcal{B}$. We investigate the existence of Taub-Newman-Unti-Tamburino/bolt solutions and find that in addition to the two conditions of uncharged Newman-Unti-Tamburino solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the black hole. We find that for all nonextremal Newman-Unti-Tamburino solutions of Einstein gravity having no curvature singularity at $r=N$, there exist Newman-Unti-Tamburino solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have nonextreme Newman-Unti-Tamburino solutions in $2+2k$ dimensions only when the $2k$-dimensional base space is chosen to be ${\mathbb{C}\mathbb{P}}^{2k}$. We also find that the Gauss-Bonnet-Maxwell gravity has extremal Newman-Unti-Tamburino solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.