A Magnetostatic Model for Square Spiral Inductors Incorporating a Magnetic Layer

Embedding magnetic layers in inductors is an attractive option for increasing inductance density, which is a critical issue for radio-frequency applications. In this letter, we develop a magnetostatic model for square spiral inductors incorporating a magnetic layer. In our model, we assume that the permeability of the magnetic layer is isotropic and infinite. The model provides a fast and effective numerical calculation of the inductance of inductors incorporating a magnetic layer. We show the derivation of the model and provide calculation results for various inductor structures.      

Finite element solution of 3D magnetostatic field problems involving distributed current using a single scalar potential--The modification and application of the fictitious magnetic monopole model

In this paper the authors present a new model for magnetostatic field problems - the modified fictitious magnetic monopole model, in which a new kind of scalar potential is used which is suitable for the whole region, including the distributed current region. In the FMMM the exciting action of the distributed current density has been replaced by that of a distributed fictitious magnetic monopole density, and the problem of loss of precision (subtraction of two large but similar quantities in the computer) has been solved by putting a magnetic shell into the coil and/or current-carrying conductor loop. According to the new model, the formulation of a magnetostatic problem has almost the same form as that of an electrostatic problem, thus the calculation of magnetostatic problems can be simplified significantly. The new model can also be regarded as a modification for the two-scalar potential model or for the T-Q method in magnetostatic cases. Calculation and test results of some examples of 3D magnetostatic problems are given to verify this new method.     

Diffraction of normal compression waves by a penny-shaped crack in the presence of an axial magnetic field

The problem of diffraction of normally incident compressional waves by a penny-shaped crack located in a perfectly conducting, infinite, isotropic, elastic solid permeated by an uniform magnetostatic field is considered. Using an integral transform technique, the problem is reduced to that of solving a Fredholm integral equation of the second kind having a finite integral kernel. The dynamic singular stress distributions near the crack tip are obtained in closed form and the effects on the dynamic stress-intensity factors due to the presence of the magnetic field are shown graphically. For low frequencies, the dynamic stress-intensity factors are expressed in series of ascending powers of the normalized frequency. The approximate solutions are compared with exact solutions.     

Three-dimensional magnetostatic field calculation using boundaryelement method

The boundary-element calculation of three-dimensional magnetostatic field problems using the reduced and total magnetic scalar potential formulation is described. The method is based on a boundary integral equation that can be derived from Green's theorem. Two regions, a current-free iron region and an air region including the source domains, are considered. The material properties of the iron are assumed to be linear and either isotropic or anisotropic (orthotropic). Two examples are investigated: a C-shaped magnet and an iron cylinder of finite length immersed in the magnetic field of a cylinder coil     

Penalized-likelihood image reconstruction for digital holography

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.     

Impact response of a cracked soft ferromagnetic medium

A solution is given for the problem of an infinite soft ferromagnetic solid containing a central crack subjected to normal impact load. The solid is permeated by a uniform magnetostatic field normal to the crack surface. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of integral equations in the Laplace transformed plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factor, and the results are compared with the corresponding elastodynamic values to reveal the influence of magnetic field on the dynamic stress-intensity factor. The dynamic stress intensity factor is found to increase with increasing values of the magnetic field.With 4 Figures     

Magnetic recording on domain walls in a single crystal film

The existing magnetic data recording media employ polycrystalline tracks, on which data are encoded using domains with different orientations of magnetic moments. We have numerically simulated data recording on the track in a single crystal film, in which the domain structure is formed using an intrinsic magnetostatic field of the crystal and the Bloch domain walls play the role of information bits.     

Eigenvalue solutions for free motion of electroconductive plate in magnetic field

Free flexural motion of a homogeneous plate in a large magnetostatic uniform field is re-examined. Linearized theory of thin plates made of an elastic electroconductive non-magnetizable isotropic material is applied. The intermediate approach (three-dimensional in the electromagnetic part and two-dimensional in the mechanical part), four two-dimensional models using various electromagnetic thickness assumptions as well as the perfect conduction case are reviewed. The resulting eigenvalue solutions of first-order approximation with respect to the bias magnetic field are compared analytically and numerically for both the in-plane and transverse bias magnetic field. Some estimations and improvements are included.     

Nonlinear 3D magnetostatic field calculation by the integralequation method with surface and volume magnetic charges

The authors present a mathematical model for the 3-D nonlinear magnetostatic field based on integral equations with fictitious surface and volume magnetic charges. The solution is performed by the extended boundary element method including surface elements and volume elements. Examples of calculation for both linear and nonlinear magnetic systems are presented. The method has been shown to be accurate and efficient     

Numerical analysis for eddy current characteristics of magnetically saturated ferromagnetic tubes

Magnetic saturation is applied to ferromagnetic tubes inspected by the encircling or inner coil because suppressing magnetic noise is important for the eddy current testing technique. Eddy current signal characteristics in magnetically saturated tubes are different from those in nonmagnetic tubes. In ferromagnetic tubes, defect signal phase angle is not useful for estimating defect depth because it does not depend on the defect depth. In this paper, numerical eddy current analysis has been done in order to explain the relationship between the defect depth and the phase angle in magnetically saturated tubes. This analysis is performed as follows: 1) The magnetic permeability near the defect is calculated as the non-linear magnetostatic problem. 2) The eddy current distribution is calculated as the linear magnetodynamic problem using the incremental permeability value calculated in step 1. The numerical analysis results reveal that the permeability around the defect remains inhomogeneous and it causes the unique eddy current characteristics. Based on these calculated results, a quantitative evaluation method of determining defect depth is proposed. After determining the defect shape by using signal characteristics obtained from the strongly magnetizing state, the defect depth can be estimated by using the signal amplitude.     

Three‐dimensional magnetostatic problem

The paper is devoted to an approximation of the solution of Maxwell's equations in three‐dimensional space. We present two methods which couple a finite element method inside the magnetic materials with a boundary integral method which uses Poincaré–Steklov's operator to describe the exterior domain. A computer code has been implemented for each method and a number of numerical experiments have been performed to validate each proposed methodology. Namely, we present numerical results concerning a non‐linear magnetostatic problem in ℝ³. Copyright © 1999 John Wiley & Sons, Ltd.     

Magnetic imaging of reinforcing steel

A new nondestructive evaluation technique is proposed to image steel reinforcement in reinforced concrete structures. One imposes a static magnetic field on a reinforced concrete member and measures the distortion of that field due to the magnetization of the reinforcement. The distribution of magnetization within the member is determined by inverting linearized fundamental equations of magnetostatics. A second set of equations, involving the ambient magnetic field and the magnetic susceptibility of steel, relates the magnetization to the volume of steel. Simple finite-element simulations were performed to investigate the performance of the reconstruction algorithm. The present version of the algorithm differentiated clearly between widely-spaced cubes of steel and air. The reconstructions were less successful when the cubes were adjacent. Some areas that deserve further development were identified. The magnetostatic principles underlying the imaging technique could also be applied to locate ferromagnetic objects for other applications.     

Magnetothermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating

A solution is given for the induced temperature and stress fields in an infinite transversely isotropic solid continuum with a cylindrical hole. The solid medium is considered to be exposed to a magnetic field and the cavity surface is assumed to be subjected to a ramp-type heating. Green and Lindsay model has been used to account for finite velocity of heat conduction. Magnetic field induced within the cavity is also determined. The problem is solved analytically by using integral transform technique.     

SQUID tomographic neuromagnetic imaging

The human brain emits a measurable magnetic field in response to stimulation. The aim of neuromagnetic imaging is to produce maps of the underlying neuronal activity from measurements of the emitted magnetic field. Modeling neuronal activity by dipolar current sources, we have previously reported simulation studies to reconstruct planar source distributions using the algebraic reconstruction technique, with the constraint that the sources could only have two orientations. We now present a general solution for two-dimensionally distributed sources, which is based on measuring both the normal and tangential components of the magnetic field. Also, using a single-channel SQUID neuromagnetometer, we present results of a tomographic imaging experiment conducted with wires carrying currents to demonstrate the potential of neuromagnetic imaging in reconstructing extended cortical sources.     

Numerical Analysis for Eddy Current Characteristics of Magnetically Saturated Ferromagnetic Tubes

Abstract

Magnetic saturation is applied to ferromagnetic tubes inspected by the encircling or inner coil because suppressing magnetic noise is important for the eddy current testing technique. Eddy current signal characteristics in magnetically saturated tubes are different from those in nonmagnetic tubes. In ferromagnetic tubes, defect signal phase angle is not useful for estimating defect depth because it does not depend on the defect depth. In this paper, numerical eddy current analysis has been done in order to explain the relationship between the defect depth and the phase angle in magnetically saturated tubes. This analysis is performed as follows: 1) The magnetic permeability near the defect is calculated as the non-linear magnetostatic problem. 2) The eddy current distribution is calculated as the linear magnetodynamic problem using the incremental permeability value calculated in step 1. The numerical analysis results reveal that the permeability around the defect remains inhomogeneous and it causes the unique eddy current characteristics. Based on these calculated results, a quantitative evaluation method of determining defect depth is proposed. After determining the defect shape by using signal characteristics obtained from the strongly magnetizing state, the defect depth can be estimated by using the signal amplitude.     

An evaluation of the computational error near the boundary withmagnetostatic field calculation by BEM

A 3-D magnetostatic field is calculated using the reduced scalar potential method for a two-region model: a current-free iron region with linear and isotropic property, and an air region including the source domain. An unstable computational error near the boundary is investigated from the viewpoints of numerical integration and discretization. Specifically it is shown that near the boundary elements, the calculated results of the magnetic flux density often contain an unstable error. The error is affected by the fineness of the discretization, the point number for Gaussian quadrature, and the distance from the boundary elements. It is found that close integration of the internal field calculation effectively removes the unstable computational error     

Magnetostatic interactions in antiferromagnetically coupled patterned media

In an array of closely spaced magnetic islands as in patterned media, magnetostatic interactions play a major role in widening the switching field distribution and reducing the thermal stability. Patterned antiferromagnetically coupled (AFC) media provide interesting systems for studying the effect of magnetostatic interactions on the reversal of closely spaced AFC bits in an array, as AFC structure helps to reduce the remanent magnetization (M(r)), leading to reduced magnetostatic interactions. Here, we study the magnetic reversal of single domain-patterned AFC CoCrPt:oxide bilayer system with perpendicular magnetic anisotropy, by imaging the remanence state of the bits after the application of a magnetic field with magnetic force microscopy (MFM). The influence of magnetostatic fields from the neighboring bits on the switching field distribution (SFD) for an entity in a patterned media is studied by varying the stabilizing layer thickness of the AFC structure and bit spacing. We observe a distinct increase in stability and coercivity with an increase in stabilizing layer thickness for the 40 nm spaced bits. This demonstrates the effectiveness of the AFC structure for reducing magnetostatic interactions in patterned media, such that high thermal stability can be achieved by the reduced M(r), without writability issues.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Computation of magnetostatic fields in three-dimensions based on Fredholm integral equations

An integral equation method is described for solving three-dimensional magnetostatic problems involving linear permeability interfaces and current sources. The interface is replaced by magnetic charges in free space to provide an equivalent interface condition. Application has been made to leakage field calculations in transformers. Numerical methods are combinations of analytical formulas and numerical integration; basis functions approximate the charge distribution.