Measuring the temperature dependence of resistivity of high puritycopper using a solenoid coil (SRPM method)

The resistivity of high purity copper was measured by a method which estimates it by using the difference in the impedance between a circular multilayer solenoid coil with a circular rod-shaped copper sample and a similar coil without a copper sample (SRPM method). The residual resistivity ratio (RRR) of high purity copper measured at 100 Hz by the SRPM method has correlated well with the values measured by the DC four-probe method. It was confirmed that an accurate measurement of the resistivity to 10^-12 Ωm is possible by the SRPM method. Frequency dependence was confirmed to exist in high purity copper with very low resistivity. As the measuring frequency is raised, the decrease in skin depth seems to affect the resistivity     

A method for simultaneously measuring resistivity and permeabilitywith a multilayer solenoid coil

A formula is given for a more accurate estimate of either the resistivity and permeability of a cylindrical magnetic material or the resistivity and penetration depth of a cylindrical superconductor, using the difference in the complex impedance between a circular multilayer solenoid coil having a conductor and a similar coil without a conductor. In comparison with the conventional method which uses a single-layer solenoid coil, it is shown experimentally that a multilayer solenoid coil is more effective for a short sample conductor because a larger difference in the complex impedance is obtained without increasing the width of the solenoid coil. The results of measurements of magnetic and superconductive materials are included     

Calculation of the difference in impedance for a solenoid coil withand without a sample conductor

Either the resistivity and permeability of a magnetic material or the resistivity and magnetic penetration depth of a superconductor can be simultaneously estimated from the difference in the complex impedance between a circular solenoid coil coaxially surrounding a cylindrical conductor and an identical coil without a sample conductor. A method for calculating the difference in the complex impedance at a high frequency including the displacement current to an accuracy of 0.1% is reported. Comparison of the values calculated by this method and the values obtained by a conventional method which does not include the term of displacement current is also included     

Simultaneous measurement of electric and magnetic properties of aspherical sample

A method using a solenoid coil for simultaneously estimating the electric and magnetic properties of a spherical conductor was studied. These properties are estimated by finding the difference in the complex impedance of the coil with and without a sample to find out the measuring value that best coincides with the theoretical value. A new formula applicable to a nonmagnetic, a magnetic or a superconductive spherical sample was derived. The conductivities a and permeabilities μ measured by this method and by the conventional methods were compared using various samples. The deviations were no larger than 3% for a nonmagnetic samples, and 1.5% for μ of magnetic samples     

Reconstructing electrical conductivity profiles from variable-frequency eddy current measurements

A method for reconstructing radially varying conductivity profiles in cylindrical conductors is described. Solenoidal driving and sensing coils surround the cylindrical sample and an AC magnetic field applied by the driving solenoid induces axisymmetric eddy currents in the sample. It is shown how a radially varying conductivity profile can be recovered from measurements of the complex impedance recorded as a function of frequency, where impedance here is defined as the ratio of the induced electromotive force (EMF) in the sensing coil to the current in the driving coil. An iterative nonlinear least-squares algorithm is employed to reconstruct the profiles. Demonstrations of the reconstruction method are presented based on both simulated and experimentally recorded impedance data.     

Measurement of the magnetic susceptibility of a rod-shapedsuperconductor using a solenoid coil (SRPM method)

An effective method for the measurement of the magnetic susceptibility (χ) of a circular rod-shaped superconductor, in which χ is estimated by substituting the magnetic penetration depth (λ) into a formula after obtaining λ from the difference in the impedance between a solenoid coil with a sample and an identical one without a sample, is proposed. The temperature dependence of χ obtained from this method has correlated well with the values measured with a SQUID magnetometer     

Simultaneous measurement of the resistivity and permeability of afilm sample with a double coil

A method is proposed for a simultaneous measurement of the resistivity and permeability of a film inserted between two coils facing each other. Connecting in series, the total impedance of the coils was measured in two ways, i.e., 1) the current passes through the coils in the same direction, and 2) the current passes through each coil in opposite directions to each other. The resistivity and permeability of the film were simultaneously obtained from the difference in the impedance for the two cases. It was theoretically found that the optimum frequency for high accuracy in the measurement was proportional to the resistivity and inversely proportional to a thickness of a sample film. The results of the simultaneous measurements of the resistivity and permeability of nickel films of a thickness ranging from 0.01-0.08 mm at a frequency range of 1-100 kHz are shown in this paper. The measured values of the resistivity and permeability with this method agreed with the values obtained by conventional methods, i.e., the dc four-probe method for the resistivity measurement and the toroidal coil method for the permeability measurement     

The Electromagnetic Basis for Nondestructive Testing of Cylindrical Conductors

Using an idealized model, we deduce the impedance per unit length of long solenoid of many turns that contains a cylindrical sample. The sample with a specified conductivity and magnetic permeability need not be centrally located within the solenoid provided all transverse dimensions are small compared with the free-space wavelength. The derivation is relatively straightforward and it provides a justification for earlier use of the impedance formula. The dual problem , where the solenoid is replaced by a toroidal coil is also considered. It is shown that both excitation methods have merit in nondestructive testing procedures.     

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.     

Analysis of current distributions in a multi-laminated HTS tape conductor for solenoid coils

A multi-laminated HTS tape conductor has been recently developed for large coils. If the HTS tapes are simply laminated to form the conductor, the current distribution in the laminated tape conductor of the coil is imbalanced because of the differences among inductances of tapes. Transposition of the tapes in the conductor is effective for homogeneous current distribution, but the tape may be damaged due to the lateral bending. The solenoid coil has enough space to transpose the tapes at both ends. However, a proposed theory so far requires a restriction in the number of coil layers for homogeneous current distribution in the laminated tape conductor. It is very important to analyze current distributions in the multi-laminated tape conductor for the solenoid coil with arbitrary layers. In this paper, we apply the Maxwell integral equation to the region contoured by adjacent laminated tapes to analyze the current distributions of the tapes in an infinite solenoid coil, and demonstrate that the flux across the region is conserved as long as the tapes are not saturated, and finally induce the fundamental equations as functions of coil construction parameters, such as layer radii, laminated tape spaces, and winding pitches. We use the fundamental equations for 2-layer and 4-layer coils to verify the homogeneous current distribution of the laminated tape conductor for an arbitrary layer number. Since the flux between the tapes in the inner layer of a 2-layer coil is contributed from the outer layers, the tape space in the outer layer must be larger than that in the inner layer because of the balance between the two fluxes. Moreover, we have developed an analysis method for a finite solenoid coil.     

Alternating-Current Solenoid of Finite Length in a Medium with Hall Conductivity

The electric field of an alternating-current solenoid of finite length in conducting media is investigated. The first-order (Hall) effect of an externally applied, constant, axial magnetic field on the electric field is considered. The coil impedance and the electromotive force induced in a certain closed path are calculated numerically for small frequencies.     

Measurements of current distributions in a multi-laminated HTS tape conductor for solenoid coils

A multi-laminated HTS tape conductor has recently been developed for large coils. If the HTS tapes are simply laminated to form the conductor, the current distribution in the laminated tape conductor of the coil is unbalanced because of the differences among all tape inductances. Transposition of the tape in the conductor is effective for homogeneous current distribution, but the tape may be damaged due to the lateral bending. In our previous paper, we proposed a new theory to analyze and control current distributions in the multi-laminated tape conductor for a solenoid coil with arbitrary layers. We applied the Maxwell integral equation to the region contoured by adjacent laminated tapes to analyze the current distributions of the tapes in the infinite solenoid coil, demonstrated that the flux across the region is conserved as long as the tapes are not saturated, and finally induced fundamental equations as functions of coil construction parameters, such as layer radius, laminated tape space, and winding pitch. In order to verify the theory, we designed two kinds of coils with homogeneous and inhomogeneous current distributions in the two-laminated tape conductor by adjusting the space between the tapes in the second layer, and fabricated them. In the case when the space between the tapes in the second layer is the same as that of the first layer, 0.31 mm in thickness, we measured the tape currents of 7:3 for the inner and outer tape of the first layer, respectively. We adjusted the space between the tapes of the second layer, 1.78 mm in thickness, while the space of the first layer remained unchanged, 0.31 mm in thickness. We obtained the homogeneous current distribution in the tape conductor. The experimental data were in good agreement with the theory.     

Generation of uniform magnetic field using a single-layer solenoid with multi-current method

The magnetic field of a single-layer solenoid (length L=1020 mm, average radius R=114.67 mm, pitch p=1.0001 mm and wire diameter d=0.799 mm) with a multi-current method was calculated to improve the uniformity and optimized by using Legendre polynomials. The optimum conditions obtained by the calculations for the uniform magnetic field lead to insensitive magnetic field with respect to the radius variations. Therefore, the uncertainty of the generated magnetic field within ±2 cm from the center of the solenoid amounts to about 1 × 10⁻⁷ normalized by the central magnetic field. The solenoid coil constant was measured to be 1.2548214 mT/A obtained under compensation of the Earth’s magnetic field in 25 °C air.     

The impedance of a finite length coil immersed in a circular cylindrical conducting structure

The problem of calculating the impedance of a finite length solenoid immersed in a multiregion cylindrical structure is examined. The transmission line modelling technique is introduced to deal with a large number of regions in a simple and routine way. Bessel functions are completely avoided by replacing each region equivalent T.L. by a cascade connection of elementary T-circuits. The input impedance calculated for a finite length solenoid which was either air-cored, or closely encircling an infinitely long conducting cylinder, was found to agree closely with published values.     

Construction and testing of a 3 m diameter × 5 m superconducting solenoid for the fermilab collider detector facility (CDF)

A thin 3 m diameter × 5 m, 1.5 T superconducting solenoid for the Fermilab collider detector facility (CDF solenoid) was constructed. Cool-down and excitation tests of the solenoid were carried out. The design current is 5000 A and the stored magnetic energy is 30 × 10⁶ J. The solenoid utilizes the forced flow cooling method of two-phase helium and does not have a permanent inner bobbin. The material thickness of the solenoid is 0.85 radiation length in the radial direction. An aluminum-stabilized NbTi/Cu superconductor fabricated with the EFT method was used. Radially outward magnetic forces must be supported with an outer support cylinder shrink-fitted outside the coil. The helium cooling tube of 20 mm in inner diameter and about 140 m in length was welded to the outer support cylinder.The maximum excitation current was limited to 2800 A in the present tests without an iron return yoke. Thermal response of the solenoid during the cool-down and excitation tests was very steady. A series of heater quench tests was attempted by using a heater installed at the outer support cylinder. The solenoid did not quench even for a heater input of about 10 kJ. In a warm-up test the liquid helium supply was shut off. The coil stayed superconducting for about 90 min and then the entire coil became normal very uniformly. This result is consistent with the measured heat load of the solenoid of about 35 W. The results of the present tests indicate the excellent thermal stability of the solenoid.     

电磁胀形管坯所受磁压力的瞬态分布

管坯所受磁压力的准确求解是电磁成形变形分析,优化成形系统工艺参数的基础.通过ANSYS/EMAG软件,用远场单元来说明磁场在远场区间的耗散问题,对电磁胀形时作用在管坯上的磁压力进行准确计算.在线圈长度一定的条件下,讨论了管坯尺寸对磁压力瞬态分布和磁场扩散的影响,并根据管坯端部径向磁压力和中部径向磁压力的比值,提出以磁压力分布不均匀系数来反映磁场不均匀分布的程度.计算结果表明:当管坯和线圈的相对长度大于1时,管坯上与线圈等高处承受轴向拉应力,磁场扩散现象不严重;当相对长度小于0.92时,管坯端部承受轴向压应力,磁场扩散现象严重,相对长度0.92时为电磁胀形均匀成形的条件.     

Systematic Analysis of the Improvements in Magnetic Resonance Microscopy with Ferroelectric Composite Ceramics

The spatial resolution and signal‐to‐noise ratio (SNR) attainable in magnetic resonance microscopy (MRM) are limited by intrinsic probe losses and probe–sample interactions. In this work, the possibility to exceed the SNR of a standard solenoid coil by more than a factor‐of‐two is demonstrated theoretically and experimentally. This improvement is achieved by exciting the first transverse electric mode of a low‐loss ceramic resonator instead of using the quasi‐static field of the metal‐wire solenoid coil. Based on theoretical considerations, a new probe for microscopy at 17 T is developed as a dielectric ring resonator made of ferroelectric/dielectric low‐loss composite ceramics precisely tunable via temperature control. Besides the twofold increase in SNR, compared with the solenoid probe, the proposed ceramic probe does not cause static‐field inhomogeneity and related image distortion.     

Thermal stability of high current density magnets

The stabilization theories hitherto proposed for superconducting (SC) magnets are not fully developed for application to high current density magnets such as pulsed dipole magnets for a synchrotron. Hence, thermal stability in such high current density magnets is studied by obtaining a minimum energy of thermal disturbances which barely leads a magnet to quench. To find the minimum energy by calculation a dynamic simulation of temperature distribution along a conductor is carried out following an application of the disturbances on the conductor. The minimum energy is found to depend largely on time duration and spatial length of the disturbances. The values of the minimum energy given by calculation agree almost with the experimental results obtained for a coil which simulates a pulsed dipole magnet from the viewpoint of cooling. Discussion is also made in relation to the minimum energy on the performance of a pancake type solenoid magnet which has the same cooling as in the simulating coil.     

High-Frequency Giant Magnetoimpedance Measurement and Complex Permeability Behavior of Soft Magnetic Co-Based Ribbons

We present a method for extracting the magnetic parameters of a soft magnetic Co-based alloy (Co$_68.25$Fe$_4.5$Si$_12.25$B$_15$) in the high-frequency regime (100 MHz–2.5 GHz). The method uses the magnetic sample (as-cast ribbon) as the conductor of a terminated microstrip transmission line. It uses the complex propagation constant of the line, obtained from open/short circuit input impedance measurements, to extract the per-unit-length series impedance. It then uses a theoretical model, based on the distributed parameters and the skin effect, to extract the bulk transverse relative permeability. The model considers the geometrical configuration of the magnetic conductor (ribbon) when determining the series impedance as well as the complex transverse relative permeability$(mu_ tr= mu'_ tr- j mu'_ tr)$. We report on the effect of applying and varying an external dc magnetic field.     

A double coil method for simultaneously measuring the resistivity,permeability, and thickness of a moving metal sheet

A method to determine the resistivity, permeability and thickness of moving magnetic sheets is described. The parameters of a sample sheet inserted between two coils facing each other are determined by measuring the impedance of the two coils at two different frequencies. To compare the experimental data with theoretical values, the difference in the impedance of the coils between two cases is used: when the current passes through the coils in the same direction, and in opposite directions. The method was tested by measuring the resistivity, permeability and thickness of nickel and iron sheets, 1 mm thick, moving at velocities varying from 0 to 6 m/s. It was possible to accurately determine the resistivity, thickness, and permeability within 10%, 10%, and 20%, respectively, at frequencies of 400 and 800 Hz