Tangential Component Of Magnetic Field Research Articles

Prandtl boundary layer expansion with strong boundary layers for inhomogeneous incompressible magnetohydrodynamics equations in Sobolev framework

We consider the validity of Prandtl boundary layer expansion of solutions to the initial boundary value problem for inhomogeneous incompressible magnetohydrodynamics equations in the half-plane when both viscosity and resistivity coefficients tend to zero, where the no-slip boundary condition is imposed on velocity while the perfectly conducting condition is given on magnetic field. Since there exist strong boundary layers, the essential difficulty in establishing the uniform L∞ estimates of the error functions comes from the unboundedness of vorticity of strong boundary layers. Under the assumptions that the viscosity and resistivity coefficients take the same order of a small parameter and the initial tangential component of magnetic field has a positive lower bound near the boundary, we prove the validity of Prandtl boundary layer ansatz in L∞ sense in Sobolev framework. Compared with the homogeneous incompressible case considered in [33], there exists a strong boundary layer of density. Consequently, some suitable functionals should be designed and the elaborated co-normal energy estimates will be involved in analysis due to the variation of density and the interaction between the density and velocity.

VARIATIONS IN MAGNETIC PROPERTIES PROPAGATION IN STEEL SHELL STRUCTURE CAUSED BY WELDING (PART 2)

The first stage of the research involves analyzing primary and secondary acoustic wave propagation behavior. The results of the first stage suggest that the properties of shell structures used at every stage of the experiment are distributed unevenly along the generator lines and across the width of the test pipes. In order to conduct a comparative study of properties, the authors of the research introduce the heterogeneity parameter. During the experiment, the parameter is changing locally within two orders of magnitude, even in case of test pipes in their initial state. Equal sensitivity to heterogeneities across steel products is found in its magnetic properties. As numerous studies prove, analyzing variations in magnetic properties makes it possible to detect flaws and areas of their concentration. This method can also be used to estimate the remaining service life. This is a crucial aspect to consider when assessing properties and using the findings to develop digital twins of shell structures. The authors focus on identifying acoustic and magnetic signals coming from flawed shell structures and weld joint areas in particular. For this purpose, magnetic memory method and X-ray analysis are used. It is found that both normal and tangential magnetic field components are sensitive to structural heterogeneities across a steel product. The combination of magnetic memory method and X-ray analysis make it possible to determine how typical weld joint flaws occurring during welding affect the magnetic properties. Sufficient measurements are required for statistical analysis of the findings. It is also possible to introduce further criteria in order to import metal properties correctly into the modelling program using numerical methods.

EMC Impact of Disturbances Generated by Multiple Sources

In this paper, the impact of an increasing number of arbitrary electrical/electronic devices on the overall radiated emissions is investigated. Understanding and quantifying such an impact are prerequisites to the proper evaluation of electromagnetic compatibility (EMC) of various electronic systems and devices and, if needed, to revisiting the international standards. To evaluate the radiated emissions from multiple electronic devices, each arbitrary electronic device is characterized using an equivalent Huygens’s surface, in which the tangential components of electric and magnetic near fields are calculated (or measured). The radiated emission from the arbitrary electronic device can be calculated using the electric and magnetic near fields for an arbitrary phase (correlated or uncorrelated), position, and orientation. The influence of several parameters affecting the radiated emissions from multiple arbitrary electronic devices, including the number of disturbance sources, the polarization of each device, the radiation pattern of each device, the location and orientation of each device, and the phase shifts between devices, are analyzed. The numerical results show that the mentioned parameters have a significant effect on the radiated emissions, and cannot be neglected in EMC considerations. In general, increasing the number of electronic devices leads to an increase in the level of radiated emissions. However, the increase depends on other parameters such as the arrangement (the radiation pattern for each device, the distance between the devices, and the orientation and/or polarization of each device). The proposed method can be straightforwardly applied to devices characterized by near-field measurements or multimodular large equipment with long cables.

A Boundary Element Procedure for 3D Electromagnetic Transmission Problems with Large Conductivity

We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.

A High-Sensitivity and Shielding-Free Rabbit Brain MIPS Scanner

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Goal:</i> The purpose of this paper is to improve the detection sensitivity and quantitative assessment of different levels of cerebral hemorrhage (CH), a high-sensitivity and shielding-free rabbit brain magnetic induction phase shift (MIPS) scanner was developed and validated. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> First, a uniform rotating magnetic field generated by a birdcage coil was utilized instead of the divergent magnetic field for the first time, and the birdcage structure has inherent characteristics of shielding external interference. Furthermore, the primary field was cancelled, and the axial and tangential magnetic field components of the secondary magnetic field were synchronously detected and then synthesized for the first time using a magnetron sensor coil and a circular solenoid coil. Specifically, a field programmable gate array-based spectrometer was used to guarantee the two-channel signal of high-precision quadrature excitation for birdcage coil, signal acquisition, and data processing. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> Experimental results indicated that the phase shift difference decreases linearly with the volume increase of blood injection, and the average MIPS caused by a 3-ml blood injection of rabbit inner capsule hemorrhage was 2.709°, which was 7.7 times higher than that of the traditional single excitation coil and single receiving coil (single coil–coil) method. The results have proven that this scanner has high sensitivity, strong anti-interference ability, and potential to realize the quantitative detection of hematoma volume.

The properties of mid infrared surface modes at the interface of air and one dimensional ternary photonic crystal

In the present manuscript, theoretical design of truncated one dimensional ternary photonic crystal is proposed for analyzing the properties of transverse electric (TE) surface modes viz. band structures, its localization in photonic band gaps (PBGs), field profiles and energy carried by these modes. The periodicity of the structure (comparable to the wavelength of incident electromagnetic waves) is chosen as such the modes are localized in mid-infrared frequency domain (600cm−1 to 1800cm−1 or 5μm to 16μm). The dispersion relation of surface modes is derived by using continuity condition of tangential components of electric and magnetic fields and transfer matrix method. It is found that by varying the cap layer thicknessdc and thickness of first layerdt of each unit cell, surface modes are either strongly (near center of PBG with decay length ~8.8μm) or weakly (near edge of PBG with decay length ~42.5μm) bounded to the interface. The energy carried by the surface modes along the interface plane is around 3.3mJ while across the interface plane it is of the order of10−14. It has been proved that the material rich modes (~2V/m) have high field enhancement compared to material deficient modes (~1V/m). The study stresses on different aspects of the proposed model that can be sought for suitable practicable applications in mid-infrared photonics, especially in design of mid-infrared bio-chemical sensors, mid-infrared temperature sensors, waveguides, omnidirectional reflectors, optical filters, band edge lasers, multiplexers, mitigators, compensators, etc.

Investigation on arc characteristics in cup‐shaped contacts with different structure for transverse magnetic field vacuum circuit breaker

AbstractThe cup‐shaped transverse magnetic field (TMF) contacts contain radial components and tangential components in the TMF generated when the current is interrupted. The tangential force generated by the radial magnetic field component drives the vacuum arc to rotate, and the tangential magnetic field component generates a radial force that causes the vacuum arc to move radially outward. In this paper, in order to study the influence of the arc force direction on the arc characteristics, the influence of the contact structure parameters such as the inclination of the inner wall on the arc force direction is simulated, and the breaking tests of different levels of current are carried out on the contact with different structure parameters. It is found that the direction of the Lorentz force has a significant effect on the breaking characteristics of the current, and the tangential and radial force components have varying degrees of influence on the motion characteristics of the arc during the start process and the metal droplet splashing.

Analytical Model of Open-Circuit Air-Gap Field Distribution in Interior Permanent Magnet Machines Based on Magnetic Equivalent Circuit Method and Boundary Conditions of Macroscopic Equations

To accurately and quickly predict the open-circuit air-gap magnetic field in interior permanent magnet synchronous machines (IPMSMs), an analytical model based on magnetic equivalent circuit (MEC) method is proposed. The analytical model can provide radial and tangential components of open-circuit magnetic field in the slotless air gap. The radial component is obtained from the MEC model, and the tangential component is obtained from boundary conditions of macroscopic equations. Then, a complex relative air-gap permeance is applied to take the effect of slots into account. As a result, an accurate solution of both radial and tangential components of the flux density in the slotted air gap is obtained. Additionally, the no-load back electromotive force (EMF) and cogging torque are calculated based on the open-circuit air-gap magnetic field. All the analytical results are verified by the finite element (FE) analysis and they are well matched. In the end, a direct measurement experiment of open-circuit air-gap magnetic field is proposed to verify the validity of both radial and tangential open-circuit air-gap magnetic fields.

Scattering and diffraction of a uniform complex-source beam by a slit in a perfectly conducting plane screen

Abstract. A new multipole solution in plane-polar coordinates for the scattering of an arbitrary TE- or TM-polarized incident field by an infinitely extended slit in a plane screen is derived. To this end a classical three-domain problem with a complete multipole expansion in each of the domains is formulated. The unknown multipole amplitudes are found from the continuity conditions of the tangential electric and magnetic field components. Finally an infinite system of linear equations is derived which can be approximated by a numerically tractable finite one leading to a solution with an arbitrary accuracy. The results are numerically successfully compared to those ones obtained by classically solving the strip problem using Mathieu functions and by a subsequent application of the rigorous form of the Babinet principle. Numerical results include the comparison of the scattered fields obtained for an incident uniform complex-source beam and for an incident plane wave.

Экспериментальное исследование поверхностного натяжения ферроколлоида в магнитном поле

Direct measurements of surface tension, viscosity and surface elasticity under the action of external forces are often impossible. In many tasks, the magnetic fluid surface tension is considered to be independent of the magnitude of the applied magnetic field and is determined by the properties of the base fluid. The anisotropy of the magnetic properties at the interface due to the jump in the fluid’s magnetization suggests the dependence of the surface tension tensor on the magnetic field. In this paper, we propose a new experimental method for studying the surface tension of a magnetic fluid in an external uniform magnetic field, depending on the orientation of the magnetic field intensity towards the liquid-gas interface. The study was carried out with the help of modified capillary wave method in a magnetic field orthogonal to the liquid surface and with the ring detachment method in the case of a longitudinal field. It was shown experimentally that the surface tension of a ferrocolloid fluid base (kerosene) does not depend either on the frequency of capillary waves excitation or on intensity of an applied external magnetic field, and corresponds to the value determined with the help of a commercial tensiometer by the standard method of ring detachment. The surface tension of the ferrofluid decreases with increasing intensity of the orthogonal magnetic field interface and with increasing frequency of acoustic vibrations. However, an increase in the field strength longitudinally directed to the interface, provokes an increase in the surface tension of the magnetic fluid. The experimental results are in qualitative agreement with theoretical predictions by A. V. Zhukov: the eigenvalues of the surface tension tensor monotonically increase with the tangential magnetic field component and monotonically decrease with an increase in its normal component.

Deep neural network Grad–Shafranov solver constrained with measured magnetic signals

A neural network solving the Grad–Shafranov equation constrained with measured magnetic signals to reconstruct magnetic equilibria in real time is developed. The database created to optimize the neural network’s free parameters contains off-line EFIT results as the output of the network from 1118 KSTAR experimental discharges of two different campaigns. Input data to the network constitute magnetic signals measured by a Rogowski coil (plasma current), magnetic pick-up coils (normal and tangential components of magnetic fields) and flux loops (poloidal magnetic fluxes). The developed neural networks fully reconstruct not only the poloidal flux function but also the toroidal current density function with the off-line EFIT quality. To preserve the robustness of the networks against missing input data, an imputation scheme is utilized to eliminate the required additional training sets with a large number of possible combinations of the missing inputs.

An Experimental Phantom Study for Air-Based Quasi-Resonant Microwave Breast Imaging

The tumor detection performance of two air-based metallic microwave breast imaging systems is evaluated experimentally using breast phantoms having realistic tissue permittivities. The first system has a circular-cylindrical shape, whereas the second has a faceted hemispherical shape. No immersion medium is utilized making these systems low-loss quasi-resonant structures. The breast phantoms are composed of three distinct volumes representing structurally simplified adipose, fibroglandular, and tumor regions filled with tissue-mimicking fluids. Scattered-field data are collected, at multiple frequencies, on the inside surface of the chambers: the normal component of the electric field at 18 locations in the cylindrical chamber and 24 tangential magnetic field components in the faceted chamber. Quantitative 3-D imaging of these high-contrast phantoms is performed utilizing the finite-element contrast-source-inversion algorithm wherein an inhomogeneous numerical background, constituting prior information, is introduced. Experiments are conducted with various accuracies of this prior information, both in terms of the permittivity that is used as well as the accuracy of the geometry compared with the true regions within the phantom. Image segmentation techniques based on thresholding the 3-D reconstructed images are evaluated for tumor detection. Utilizing receiver operating characteristic (ROC) curves, it is shown that taking the intersection of multifrequency thresholded 3-D images performs the best for detecting tumors.

Multi-field variational formulations and mixed finite element approximations for electrostatics and magnetostatics

In this paper we propose different multi-field variational formulations for electrostatics and magnetostatics, which can provide optimal discrete approximation of any particular vector field. The proposed formulations are constructed by appealing to mechanics point of view amenable to using general constitutive equations, which is quite different from electrostatics and magnetostatics formulations typical of physics and electrical engineering focusing on the corresponding global form suitable only for linear case. In particular, the formulations we propose can be combined with mixed discrete approximations that can ensure the continuity of tangential component of electric or magnetic field and normal component of electric displacement and magnetic flux even for low order interpolations. The choice of this kind is quite different from currently favorite choice of high order finite element interpolations used for coupling electromagnetism with mechanics. The discrete approximation is based upon Whitney’s interpolations representing the vector fields in terms of corresponding differential forms, with electric and magnetic fields as one-form and electric displacement and magnetic flux as two-form. The implementation of interpolations of this kind is made for 3D tetrahedron elements with non-standard approximation parameters defined not only at vertices (for zero-form), but at edges (for one-form) and at facets (for two-form). The results of several numerical simulations are presented to illustrate the performance of different formulations proposed herein.

Magnetic field analytical model for magnetic harmonic gears using the fractional linear transformation method

Magnetic harmonic gears with high gear ratios exhibit high torque densities. However, the revolution and rotation of the eccentric rotor makes the magnetic field analysis complex. In this study, an analytical model of magnetic fields for magnetic harmonic gears is developed by using the fractional linear transformation method. The transformation formula is accurate in theory and suitable for the analysis of magnetic fields with large eccentricity. The rotor eccentricity region in the z-plane is mapped onto a uniform region in the w-plane. The magnetic field solutions are obtained by modulating the magnetic field distributions without rotor eccentricity with the relative permeance function derived from the effect of rotor eccentricity. The torque of magnetic harmonic gears is calculated from the radial and tangential components of the air-gap magnetic fields. Results of the finite element method and prototype test confirm the validity of the analytical prediction.

Dispersion properties of one-dimensional magnetized ferrite photonic crystals in transverse magnetization configuration for transverse magnetic modes

The dispersion characteristics of electromagnetic wave in one-dimensional magnetized ferrite photonic crystals containing yttrium iron garnets and nickel ferrite in a unit cell is investigated for transverse magnetic mode when external magnetic field is perpendicular to the plane of wave propagation. The dispersion relation is derived using transfer matrix method based on the continuity conditions of tangential electric and magnetic field components. It is observed that dispersion properties and phase index are strongly dependent on the normalized parallel wave vector and the filling factor. At the Brewster angle, width of photonic band gap shrinks to zero. Also, the considered structure indicates its dielectric behavior for electromagnetic wave propagation.

Electromagnetic scattering by gyrotropic semiconductor spheres when considering spatial dispersion

A new solution is presented to analyze the electromagnetic response of an anisotropic sphere when both the spatial dispersion and gyrotropy are simultaneously accounted for. By employing the Mie theory, the electromagnetic fields that can be decomposed into source-free and curl-free vector spherical harmonics are derived analytically by applying appropriate boundary conditions, namely, the continuity of the tangential components of electric fields and magnetic fields, respectively, together with the continuity of the normal components of the polarization phasor current density. Moreover, all expressions involving gyrotropic tensors are calculated in the corresponding principle coordinates, yielding analytical expressions. The derived solutions are capable of dealing with incident electromagnetic waves at an arbitrary incident angle and for arbitrary polarizations. Numerical validations are performed by comparing our results with those obtained for simplified models and also with numerical solutions, as well as with the results obtained from other existing approaches. The impact of the temperature and the dispersion effects on the modified circular dichroism has been investigated. It is demonstrated that the interplay of spatial dispersion and gyrotropy can bring narrower relative frequency shifts between the magneto-plasmonic resonances of the left-circularly-polarized and the right-circularly-polarized wave excitations, along with a blue-shift of the resonance and the reduced magnitude of the spectrum. The proposed method shows its capability and flexibility to analyze the nonlocal response of gyrotropic plasmonic semiconductors under an external static magnetic field, which enables us to rapidly validate nonlocal magneto-plasmonic applications.

Analysis and Calculation of Radial Electromagnetic Force on Brushless Doubly Fed Machine

Brushless doubly fed machine has reliable structure, low system cost, and advantages of outstanding application. BDFM achieves electric energy exchange depending on the effective magnetic field components, which leads to some problems of unbalanced radial electromagnetic force, vibration and noise. On the basis of analyzing the mechanism of radial electromagnetic force, the analytical method and finite element method are used to analyze the magnetic field of air gap. Take 4/2 pole and 8/4 pole as the example, the radial electromagnetic force of different pole numbers are obtained by means of tangential magnetic field component. The conclusions are useful for the development and design of brushless doubly fed machine.

Hybrid Prediction Method for the Electromagnetic Interference Characteristics of Printed Circuit Boards Based on the Equivalent Dipole Model and the Finite-Difference Time Domain Method

In this paper, we propose a hybrid modeling method for analyzing the electromagnetic compatibility characteristics of printed circuit boards (PCBs). The method uses an equivalent magnetic dipole array deduced from near-field scanning results obtained at a certain height over the PCB surface under test and the finite-difference time domain (FDTD) algorithm. The array of dipoles can simulate the PCB electromagnetic emissions, including the ground plane effect at a particular high frequency; the equivalent dipole array can then be imported into the FDTD calculation space for calculating the electromagnetic fields generated by the dipole array. In our experiment, we obtained the tangential magnetic field distribution of the PCB surface using near-field scanning, from where the tangential magnetic field component, orientation, and the magnitude and phase of the dipoles could be deduced. We used the proposed method to model two different modules on a highly integrated circuit. The results of the proposed method and those obtained by near-field scanning are nearly the same, which demonstrates the effectiveness and accuracy of the proposed method. We therefore conclude that the proposed modeling approach presents a new technique for studying the electromagnetic interference of PCBs.

Hardware for Inspection of Ferromagnetic Low Coercive-Force Articles

Hardware that uses plug-in detectors and allows one to measure coercive force in the range of few to several hundred A/m in industrial products of different shapes is presented. The operating principle is based on a functional relationship between the tangential component of the magnetic field close to the surface of a residually magnetized article and the coercive force of the article material as well as a connection between the gradient of the field of a magnetic pole formed at the article surface after local magnetization and the coercive force.

Investigation of linearity of the ITER outer vessel steady-state magnetic field sensors at high temperature

Three vacuum vessel sectors in ITER will be instrumented by the outer vessel steady-state magnetic field sensors. Each sensor unit features a pair of metallic Hall sensors with a sensing layer made of bismuth to measure tangential and normal components of the local magnetic field. The influence of temperature and magnetic field on the Hall coefficient was tested for the temperature range from 25 to 250 ̂C and the magnetic field range from 0 to 0.5 T. A fit of the Hall coefficient normalized temperature function independent of magnetic field was found, and a model of the Hall coefficient functional dependence at a wide range of temperature and magnetic field was built with the purpose to simplify the calibration procedure.