Integral Equation Method for Evaluation of Eddy-Current Impedance of a Rectangular,Near Surface Crack Inside a Cylindrical Hole

An integral equation method for solving the eddy-current nondestructive evaluation problem of a flat, rectangular, near surface crack inside of a cylindrical hole in a conducting material is presented. The method involves expanding the Green’s tensor, the incoming field, and the jump in electric potential over the crack in suitable basis functions. Here, plane waves, cylindrical waves, and basis functions related to the Chebyshev polynomials, are used. The way of discretization in this method leads to a formulation where the scattering is defined by a scattering matrix, independent of the incoming field. This presents an advantage, when conducting numerical simulations, since the scattering matrix does not have to be recalculated for every probe position. The numerical calculations are straightforward to perform and model predictions are compared with finite element results.     

Matrix Analysis of 2-D Eddy-Current Magnetic Fields

We present an accurate equivalent circuit model to represent a 2-D eddy-current magnetic field. The magnetic field can be coupled with stranded windings and solid conductors. For use in developing formulations of impedance computation, we present two systematic matrix analysis methods based on the system equations, one using the loop method and the other using the nodal method. In the model, each solid conductor is represented by circuit branches. With this approach, the effect of eddy currents can be fully included. We also present the formulations for the computation of the total power loss for magnetic field-circuit coupled problems. We discuss a common mistake in many applications.      

Dielectric Resonators for the Measurement of Superconductor Thin Films Surface Impedance in Magnetic Fields at High Microwave Frequencies

We present the design and realization of cylindrical dielectric resonators operating in the 40–60 GHz frequency range, designed for the measurement of the surface resistance and of the surface reactance shift in High-T _c Superconductors (HTS) thin films in a dc magnetic field. The resonators are single tone, based on the TE ₀₁₁ mode, and multiple tone, the latter allowing in principle to exploit the simultaneous determination of the surface impedance at different frequencies. As an application example, we report the temperature and field dependencies of the effective surface impedance of some cuprate superconductors thin films. The results are compared with those obtained through the use of a standard metal cavity with a similar Q-factor and operating in the same frequency range. The comparison highlights a superior stability and a higher sensitivity, resulting in an increase of about two orders of magnitude in the resolution of the surface impedance measurement. By contrast, the dissipative part of the superconducting transition (above T/T _c = 0.97) is better studied with the metal cavity. We also present measurements in the vortex state in YBaCa₂Cu₃O_7−δ and Tl₂Ba₂CaCu₂O_8+x that show significantly different physics. PACS: 74.25 Nf.     

Magnetic Field-Based Eddy-Current Modeling for Multilayered Specimens

Eddy-current inspection for nondestructive evaluation has traditionally been investigated in terms of coil impedance signals via theoretical and experimental methods. However, advanced eddy-current techniques use solid-state sensors such as Hall devices, giant magnetoresistive sensors, anisotropic magnetoresistive sensors, and superconducting quantum interference devices for magnetic field measurement to achieve better sensitivity and high temporal and spatial resolution in material evaluation and characterization. Here, we review the Dodd and Deeds integral model and use the truncated region eigenfunction expansion (TREE) method for computation of the magnetic field. This results in series expressions instead of integral ones. Thus, the computation is both simplified and speeded up so that it becomes convenient for solving one-dimensional eddy-current inverse problems. We compare the theoretical results from the analytical model with the results from a numerical simulation based on the finite-element method in terms of accuracy and computation time.     

Error Evaluation of Surface Impedance Boundary Conditions With Magnetic Vector Potential Formulation on a Cylindrical Test Problem

Surface impedance boundary conditions (SIBCs) are used for analysis of a wide range of practical applications such as micro strips, transformers or electrical machines. In this work the SIBC was implemented with classical edge elements using the magnetic vector potential. As known, the SIBC is afflicted with errors when it is being used on curved surfaces and near corners and edges. For this reason this paper investigates the error of the SIBC on curved surfaces. Therefore, simulations have been carried out for different radii and frequencies. The simulation results of the SIBC formulation have been compared with the common formulation for eddy current regions. It will be shown, that the error of the SIBC depends on the relation of the radius to the skin depth. Results are presented and discussed by means of a canonical problem.     

Disk Resonators as Nonlinear Surface Impedance Measurement Tools

The edge-current–free rotational symmetric disk resonator mode, TM₀₁₀, was used as characterization tool for nonlinear surface impedance measurement of Y₁Ba₂Cu₃O_7–x (YBCO) thin films. The microwave surface resistance of high quality epitaxial YBCO thin films as a function of frequencies and rf surface magnetic field H _rf was measured using the circular disk resonator technique. Using this technique the properties degradation of the resonators by edge current crowding effect was avoided. The measured R _s values are divided into three regions. In the low field region (H _rf H _c1J), R _s is independent of H _rf. In the intermediate H _rf region, R _s can be well fitted to the formula of R _s(H _rf) = a(f) + b(f) H _rf ², and b(f) is proportional to f ². This form of microwave surface resistance quantitatively agrees with the modified coupled-grain model with the idea that the materials are composed of identical superconducting grains coupled together by identical intergranular regions that function as Josephson junctions. The experimental results show that the loss mechanisms are extrinsic properties resulting from defects in the films.     

Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials

In this paper, we address the imaging of the spatial distribution of the resistivity of conductive materials by using data from eddy-current nondestructive testing. Specifically, the data consists of measurements of the impedance matrix at several frequencies acquired using a coil array. The imaging method processes the second-order term (estimated from the measured data) of the power series expansion, with respect to frequency, of the impedance matrix. This term accounts for the resistive contribution to changes of the impedance matrix, due to the presence of anomalies in the conductor under test, occurring at relatively low frequencies. The operator mapping a given resistivity distribution inside the conductor into the second-order term satisfies a proper monotonicity property. The monotonicity makes it possible to apply a fast noniterative imaging method initially developed by the authors for elliptic problems such as electrical resistance tomography. Numerical examples show the main features of the proposed method, and demonstrate the possibility of real-time imaging.     

关于轴对称模锻剪切曲面形状的探讨

用上限法研究了轴对称模锻最终阶段变形域与未变形域间边界,即所谓剪切曲面的形状。本文采用抛物线的形式来描述剪切曲面形状,计算结果表明采用抛物线形式来描述剪切曲面形状要比采用矩形线,菱形线、梯形线更符合实际情况,为准确地计算轴对称模锻变形功率奠定了基础。     

A Composite Grid Method for Moving Conductor Eddy-Current Problem

We present fundamentals and procedures of a composite grid method (CGM) for determining eddy currents in moving conductors. Based on the finite-element method (FEM), CGM uses two separate mesh grids - one coarse and one fine - to calculate in the global region and local region separately. The results of the coarse mesh are interpolated onto the boundary of the fine mesh as its Dirichlet's condition. Then two equations are solved in the fine mesh region in order to obtain the reaction force on the boundary, which is reacted on the coarse mesh to modify its right-hand-side load vector. And the equations in the coarse mesh are re-solved. The iteration continues until the results converge. The advantage of CGM is that it allows two overlapped grids differing greatly in size to be meshed independently. Also, the program is easy to modularize and thus has great flexibility and adaptability. Above all, it ensures good numerical accuracy in each grid set. As an example indicates, CGM is effective in handling 2-D moving conductor eddy-current problems that are tedious to solve by conventional methods such as re-meshing or using a Lagrange multiplier.     

Ultrasonic Beam Models for Angle Beam Surface Wave Transducers

ABSTRACT

Explicit three-dimensional (3D) point source and multi-Gaussian beam models are obtained for the Rayleigh waves generated by a surface wave angle beam transducer using an angular plane wave spectrum approach. Simulations show that the multi-Gaussian surface wave beam model agrees well with the point source model while being computationally more efficient. The theoretical predictions obtained with the models are also compared to the experimental measurement results where good agreement with the models is found for both on-axis and off-axis field comparisons.     

An Efficient Harmonic Balance Method for Nonlinear Eddy-Current Problems

A method is presented which determines the steady-state solution of nonlinear eddy current problems. The unknown potentials are represented by Fourier-series and the nonlinear behavior of the material is split into a linear and a nonlinear term using a fixed-point technique. This approach leads to decoupled linear equations for each harmonic component. To take the nonlinearity into account, several fixed-point iterations have to be made. The method avoids calculating transient processes which normally have to be stepped through if using time-stepping methods. The present method is illustrated by two 2-D examples     

An Efficient Harmonic Method for Solving Nonlinear Time-Periodic Eddy-Current Problems

An iterative solution to nonlinear problems of time-periodic eddy currents is performed by directly using the time-harmonic content of the field quantities instead of time-domain techniques employing successive time steps. A linear sinusoidal steady-state field problem is solved to determine the magnetization harmonics at each iteration, with the harmonic values corrected in terms of the actual magnetic induction by applying a fixed-point procedure. To further improve its efficiency, the solution process can be started by retaining a small number of harmonics, with more harmonics subsequently added as needed to achieve the desired accuracy. The proposed method always yields stable results, even when the characteristic B-H is strongly nonlinear, and has a superior computational efficiency with respect to various time-stepping techniques and to the "harmonic balance method."     

Standard Errors for the Eigenvalues in Second-Order Response Surface Models

In the interpretation of the geometry of second-order response surface models, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. In this article, we propose a new method for estimating the standard errors, and hence approximate confidence intervals, of these eigenvalues. The method is simple in both concept and execution. It involves the refitting of a full quadratic model after rotating the coordinate system to coincide with the canonical axes. The estimated standard errors of the pure quadratic terms from this refitting are then used as approximate standard errors of the eigenvalues. Because this approach is based on the canonical form, it is geometrically intuitive and easily taught. Our method is intended as a way for practitioners to get quick estimates of the standard errors of the eigenvalues. In our justification of the approach, we show that it is equivalent to using the delta method proposed by Carter, Chinchilli, and Campbell.     

Substrate Contribution to the Surface Impedance of HTS Films on Si

We study the effects of semiconductor substrates on the surface impedance of high-T _c Superconductor (HTS) YBa₂Cu₃O_7−δ (YBCO) films. The characteristic impedance of silicon (Si) (for different doping levels and for different charge carrier scattering times) is evaluated. In particular, the most relevant features of Si electrodynamics are highlighted by the introduction of suitable normalized quantities. The effective surface impedance of the YBCO films on Si substrates is then calculated and discussed for different temperatures and frequencies in the microwave range, comparing the obtained results to their limiting expressions for bulk and thin-film HTS. Our analysis shows how the widely used thin-film approximation for the surface impedance can fail, critically highlighting the conditions it requires to be correctly used. We show that substrate contributions can heavily influence the overall response.     

用于偏转线圈三维磁场计算的谐波表面磁荷法

将三维磁场计算的表面磁荷法和空间谐波展开技术相结合 ,提出了一种用于偏转线圈磁场计算的谐波表面磁荷法。利用空间谐波的正交性 ,导出了与铁芯表面感应的磁荷各次谐波一一对应的磁场谐波。根据铁芯表面的法向磁场关系 ,建立各次磁荷谐波的积分方程 ,并进行了离散化。此方法将三维问题简化为一维积分方程问题 ,可以处理铁芯磁导率为有限值及铁芯与线匝间具有任意间隙的情况 ,具有较大的普遍适用性。用此方法计算了一个偏转线圈的例子 ,取得了较好的结果。     

Determination of the Effective Impedance of a Cylindrical Induction Heating Device Excited by Rotary Magnetic Fields

In this paper mathematical modeling of circuit parameters that feature the electric performance of a traveling-wave heating induction device is carried out. Rotary magnetic fields are the excitation source, and they come from axial windings having one pair of magnetic poles. The method employed for obtaining impedance parameters is based on main magnetic flux decomposition to partial fluxes along different regions that comprise the assembly. The modeled parameters are compared to those estimated from measurements of an experimental device at 60 Hz. Trials on both magnetic and non-magnetic load showed deviation between theoretical and measured parameters around 7%.     

Design and Evaluation of Magnetic Fields for Nanoparticle Drug Targeting in Cancer

The retention of superparamagnetic nanoparticles under the influence of a high-gradient magnetic field was investigated. A simulation algorithm for prediction of the particle's trajectories and, therefore, the total amount of adhered particles in an artificial vessel was developed. Comparisons between in vitro experiments and simulations showed that the required experimental magnetic moments were greater than the theoretically estimated magnetic moments. This paper presents a method for investigating magnetic fields and for determining the magnetic moment of particles by simulation of their trajectories. The detailed function of magnetic drug targeting is of great importance in animal studies and in human therapies     

THz Wave Emission from Intrinsic Josephson Junctions Controlled by Surface Impedance

Recently terahertz wave emission from intrinsic Josephson junctions without external magnetic fields has been intensively studied, and some emission states have been proposed numerically or theoretically. For the surface impedance Z=1, the McCumber-like state with small spatial dependence of the electric field in the junction becomes stable, while for large and complex Z, the π-phase kink state characterized by translational symmetry breaking along the layered structure becomes stable. In the present study, the relations between these two extreme cases are clarified numerically by solving the coupled equations of the Josephson relations and the Maxwell equations for an experimental width of the junction, 86 μm. The dynamical phase diagram in the surface impedance (Z)–current (J) plane and the optimal value of Z for the strongest emission are evaluated.     

The Surface Tension of Binary Alloys: Simple Models for Complex Phenomena

Surface segregation is the key to understanding the surface tension γ of alloys. The basic phenomena can be demonstrated qualitatively by using the ideal solution model. For a binary system, this model is first used to explain the temperature dependence of the surface tension. A simple criterion is established for sign reversal of the temperature coefficient. The ideal solution model is then extended to include the effect of compound formation. A simple explicit equation is proposed which fits existing data surprisingly well. Paper presented at the Seventh International Workshop on Subsecond Thermophysics, October 6-8, 2004, Orléans, France.     

用交流阻抗法评定输油管道外用防腐蚀涂料

针对江苏油田泄洪道区输油管道所在土壤水分含量大,1 a不定期泄洪的特点,结合各种防腐蚀涂料的实际应用情况和涂层的不同性能,选择3～5种涂料通过现场埋片试验和实验室交流阻抗技术进行了综合评价及比较.结果表明:适合于江苏油田泄洪道区输油管道外用防腐蚀涂料的涂层体系为IPN/IPN、环氧富锌/环氧煤沥青.