Showing papers on "Magnetic potential published in 2006"

Ferroelectricity in spiral magnets

Abstract: It was recently observed that the ferroelectrics showing the strongest sensitivity to an applied magnetic field are spiral magnets. We present a phenomenological theory of inhomogeneous ferroelectric magnets, which describes their thermodynamics and magnetic field behavior, e.g., dielectric susceptibility anomalies at magnetic transitions and sudden flops of electric polarization in an applied magnetic field. We show that electric polarization can also be induced at domain walls and that magnetic vortices carry electric charge.

Determining a magnetic Schroedinger operator from partial Cauchy data

Abstract: In this paper we show, in dimension n >=3, that knowledge of the Cauchy data for the Schroedinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential.

Absolute Conductivity Reconstruction in Magnetic Induction Tomography Using a Nonlinear Method

Abstract: Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential V, a so called A, A-V formulation. A theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise

Semiclassical Pseudodifferential Calculus and the Reconstruction of a Magnetic Field

Abstract: We give a procedure for reconstructing a magnetic field and electric potential from boundary measurements given by the Dirichlet to Neumann map for the magnetic Schrodinger operator in R n , n ≥ 3. The magnetic potential is assumed to be continuous with L ∞ divergence and zero boundary values. The method is based on semiclassical pseudodifferential calculus and the construction of complex geometrical optics solutions in weighted Sobolev spaces.

An Unstaggered, High-Resolution Constrained Transport Method for Magnetohydrodynamic Flows

Abstract: The ideal magnetohydrodynamic (MHD) equations are important in modeling phenomena in a wide range of applications, including space weather, solar physics, laboratory plasmas, and astrophysical fluid flows. Numerical methods for the MHD equations must confront the challenge of producing approximate solutions that remain accurate near shock waves and that satisfy a divergence-free constraint on the magnetic field. Failure to accomplish this often leads to unphysical solutions. In this paper, a high-resolution wave propagation method is developed that utilizes a novel constrained transport technique to keep the magnetic field divergence-free. This approach is based on directly solving the magnetic potential equation in conjunction with a new limiting strategy to obtain a nonoscillatory magnetic field. It is demonstrated in this work that an unstaggered definition of the divergence is the correct one to use in the case of wave propagation methods. Therefore, we solve the magnetic potential equation on the same grid as the MHD equations; hence the usual grid staggering that is found in constrained transport methods is eliminated. We demonstrate through truncation error analysis and direct numerical simulation that the resulting method is second order accurate in space and time for smooth solutions and nonoscillatory near shocks and other discontinuities. The resulting numerical method has been implemented as an extension to the clawpack software package and can be freely downloaded from the Web.

Time-odd triaxial relativistic mean field approach for nuclear magnetic moments

Abstract: The time-odd triaxial relativistic mean field approach is developed and applied to the investigation of the ground-state properties of light odd-mass nuclei near the double-closed shells. The nuclear magnetic moments including the isoscalar and isovector ones are calculated, and good agreement with Schmidt values is obtained. Taking F-17 as an example, the splitting of the single-particle levels (around 0.7 MeV near the Fermi level), the nuclear current, the core polarizations, and the nuclear magnetic potential, i.e., the spatial part of the vector potential due to the violation of the time reversal invariance, are investigated in detail.

Fabrication of three-dimensional magnetic microdevices with embedded microcoils for magnetic potential concentration

Abstract: Novel magnetic microdevices were developed for magnetic field generation and concentration and successfully characterized and tested for magnetic potential focusing which is very important for various MEMS applications such as magnetic particles manipulation. These microdevices have been fabricated using an innovative processing sequence which eliminates many problems associated with other fabrication techniques and provides a platform for adding other subsequent fabrication steps required to integrate the microcoils with other microcomponents. They consist of high aspect ratio planar coils made of electroplated copper embedded in the silicon substrate, with ferromagnetic pillars and backside plates made of a CoNiP ternary alloy. A large magnetic field gradient is generated and enhanced by two structural parameters: the small width and high aspect ratio of each single conductor and the ferromagnetic pillars positioned at high flux density locations. This arrangement creates very steep magnetic potential wells, in particular at the vicinity of the pillars. The manipulation of micromagnetic particles in a static and continuous flow conditions has been demonstrated.

Iron losses under PWM excitation using a dynamic hysteresis model and finite elements

Abstract: A dynamic hysteresis model is used with a 2-D magnetic vector potential finite element formulation. The scheme models traditional eddy current, static BH and anomalous losses. The model is used to predict the BH trajectory and hence the losses for a FeSi lamination with a PWM type excitation. The experimental results show good agreement with the finite element predictions

3-D eddy current analysis in the end region of a turbogenerator by using reduced magnetic vector potential

Abstract: This paper presents a novel strategy to model the full three-dimensional structures of end region of huge turbine-generators with power level up to 1000MW. The 3-D nonlinear anisotropic magnetic field including the eddy current losses is calculated by utilizing the reduced magnetic vector potential formulation. With the help of Biot-Savart's law, the magnetic field caused by currents in the stator and rotor windings, which are very complex in geometric shapes, can be calculated in a far easy way. The flux density distribution in the end region and the eddy current distribution in the structural parts under different operating conditions are presented

A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading

Abstract: The analysis of intensity factors for a penny-shaped crack under thermal, mechanical, electrical and magnetic boundary conditions becomes a very important topic in fracture mechanics. An exact solution is derived for the problem of a penny-shaped crack in a magneto-electro-thermo-elastic material in a temperature field. The problem is analyzed within the framework of the theory of linear magneto-electro-thermo-elasticity. The coupling features of transversely isotropic magneto-electro-thermo-elastic solids are governed by a system of partial differential equations with respect to the elastic displacements, the electric potential, the magnetic potential and the temperature field. The heat conduction equation and equilibrium equations for an infinite magneto-electro-thermo-elastic media are solved by means of the Hankel integral transform. The mathematical formulations for the crack conditions are derived as a set of dual integral equations, which, in turn, are reduced to Abel's integral equation. Solution of Abel's integral equation is applied to derive the elastic, electric and magnetic fields as well as field intensity factors. The intensity factors of thermal stress, electric displacement and magnetic induction are derived explicitly for approximate (impermeable or permeable) and exact (a notch of finite thickness crack) conditions. Due to its explicitness, the solution is remarkable and should be of great interest in the magneto-electro-thermo-elastic material analysis and design.

Thermal Stress Analysis in Magneto-Electro-Thermo-Elasticity with a Penny-Shaped Crack Under Uniform Heat Flow

Abstract: The magnetoelectroelastic material possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. Piezoelectric-piezomagnetic materials exhibit magneto-electric effect. When magneto-electro-elastic materials are subjected to thermal flow, they can fracture prematurely due to their brittle behavior. Hence, it should be important to know the fracture behavior of magneto-electro- elastic materials. The penny-shaped crack problem in a medium possessing coupled electro-magneto-thermo-elastic is considered in this paper. It is assumed that the crack is isothermal. The analysis is an exact treatment of penny-shaped crack in a magneto-electroelastic solid subjected to uniform heat flow far away from the crack region. The governing equations of temperature, elastic displacements and electric potential as well as magnetic potential for an anisotropic magneto-electro-elastic medium are partial differential equations of second order, ...

Magnetic vector potential based model for eddy-current loss calculation in round-wire planar windings

Abstract: An analytical development of the magnetic vector potential is used to investigate the losses in round-wire planar windings. The current distribution in wires is affected by the skin effect and the field created by adjacent wires (proximity effect). This field depends on the current distribution in conductors, resulting in a closed-form problem. In this paper, we obtain the vector potential outside a conductor to estimate the effect of induced currents in the field shape over the neighboring conductors. We use the results to calculate the losses in planar windings such as those in domestic induction heaters. We obtain an equivalent resistance representing the losses in windings and compare it with measurements. This solution provides an accurate analytical approach to modeling the losses in close-packed windings

Scattering by magnetic fields

Abstract: Consider the scattering amplitude s(ω, ω′;λ), ω, ω′ ∈ Sd−1, λ > 0, corresponding to an arbitrary short-range magnetic field B(x), x ∈ Rd. This is a smooth function of ω and ω′ away from the diagonal ω = ω′ but it may be singular on the diagonal. If d = 2, then the singular part of the scattering amplitude (for example, in the transversal gauge) is a linear combination of the Dirac δ-function and of a singular denominator. Such structure is typical for long-range magnetic scattering. We refer to this phenomenon as to the long-range Aharonov-Bohm effect. On the contrary, for d = 3 scattering is essentially of short-range nature although, for example, the magnetic potential A(tr)(x) such that curlA(tr)(x) = B(x) and 〈A(tr)(x), x〉 = 0 decays at infinity as |x|−1 only. To be more precise, we show that, up to the diagonal Dirac function (times an explicit function of ω), the scattering amplitude has only a weak singularity in the forward direction ω = ω′. Our approach relies on a construction in the dimension d = 3 of a short-range magnetic potential A(x) corresponding to a given short-range magnetic field B(x).

Symplectic duality system on plane magnetoelectroelastic solids

Abstract: By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic industion, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.

Stationary field-aligned MHD flows at astropauses and in astrotails - Principles of a counterflow configuration between a stellar wind and its interstellar medium wind

Abstract: Context. A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. Aims. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few governing parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points (neutral points) of the magnetic field within these flows. Methods. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the governing MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. Results. The topological structure, i.e. the distribution of magnetic neutral points, determines the geometrical structure of the interstellar gas – stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail/astrosheath region beyond the reverse shock. Conclusions. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows.

Streamline upwinding in a 3-D edge-element method modeling eddy currents in moving conductors

Abstract: A vector form of streamline upwinding is proposed for a three-dimensional edge-element formulation modeling static eddy currents in moving conductors. The streamline upwinding has been implemented in a formulation using a magnetic vector potential and an electric scalar potential and is shown to be very effective in improving convergence

Electromagnetic analysis and control parameter estimation of moving-coil linear oscillatory actuator

Abstract: This paper deals with an electromagnetic analysis and control parameter estimation of a moving-coil linear oscillatory actuator (MCLOA). Analytical solutions for electromagnetic characteristics of the MCLOA are obtained from transfer relations derived in terms of a magnetic vector potential and two-dimensional (2D) rectangular coordinate systems. And then, on the basis of 2D analytical solutions, control parameters such as the thrust constant, the back-emf constant, and winding inductances are estimated. Finally, analytical results for both electromagnetic characteristics and control parameters of the MCLOA are validated extensively by finite element analyses. In particular, test results such as static thrust, resistance, and inductance measurements are given to confirm the analyses.

A time‐domain finite element homogenization technique for lamination stacks using skin effect sub‐basis functions

Abstract: Development of an homogenization technique to directly and efficiently take the eddy current effects in laminated magnetic cores within time domain finite element (FE) analyses. The technique is developed for being used within a 3D magnetodynamic b-conform FE formulation, e.g., using a magnetic vector potential. To avoid a fine FE discretization of all the laminations of a magnetic core, this one is considered as a source region that carries predefined current and magnetic flux density distributions describing the eddy currents and skin effect along each lamination thickness. Both these distributions are related and are first approximated with sub-basis functions. Through the homogenization or averaging of the sub-basis functions contributions in the FE formulation, the stacked laminations are then converted into continuums, thus implicitly considering the eddy current loops produced by parallel magnetic fluxes. The continuum is then approximated with classical FE basis functions and can be defined on a coarser discretization. The developed method appears attractive for directly and efficiently taking into account within finite element analyses the eddy current effects, i.e., the associated losses and magnetic flux reduction, that are particularly significant for high frequency excitations. The time domain analysis allows the consideration of both nonlinear and transient phenomena. The averaging of sub-basis functions contributions, describing fine distributions of fields in a FE formulation, leads to an original way to homogenize laminated regions. The proposed method is naturally adapted for time domain analyses and in some sense generalizes what can be done more easily in the frequency domain.

On the structure of the lower edge of the spectrum of the periodic magnetic Schrödinger operator with small magnetic potential

Abstract: For the periodic magnetic Schrödinger operator, the structure of the lower edge of the spectrum is investigated. It is known that in the nonmagnetic case the energy depends quadratically on the quasimomentum in the neighborhood of the lower edge of the spectrum. Herewith, the operator admits a convenient “multiplicative” factorization, which makes it possible to investigate the threshold effects efficiently. It is shown that for sufficiently small magnetic potential the magnetic Schrödinger operator also admits a similar factorization. §0. Introduction 0.1. Let Γ be a lattice in R, d ≥ 1, and let Ω be an elementary cell of the lattice Γ. It is known (see, e.g., [Sk]) that the Γ-periodic differential operators (DOs) can be partially diagonalized with the help of the Gelfand transformation. Then the initial DO is represented as a direct integral of a family of DOs that depend on a parameter k ∈ R (called the quasimomentum) and act on the torus associated with Ω. We consider lower semibounded selfadjoint DOs. For most of the DOs occurring in mathematical physics, the spectrum of the associated operators acting in L2(Ω) is discrete. Let Ej(k), j = 1, 2, . . . , be the corresponding eigenvalues arranged in nondecreasing order. The functions Ej(k) depend on k continuously. Then the spectrum of the initial DO has a band structure. The bands coincide with the images of the band functions Ej(·). It is convenient to assume that the lower edge of the spectrum is λ = 0. It turns out that the solution of certain questions only requires the knowledge of the structure of the spectrum lower edge. In such cases we talk about threshold effects. One of the brightest examples of a threshold effect is the homogenization problem, i.e., the study of the behavior of a periodic DO in the small period limit. 0.2. In [BSu], a general method was developed to investigate threshold effects for operators admitting a convenient (“regular”) factorization. In the scalar case this factorization is described by the following condition: the operator M in question admits a representation in the form (0.1) M = f−1(x)b(D)∗G(x)b(D)f−1(x), b(D) := d ∑

Determination of frequency dependent characteristics of substation grounding systems by vector finite element analysis

Abstract: A three-dimensional finite-element tool was developed to compute time-harmonic electromagnetic fields and impedance of substation grounding systems. The formulation employs edge-based finite elements for the magnetic vector potential A and nodal shape functions for the electric scalar potential V. The method has been applied in several configurations presented in the literature. The results are compared with both analytical and experimental data reported by other authors, with overall good agreement

Spectral shift function for magnetic schrodinger operators

Abstract: In this survey article based on the papers [7, 10], and [8], we consider the 3D Schrodinger operator with constant magnetic field of intensity b > 0, perturbed by an electric potential V which decays fast enough at infinity, and discuss various asymptotic properties of the corresponding spectral shift function. More precisely, let H0 = H0(b) := (i∇+A)2−b be the unperturbed operator, essentially self-adjoint on C∞ 0 (R ). Here A = ( − bx2 2 , bx1 2 , 0 ) is the magnetic potential which generates the constant magnetic fieldB = curl A = (0, 0, b), b > 0. It is well-known that σ(H0) = σac(H0) = [0,∞) (see [1]), where σ(H0) stands for the spectrum of H0, and σac(H0) for its absolutely continuous spectrum. Moreover, the so-called Landau levels 2bq, q ∈ Z+ := {0, 1, . . .}, play the role of thresholds in σ(H0). For x = (x1, x2, x3) ∈ R we denote by X⊥ = (x1, x2) the variables on the plane perpendicular to the magnetic field. Throughout the paper we assume that the electric potential V satisfies

Approximation by point potentials in a magnetic field

Abstract: We discuss magnetic Schrodinger operators perturbed by measures from the generalized Kato class. Using an explicit Krein-like formula for their resolvent, we prove that these operators can be approximated in the strong resolvent sense by magnetic Schrodinger operators with point potentials. Since the spectral problem of the latter operators is solvable, one in fact gets an alternative way to calculate discrete spectra; we illustrate it by numerical calculations in the case when the potential is supported by a circle.

Time domain sensitivity analysis of electromagnetic quantities utilising FEM for the identification of material conductivity distributions

Abstract: Purpose – This paper aims to present effective methods for computing electromagnetic field sensitivity in the time domain versus conductivity perturbations in finite elements.Design/methodology/approach – Two‐dimensional cases in linear, isotropic media are considered and two effective methods for sensitivity analysis of a magnetic vector potential in the time domain are described.Findings – The paper finds that the convergence of numerical identification algorithm depends on exact measurement of magnetic flux density. For identification of real cracks the application of data filtering and TSVD regularization of Gauss‐Newton algorithm is necessary.Practical implications – The resultant gradient information may be used for solving inverse problems such as the identification of material conductivity distributions.Originality/value – The algorithms described are based on known methods from established circuit theory – incremental circuit and adjoint circuit, these have been expanded to apply in electromagnet...