Boundary integral equations analysis of induction devices with rotational symmetry

The application of boundary integral equations (BIE's) for the analysis of linear induction devices with rotational symmetry is considered. One-dimensional Fredholm integral equations are derived for the tangential field components at the boundary of a conducting medium with constant scalar conductivity and permeability excited by a time-harmonic azimuthal current source. The important special case of a short right circular conducting cylinder (magnetic or nonmagnetic) coaxial with one or more short coils is treated in detail. The explicit form of the kernels and the numerical solution technique are presented. Numerical results are presented for typical induction heating applications where the load length as well as the coil length are finite. Results are also presented for the magnetostatic problem of finding the demagnetization factors for short magnetic rods. In each case the results are compared with published results and the accuracy and efficiency of the proposed approach are demonstrated.     

应用于铯喷泉钟的磁屏蔽系统的设计

高质量磁屏蔽系统是铯喷泉钟的重要部件之一。首先给出评定磁屏蔽效果的3个指标,即磁场均匀区长度、磁场均匀区起点位置和磁屏蔽效率。在此基础上,讨论了利用有限元计算3层磁屏蔽系统的层间径向间距、轴向间距、端盖孔套管长度和端盖连接方式对磁屏蔽的影响,给出了相应的优化参数,并对比了按优化参数设计的3层磁屏蔽与原有4层磁屏蔽系统用有限元计算的磁屏蔽效果。有限元计算结果为中国计量科学研究院新铯喷泉钟磁屏蔽系统的技术设计提供了理论指导。     

Dynamic magnetic shield for the CLAS12 central TOF detector photomultiplier tubes

The Central Time-of-Flight detector for the Jefferson Laboratory 12-GeV upgrade is being designed with linear-focused photomultiplier tubes that require a robust magnetic shield against the CLAS12 main 5-T solenoid fringe fields of 100 mT (1 kG). Theoretical consideration of a ferromagnetic cylinder in an axial field has demonstrated that its shielding capability decreases with increasing length. This observation has been confirmed with finite element analysis using POISSON model software. Several shields composed of coaxial ferromagnetic cylinders have been studied. All difficulties caused by saturation effects were overcome with a novel dynamical shield, which utilizes a demagnetizing solenoid between the shielding cylinders. Basic dynamical shields for ordinary linear-focused 2-in. photomultiplier tubes were designed and tested both with models and experimental prototypes at different external field and demagnetizing current values. Our shield design reduces the 1 kG external axial field by a factor of 5000.     

Eddy currents induced in a finite length layered rod by a coaxial coil

We describe the calculation of eddy currents in a two-layer conducting rod of finite length excited by a coaxial circular coil carrying an alternating current. The calculation uses the truncated region eigenfunction expansion (TREE) method. By truncating the solution region to a finite length in the axial direction, we can express the magnetic vector potential as a series expansion of orthogonal eigenfunctions instead of as a Fourier integral. The restricted domain can be arbitrarily large to yield results that are as close to the infinite domain results as desired. Integral form solutions for an infinite rod are well known and relatively simple. For a finite length cylindrical conductor, however, additional boundary conditions must be satisfied at the ends. We do this by comparing series expansions term by term to match the solutions across the end of the cylinder. We derive closed-form expressions for the electromagnetic field in the presence of a finite two-layer rod. A special case of the solution is that for a conductive tube. We illustrate the end effect by calculating the coil impedance variation with respect to the axial location of the coil. The results are in very good agreement with those obtained by using a two-dimensional finite-element code.     

Thermal analysis of magnetic shields for induction heating

For the design of magnetic shields for induction heating, it is useful to analyse not only the magnetic field reduction but also the temperature behaviour of the shield. The latter is heated by its electromagnetic losses and by thermal radiation from the workpiece. A coupled thermal-electromagnetic axisymmetric finite element model is used to study the temperature of a shield for an axisymmetric induction heater, highlighting the effect of the radius, length, thickness and material of the shield on its temperature and magnetic shielding factor. Also the effect of frequency and workpiece dimensions is investigated. The model is validated by measuring magnetic induction, induced currents in the shield and temperature of the shield on the experimental setup. The temperature is unacceptably high for shields close to the excitation coil, especially if the shield length is lower than the workpiece length. Although the study is carried out for one specific induction heater geometry, the paper indicates the effect of parameters such as geometry, material and frequency on shield temperature so that the results are also useful for other induction heating configurations.     

Field attenuation as the underlying principle of cryo current comparators

This paper describes both theoretical and experimental investigations of the error behaviour of cryo current comparators (CCC) as a function of the geometric parameters of the superconducting shields. The basis of our calculations has been the attenuation of magnetic fields by a superconducting coaxial cavity. The theoretical results agree with experiments which have been performed on a special test configuration of a CCC. Its main feature is a toroidal shield made from mercury with an elongated gap region forming the coaxial cavity.The results obtained are applicable to all types of CCCs. We found that the superconducting coaxial cavity behaves like a filter which transmits only the useful signal containing information about the net current linkage. All other fields contributing to the error of the comparator are attenuated exponentially.     

Cryogenic performance of coaxial,multi-pin and coaxial-multi-pin complex bakable feedthroughs

Five BNC-type coaxial (BNC-receptacle, BNC-receptacle with floating shield, BNC-receptacle with floating and reverse sleeve, BNC-JJ, and BNC-JJ with floating shield), four N-type coaxial (N-receptacle, N-receptacle with floating shield, N-JJ, and N-JJ with floating shield), 22 pin, and 14 pin-BNC complex vacuum feedthroughs have been constructed. They are bakable (600 K) and can be used below helium lambda temperature (2.17 K), and remain leak-tight (? 10^?18 kNms^?1). Moreover, there is no leak at a pressure difference of 1.5 × 10³ kNm^?2 of helium at room temperature. BNC-JJ has a VSWR ? 1.35 from dc to 4.0 GHz. N-JJ has a VSWR ? 1.25 from dc to 6.5 GHz. 22 pin and 14 pin-BNC xcomplex vacuum feedthroughs can be quickly connected by Burndy connectors.     

Magnetic Shielding Properties of MgB2Fe Superimposed Systems

We studied the magnetic shielding properties of a MgB₂/Fe hybrid structure consisting of two coaxial cups subjected to a magnetic field applied parallel to their axis. This study was performed to analyze the magnetic shield properties of a system contemporary exploiting the opposite magnetic properties of superconducting/ferromagnetic materials. The MgB₂ cup was grown by a microwave-assisted Mg-infiltration technique that allows obtaining samples with different shapes and easily scalable sizes, meeting the requirements of different shielding applications. Measurements of mitigation of the magnetic induction were performed in applied magnetic field up to 1.5 T and in different positions along the cup axis at temperature T=20 K. A decrease of the shielding factor (SF) of the hybrid system with respect to the MgB₂ cup alone turns out at low magnetic field. On the contrary, at higher magnetic field the superposition of the two cups increases the SF of the hybrid system up to 3 times over that one of the single MgB₂ cup.     

An improved method for magnetic identification and localization of cracks in conductors

A SQUID magnetometer can be used to measure the magnetic field produced by flaws in a two-dimensional, conducting plate carrying a current. Identification of the flaw-induced magnetic field is difficult because of the large magnetic field associated with the edges of the plate and the current in the leads that connect the plate to the power supply. We have developed a technique by which the wire and edge fields can be cancelled prior to mapping the magnetic field. In this technique, a similar unflawed conducting sheet is placed adjacent to the flawed plate, with a connection between the sheet and the plate at one edge, and with the opposite edges of the sheet and of the plate connected to the two conductors of a coaxial cable. Thus, an applied current will flow along one conductor of the cable, across the cancelling sheet, cross into the flawed plate, return along the plate, and then return to the power supply along the other conductor of the coaxial cable. As a result of this geometry, there is no magnetic field from the lead-in wires because they are coaxial, and the magnetic field due to the edges of the plate is cancelled by the opposing magnetic field of the edges in the adjacent sheet. The extent of cancellation is determined primarily by the separation between the plate and the cancelling sheet, by the thickness of the plate, and by macroscopic inhomogeneities in their electrical conductivities.     

气隙对电流比较仪磁屏蔽屏蔽效能影响的研究

电流比较仪的磁屏蔽是减小磁性误差,提高测量精度的重要组成部分,但实际中磁屏蔽往往存在气隙导致屏蔽效能下降,影响比较仪的测量精度。通过建立有限元模型,研究磁屏蔽上引线穿出气隙对屏蔽效能的影响,得到了屏蔽效能随气隙高度变化的规律。对于该模型,气隙高度小于10 mm时,屏蔽效能下降不大;当气隙高度大于10 mm后,屏蔽效能下降明显。最后,搭建实验平台验证气隙对屏蔽效能的影响,实验结果与有限元计算结果相吻合,小气隙对屏蔽效能的影响不大,当气隙超过一定高度后对屏蔽效能影响很大,实际设计中应予以避免。     

Evaluation of Surface Impedance Models for Axisymmetric Eddy-Current Fields

We have investigated the range of validity of the perfect electric conductor and of the standard Rytov–Leontovich impedance boundary condition models for the analysis of axisymmetric eddy-current problems. Using these models, we derived approximate expressions for the magnetic vector potential, field quantities, Joule losses, and forces for conducting spheroids placed in external nonuniform magnetic fields produced by coaxial circular turns carrying currents varying sinusoidally with time. We compared our numerical results for the magnetic field intensity at the conductor surface, power losses, and forces (for both prolate and oblate spheroidally shaped conducting objects) with the results from analytical expressions obtained by applying the exact boundary conditions. While the simpler perfect conductor model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained by using the standard surface impedance model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis for electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis for Joule losses.      

Nanotubes of boron nitride filled with molybdenum clusters

Carbon nanotubes are known to be metallic or semiconducting, depending on their helicity and diameter. However, boron nitride (BN) nanotubes are the only nanotubular product known to date that are predicted to have stable insulating properties that are independent of their atomic structure and morphology. Thus, the BN tube has attracted prime attention as an advanced nanoinsulating shield for all types of encapsulated conducting material, i.e., metal wires, clusters, etc. However, so far there have been no successes in controlled one-dimensional filling of BN nanotubes with conductive material. We report the first experimental results on the synthesis, high-resolution transmission electron microscopy, energy dispersion X-ray analysis, and electron energy loss spectroscopy of BN nanotubes that are filled with Mo clusters over their entire length. This was accomplished by means of two-step thermochemical treatment of chemically vapor-deposited C nanotubes with B2O3, CuO, and MoO3 oxides in a flowing N2 atmosphere. The first examples of BN nanotubes filled with molybdenum clusters are reported and the formation of the first nanocable (approximately 10 nm in length), consisting of a conductive metal core and an insulating BN nanotubular shield is demonstrated.     

MHD heat transfer in the flow between two coaxial cylinders

Summary Stealy flow of an incompressible electrically conducting fluid between, two coaxial cylinders composed of non-conducting materials, is considered in the presence of a uniform radial magnetic field. The flow is due to the relative motions of the cylinders parallel to their common axis. The cylinders are maintained at constant temperatures. Heat transfer rates from the cylinders are plotted graphically against the Hartmann number.With 1 Figure     

Experimental Characterization of a Singly Loaded E-Plane Waveguide Post by Using a Tunable Coaxial Line

Equivalent-circuit parameters of a singly loaded E-plane waveguide post have been experimentally measured by loading one end of the post with a tunable coaxial line. The resulting structure shows a transmission minimum and a transmission maximum. The positions of the movable short for minimum and maximum transmission have been correlated with the parameters to be measured. It is seen that the errors due to uncertainty in the length measurement can be minimized through the use of a coaxial line with the highest feasible characteristic impedance. Agreement between theoretical and experimental results is satisfactory.     

Shielded electronic current transformer

A current transformer with nominal ratio 10 A to 10 mA, intended for low-frequency applications, was developed. It includes an electronic device to reduce the magnetizing current, and a continuous shield in the secondary winding (coaxial cable) in order to eliminate the effect of stray capacitances. No guard-source is connected to the shield. It is proposed in this paper to leave the cable-shield-potential floating. This leads to high-accuracy results (ratio errors and phase-displacements in the order of few parts in 10/sup 6/ from 50 Hz to 1 kHz).     

An integral method for extremely low frequency magnetic shielding

A novel approach for analyzing conducting shields of extremely low frequency magnetic fields in linear media is presented. It consists of an integral formulation based on the cell method, expressed in terms of network-like loop currents and magnetic vector potential line integrals on the shield surface. This formulation leads to a considerable reduction of field problem variables, thus limiting the amount of allocated memory and speeding-up the numerical procedure compared to other differential and integral techniques. Eddy currents are computed first, then the magnetic vector potential and the magnetic flux density distributions are evaluated by applying the superimposition principle. A detailed comparison between this method and a three-dimensional finite element method code demonstrates the accuracy of the results and the advantages of the method.     

Development of a turbo-molecular pump with a magnetic shield function

To safely use turbo-molecular pumps (TMPs) in a magnetic field, it is necessary to reduce the eddy current induced in a rotating rotor. Instead of adding a magnetic shield facility to the TMPs available in markets, we developed a TMP with a magnetic shield function by replacing the housing material of the TMP with a ferromagnetic substrate SUS430. Before and after machining, the SUS430 was vacuum-fired at 700 °C for 10 h in order to attain a good vacuum quality and recover its high magnetic permeability. The magnetic shield efficiency of the TMP with SUS430 housing was then examined. When a perpendicular magnetic field of 9 mT was applied, the field inside the TMP was reduced to less than 0.3 mT. Next, we confirmed that the developed TMP shows good performance in achieving an ultrahigh vacuum in magnetic fields of up to 9 mT. The limit of the magnetic shield efficiency for the developed TMP is also discussed.     

磁共振成像交替阻抗微带线射频线圈仿真分析

为研究改变交替阻抗微带线射频线圈的几何尺寸对感兴趣区内磁场分布的影响,保持微带线射频线圈总长度不变,改变宽带与窄带的长度比例和宽度比例,在HFSS中建立交替阻抗微带线射频线圈的仿真模型,与传统微带线射频线圈进行比较,利用ADS与HFSS的协同仿真实现线圈的调谐和匹配.仿真结果表明交替阻抗微带线射频线圈感兴趣区内的磁场均值比传统微带线射频线圈的提高了一倍以上.调整交替阻抗微带线射频线圈的宽带与窄带的长度比例和宽度比例,可以提高感兴趣区内的磁场强度,同时改善磁场分布的均匀性.     

Magnetic field shielding concepts for power transmission lines

High current carrying cables used in power transmission lines create strong magnetic fields in their vicinity. For ac lines at 50-60 Hz, the magnetic field is quasi-static and hence uncoupled from the electric field. Shielding of such low frequency magnetic fields is a challenge. In this paper, finite element modeling is used to study the effect of various shield geometries and shield materials around a current carrying wire. Two-dimensional analysis is sufficient for this problem because the cables are very long compared to the wire diameters. Shielding effectiveness, defined as the difference in the magnetic field intensity with and without the shield, is presented. It is concluded that a partial shield is the optimal design for shielding the region below the cable. To achieve this, the shield gap must be oriented above the high current wire