Showing papers on "Magnetic potential published in 2013"

A holographic study on vector condensate induced by a magnetic field

Abstract: We study a holographic model with vector condensate by coupling the anti-de Sitter gravity to an Abelian gauge field and a charged vector field in (3 + 1) dimensional spacetime. In this model there exists a non-minimal coupling of the vector field to the gauge field. We find that there is a critical temperature below which the charged vector condenses via a second order phase transition. The DC conductivity becomes infinite and the AC conductivity develops a gap in the condensed phase. We study the effect of a background magnetic field on the system. It is found that the background magnetic field can induce the condensate of the vector field even in the case without chemical potential/charge density. In the case with non-vanishing charge density, the transition temperature raises with the applied magnetic field, and the condensate of the charged vector operator forms a vortex lattice structure in the spatial directions perpendicular to the magnetic field.

Analytical Torque Calculations and Experimental Testing of Permanent Magnet Axial Eddy Current Brake

Abstract: This paper discusses the braking torque and normal force analysis of axial flux permanent magnet (AFPM)-type eddy current brakes (ECB) on the basis of an analytical field computation using a space harmonic method. On the basis of the magnetic vector potential and a 2D polar coordinate system, permanent magnets considering the eddy current effect are obtained. Additionally, by utilizing the derived analytical field solutions, the braking torque and normal force are predicted. Finite element analysis is employed to confirm the validity of the analysis and compare it with the experimental results obtained from the prototype AFPM-type ECB.

Winding functions in transient magnetoquasistatic field-circuit coupled simulations

Abstract: Purpose – The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation. Design/methodology/approach – The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis. Findings – This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation. Originality/value – The presentat...

Simulation of magneto-induced rearrangeable microstructures of magnetorheological plastomers

Abstract: Magneto-induced microscopic particulate structures of magnetorheological plastomers (MRP) are investigated using particle-level dynamics simulation, as this is a basis for studying the macroscopic physical or mechanical properties of MRP. In the simulation, a modified magnetic dipolar interaction force model is proposed to describe the magnetic interaction of two close magnetized iron particles. Other microscopic analytical models of particle–particle and particle–matrix interactions are also constructed. The simulation results show that chain-like and column-like particulate structures are formed when MRP is placed into a steady uniform magnetic field. When MRP is subjected to a stepwise in-plane rotating magnetic field, the microstructure rearranges to form a layered structure parallel to the rotation plane. Moreover, some other patterns or complex magneto-induced rearrangeable microstructures can be achieved by spatially changing the external magnetic field. With the evolution of the microscopic particulate structure in every changing step of the external magnetic field, the microstructure dependent magnetic potential energy and stress state vary sharply at the beginning and then approach respective stable values gradually.

Inflationary dynamics with a non-Abelian gauge field

Abstract: We study the dynamics of the homogeneous and isotropic universe with a scalar field and an SU(2) non-Abelian gauge (Yang-Mills) field. The scalar field has an exponential potential and the Yang-Mills field is coupled to the scalar field with an exponential function of the scalar field. We find that the magnetic component of the Yang-Mills field assists acceleration of the cosmic expansion and a power-law inflation becomes possible even if the scalar field potential is steep, which may be expected from some compactification of higher-dimensional unified theories of fundamental interactions. This power-law inflationary solution is a stable attractor in a certain range of coupling parameters. Unlike the case with multiple Abelian gauge fields, the power-law inflationary solution with the dominant electric component is unstable because of the existence of nonlinear coupling of the Yang-Mills field. We also analyze the dynamics for the noninflationary regime, and find several attractor solutions.

Relative Permeability in a 3D Analytical Surface Charge Model of Permanent Magnets

Abstract: The analytical surface charge model is used to calculate the magnetic field of magnets in 3D in an unbounded domain. The method combines high accuracy with a short calculation time. However, in the classical method the relative permeability of the magnet is assumed to be equal to air. This introduces an error in the resulting magnetic field strength. In this paper the permeability of the magnet is taken into account in the form of a redistribution of magnetic surface charge. As such, an exact solution for the magnetic field at low relative permeability is obtained. The interaction force between two magnets is calculated using the newly obtained expressions for the magnetic field and compared with FEM and measurements.

Magnetic Vortices, Abrikosov Lattices and Automorphic Functions

Abstract: We address the macroscopic theory of superconductivity - the Ginzburg-Landau theory. This theory %Macroscopic theory of superconductivity is based on the celebrated Ginzburg - Landau equations. First developed to explain and predict properties of superconductors, these equations form an integral part - Abelean-Higgs component - of the standard model of particle physics and, in general, have a profound influence on physics well beyond their original designation area. %These are a pair of coupled nonlinear equations for a complex function (called order parameter or Higgs field) and a vector field (magnetic potential or gauge field). They are the simplest representatives of a large family of equations appearing in physics and mathematics. (The latest variant of these equations is the Seiberg - Witten equations.)

Pyroelectric and pyromagnetic effects on multiphase magneto–electro–elastic cylindrical shells for axisymmetric temperature

Abstract: In this paper, a multiphase magneto?electro?elastic (MEE) cylindrical shell is investigated under thermal environments using semi-analytical finite element procedures. The main aim of this paper is to study the pyroelectric and pyromagnetic effects on multiphase MEE cylindrical shells subjected to a uniform axisymmetric temperature of 50?K under different boundary conditions. This numerical study is mainly focused on the pyroelectric and pyromagnetic effects on system parameters such as thermal displacements, thermal stresses, electric potential, magnetic potential, electric displacements and magnetic flux densities. It is found that there is a significant increase in electric potential due to the pyroelectric and pyromagnetic effects under clamped?free boundary conditions.

Three-Dimensional Analytical Modeling Technique of Electromagnetic Fields of Air-Cored Coils Surrounded by Different Ferromagnetic Boundaries

Abstract: This paper presents a method for the calculation of the self- and mutual inductance of coils surrounded by air, positioned on top of a ferromagnetic plate and placed in a cavity inside a ferromagnetic plate. The magnetic fields around an array of air-cored coils are obtained by means of the three-dimensional magnetic vector potential using Fourier analysis. The current density distribution of a coil is modeled by four straight bars; three different configurations to position these bars against each other are presented as an alternative to model the round corners of a coil. An error of maximum 5% has been obtained in the analytically calculated flux density distribution compared to the values obtained from 3-D finite element simulations. Self- and mutual inductances are calculated for each current density description and compared with finite element simulations and measurements. A good agreement has been found for coils modeled by four overlapping or four trapezoidal bars.

Torque Analysis and Measurements of Cylindrical Air-Gap Synchronous Permanent Magnet Couplings Based on Analytical Magnetic Field Calculations

Abstract: This paper presents the torque analysis and measurements of cylindrical air-gap synchronous permanent magnet couplings based on analytical magnetic field calculations. Employing a magnetic vector potential and a 2-D analytical model with two polar coordinate systems, we obtain the magnetic fields produced by permanent magnets. Then, the analytical torque solutions are derived using these magnetic field solutions and a Maxwell stress tensor method. The analytical results are validated by nonlinear 2-D and 3-D finite element results. Finally, torque measurements are presented to show the effectiveness of the analysis.

Modeling and Analysis of a New 2-D Halbach Array for Magnetically Levitated Planar Motor

Abstract: This paper presents two models of the flux density distribution of a new 2-D Halbach magnet array for magnetically levitated planar motor. The harmonic model is derived by the scalar magnetic potential equation. The analytical model for real-time control is built by taking the amplitude of the flux density at a certain air-gap as the effective amplitudes. Two models are validated by the finite-element method. It is verified that the new magnet array has low high-order harmonics, and can produce larger thrust force with low force ripples, which can be used to improve the performance of the magnetically levitated planar motor.

A High-Order Unstaggered Constrained-Transport Method for the Three-Dimensional Ideal Magnetohydrodynamic Equations Based on the Method of Lines

Abstract: Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must confront the challenge of controlling errors in the discrete divergence of the magnetic field. One approach that has been shown successful in stabilizing MHD calculations are constrained-transport (CT) schemes. CT schemes can be viewed as predictor-corrector methods for updating the magnetic field, where a magnetic field value is first predicted by a method that does not exactly preserve the divergence-free condition on the magnetic field, followed by a correction step that aims to control these divergence errors. In Helzel, Rossmanith, and Taetz [J. Comput. Phys., 230 (2011), pp. 3803--3829] the authors presented an unstaggered CT method for the MHD equations on three-dimensional Cartesian grids. In this approach an evolution equation for the magnetic potential is solved during each time step and a divergence-free update of the magnetic field is computed by taking the curl of the magnetic pot...

Considerations on the Finite-Element Simulation of High-Temperature Superconductors for Magnetic Levitation Purposes

Abstract: A robust and fast numerical course for investigating the magnetic levitation (maglev) performance of high-temperature superconductors (HTSs) is proposed and implemented via finite-element methods (FEMs) in this paper. This numerical course uses the magnetic vector potential as the state variable to establish the partial differential equations (PDEs) for governing the electromagnetic properties of 2-D simplified HTSs, a smoothed Bean-Kim's model of a critical state to describe the nonlinear constitutive law of HTSs, and the advanced algorithm of Jacobian-free Newton-Krylov (JFNK) to handle the nonlinear system of the FEM equation. After being tested, this homemade FEM model was applied to investigate the influence of various FEM parameters, e.g., the dimension of the computational domain, the prescribed tolerance for convergence, the coarseness of the mesh, and the time step, upon the precision of levitation/guidance force on an HTS bulk while moving in a nonuniform field generated by a permanent-magnet track. The most important findings through these studies are that the coarse choice of tolerance can cause the nonphysical phenomena such as the crossings in the force loops, and the numerical results are very robust against the dimension of the computational domain, the coarseness of the mesh, and the time step. Based on these findings, it was found that the time consumed for performing a typical cycle of levitation force calculation is merely a few seconds, making the application of this FEM model for optimizing the HTS maglev system very attractive.

A Mathematical Model for an Hourglass Magnetic Field

Abstract: Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's functions. We use this to derive an analytic form for an hourglass magnetic field pattern created by electrical currents that are concentrated near (but not confined within) the equatorial plane of a cylindrical coordinate system. Our solution is not characterized by a cusp at the equatorial plane, as in previous solutions based on a current sheet. The pattern we derive provides a very good fit to hourglass magnetic field patterns emerging from three-dimensional numerical simulations of core formation, and can in principle be used for source-fitting of observed magnetic hourglass patterns.

An educational path for the magnetic vector potential and its physical implications

Abstract: We present an educational path for the magnetic vector potential A aimed at undergraduate students and pre-service physics teachers. Starting from the generalized Ampere–Laplace law, in the framework of a slowly varying time-dependent field approximation, the magnetic vector potential is written in terms of its empirical references, i.e. the conduction currents. Therefore, once the currents are known, our approach allows for a clear and univocal physical determination of A, overcoming the mathematical indeterminacy due to the gauge transformations. We have no need to fix a gauge, since for slowly varying time-dependent electric and magnetic fields, the ‘natural’ gauge for A is the Coulomb one. We stress the difference between our approach and those usually presented in the literature. Finally, a physical interpretation of the magnetic vector potential is discussed and some examples of the calculation of A are analysed.

Analytical modeling of the transient response of a coil encircling a ferromagnetic conducting rod in pulsed eddy current testing

Abstract: Analytical solutions are obtained in the time domain for the electromagnetic response to the leading edge of a square pulse excitation of a multiple turn current coil, encircling a long ferromagnetic rod, in the linear permeability regime. The resulting equations, obtained using a magnetic vector potential formalism, describe the time-dependent progression of flux into and along the rod. Results are in agreement with finite element solutions obtained for the same geometry. The work is motivated by the requirement for rapid analytical solutions and insight into pulsed eddy current response during inspection of multilayer aluminum aircraft structures in the vicinity of ferrous fasteners.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

Abstract: Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect -- the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology of the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.

Analytical calculation of leakage inductance for low-frequency transformer modeling

Abstract: In this paper, a new method for the calculation of leakage inductances between short-circuited windings is proposed. The main objective is to find an analytical alternative to the finite element method (FEM) for the computation of short-circuit inductances in electromagnetic transients type (EMT-type) programs. Typical EMT-type tools do not provide complex FEM based computation engines for this sole purpose. The new approach is derived from the method of images and uses analytical formulations for magnetic vector potential and energy developed in this work. It is shown that the difference between the inductance calculated with the FEM in 2-D and that computed with the method of images decreases as the number of layers of images increases. Also, it is demonstrated that the classical approach, based on an axial flux distribution, can lead to considerable error if the windings have unequal heights and if they are located far from the core yokes.

A Consistency Condition for the Vector Potential in Multiply-Connected Domains

Abstract: A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply-connected conductors, at zero frequency, the standard boundary conditions on the tangential components of the magnetic field do not uniquely determine the vector potential. We describe a (gauge-invariant) consistency condition that overcomes this nonuniqueness and resolves a long-standing difficulty in inverting the magnetic field integral equation.

Structural aspects of regularized full Maxwell electrodynamic potential formulations using FIT

Abstract: In this paper regularized electrodynamic potential formulations for full Maxwell are presented within the framework of the Finite Integration Technique. The reformulation of the semi-discrete Maxwell Equations into two second order wave equations for the magnetic vector potential and a scalar electric potential is feasible with a Lorenz-type gauge condition. On the other hand, a Coulomb-type condition yields a numerically ill-posed formulation. This is shown using the differential-algebraic equation index concept.

RESEARCH ARTICLE Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Abstract: In this paper, the stress- and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account.Atypical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions obtained in this model can predict the response of the MSMA sample at a quantitative level.

Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Abstract: In this paper, the stress- and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account. A typical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions o...

Study of the load reduction for hydro-generator bearing by hybrid magnetic levitation

Abstract: To solve the problem of heat and friction existing in weight bearing of the hydraulic generator, a new type of magnetic levitation devices is proposed. The devices consist of electromagnetic and permanent magnetic levitation, which share together most of the hydraulic generator rotor weight to reduce axial load on thrust bearing. The permanent magnetic levitation is performed by new repulsive ring Halbach arrays. The new Halbach arrays are analyzed by using magnetic potential equations and superposition principle, and the magnetic flux density formulas are obtained. The formula results are verified by FEM. By further study of 3D model simulation analysis, it is confirmed that the new repulsive ring Halbach arrays can reach the design goal on actual working conditions.

A 3-D analytic eddy current model for a finite width conductive plate

Abstract: Purpose – A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues. Design/methodology/approach – The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time. Findings – The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is val...