Coil Cross-section Research Articles

Calibration Procedure for Magnetization Loop Tracers

The purpose of this paper is to calibrate the magnetic field coming out of an excitation coil of certain specifications, fabricated for non-destructing testing of electrical steel sheets. Thus, a comparison between experimental and numerical analysis is discussed. For the experimental estimation of the magnetic field, a sensitive Hall sensor is used to measure the dc field at a vertical array of three selected points inside the coil. These are the lower, the middle and the upper point of the coil cross section, respectively. The magnetic field is then computed theoretically using the finite element method and the BiotSavart law. Measured results are in agreement with the calculated results of the excitation field very well, within the limits of our experimental set-up.

The Application of Accurate Calculation of Magnetic Field Intensity in 1.5-T Superconducting MRI Magnet Design

Currently, when calculating the magnetic field generated by the solenoid coil of the superconducting wire wound, we assume that the coil cross section with a uniform current density, but actual current in superconducting wires (NbTi) in the form of a wire in channel is not evenly distributed, the current distribution only in the superconducting core, i.e., there is no current in copper, insulation, and filler, and this method of calculation will result in errors. In this paper, we model the superconducting cores of the 1.5-T superconducting magnetic resonance imaging (MRI) magnet to calculate accurate magnetic field intensity and inhomogeneity by helicoidal method in the diameter of spherical volume and find that inhomogeneity is eight times bigger than that calculated by spherical harmonic expansions, which cannot be accepted in design. Hence, in order to design a high-homogeneity MRI magnet, we amend the 1.5-T MRI magnet's original parameters by an optimization algorithm through an original interface between OPERA-3D and MATLAB according to the accurate results.

Conceptual Design of a Large-Aperture Dipole Magnet for HL-LHC Upgrade

The development of a large-aperture (120–180 mm) dipole magnet is proposed in the framework of the CERN-KEK cooperation program. The application target is the D1 magnet (separation dipoles) replacement for the HL-LHC (High Luminosity—Large Hadron Collider) upgrade. The Cos-theta type coil cross section and the shell-based structure are adopted in the conceptual design of this magnet. The nominal field is estimated to be 6–10 T at 1.9 K with a 30-mm-width coil arranged in two layers. The candidates of superconductor are <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{Nb}_{3}\hbox{Al}$</tex> </formula> , <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{Nb}_{3}\hbox{Sn}$</tex> </formula> and Nb-Ti. We present the analytical estimation of the key parameters of this magnet and the simulation of the actual design which includes the field quality, the stray field, and the stress distribution in the coil.

Performance improvement of a high-temperature superconducting coil by separating and grading the coil edge

In this paper, we establish a model to analyze the transport current performance of a high-temperature superconducting (HTS) coil, considering the dependencies of critical current and n-value of an HTS tape on magnetic field and magnetic field angles. This analysis shows that relatively large electric fields appear at the coil’s edges, preventing improvement in the transport current performance of the coil. To solve this problem, in this paper, we propose a graded coil in which several coil edges of different heights are separated and graded. Analysis of its performance shows that the coil’s critical current increases, thus confirming that there exists an optimum coil cross section at which the stored energy and central magnetic field improve 2.1 times and 45%, respectively, compared with a typical rectangular coil that employs the same total length of the HTS tape. It is recommended that these results of the coil should be applied to SMES.

An improved FEM model for computing transport AC loss in coils made of RABiTSYBCO coated conductors for electric machines

AC loss can be a significant problem for any applications that utilize or produce an ACcurrent or magnetic field, such as an electric machine. The authors investigate theelectromagnetic properties of high temperature superconductors with a particular focus onthe AC loss in superconducting coils made from YBCO coated conductors for use in anall-superconducting electric machine. This paper presents an improved 2D finite elementmodel for the cross-section of such coils, based on the H formulation. The model is used tocalculate the transport AC loss of a racetrack-shaped coil using constant and magneticfield-dependent critical current densities, and the inclusion and exclusion of a magneticsubstrate, as found in RABiTS (rolling-assisted biaxially textured substrate) YBCO coatedconductors. The coil model is based on the superconducting stator coils used in theUniversity of Cambridge EPEC Superconductivity Group’s all-superconductingpermanent magnet synchronous motor design. To validate the modeling results, thetransport AC loss of a stator coil is measured using an electrical method basedon inductive compensation by means of a variable mutual inductance. Finally,the implications of the findings on the performance of the motor are discussed.

A Method for Coil Design of Superconducting Quadrupoles Based on Sector Coils and Fourier Series

In this paper we present a novel method to optimize quadrupole coil cross-sections based on the cos 2?-type. We first approximate real coil blocks made of cables with concentric sectors powered with a constant current density to make use of analytical expressions of the magnetic field based on the Fourier series development. This allows a rapid evaluation of the field harmonics which permits an almost exhaustive scan on sectors position and dimensions for coil layouts made of up to five sectors. The coil layouts having a larger short-sample gradient can be further explored, approximating them with blocks of Rutherford cables. This second step requires a second fine tuning of the cross-section around the previously found optimum. The method has been used to design a proposed coil cross-section for the new inner triplet quadrupole for the LHC.

Design Study of a Curved Dipole Superconducting Magnet for Beam Transport

As an efficient bending magnet for a beam line, a curved dipole superconducting magnet is proposed. The magnet consists of a curved saddle shape (cosine theta) superconducting coil with multilayer structure. The curved saddle shape has an influence on the field quality at each coil cross-section. Therefore the superconducting coil is designed to fulfill the design requirement that there be a linear relationship between the radius and the integral magnetic field along an arc path of the beam line, by using the developed coil design code. In this study, the conceptual design of the curved dipole superconducting magnet for a heavy ion beam of 400 MeV/u was carried out with respect to a magnetic field. In addition, a load line of the magnet and a maximum temperature of the coil after quench were calculated.

Study on Optimal Design of High Temperature Superconducting Coil Based on AC Loss Minimization

This paper presents an optimal design method of winding cross section of high temperature superconducting coils wound by Bi2223/Ag tape based on AC loss minimization. We try to optimize the winding cross section starting from the conventional HTS coil with the rectangular cross section to minimize the AC loss. An example of the optimal cross section coil is presented. The result shows that the AC loss in the optimized coil is significantly reduced and the critical current of the optimized coil is increased compared with the rectangle cross section coil. It is verified that our optimal design method is effective to reduce the AC loss in the HTS coil. The disadvantageous points of the optimized coil are also discussed.

Study on performance improvements of a high-temperature superconducting coil with a lattice-shape cross section

For designing inexpensive high-temperature superconducting (HTS) coils, it is essential to obtain large magnetic fields and stored energy with shorter lengths of HTS tape. To improve the performance of a coil, it is necessary to improve its transport-current performance. The critical current and n-value of an HTS tape were measured at various magnetic field magnitudes and angles at 77K. The HTS tape employed in the coil was Bi-2223/Ag tape. From this measured data, fitting equations of the critical current and n-values were obtained. With these fitting equations, coil critical currents were analyzed according to our analytical model. The analysis showed that relatively large electric fields are generated at coil edges, inhibiting improvement of the transport-current performance of the coil. To solve this problem, we propose an HTS coil, which is produced by cutting and displacing the central portion of the rectangular cross section. By this rearrangement, the magnetic field distribution changes, resulting in an improvement in the coil critical current. We calculated performances of the proposed coil by varying the magnitude of displaced coils while maintaining a constant total HTS tape length. We found that there is an optimum cross section shape of the proposed coil, which provides improvements in the stored energy and the central magnetic field. In particular, the stored energy improves by approximately 43% compared with a rectangular cross section coil employing the same HTS tape length.

A Study on the Performance Improvement of an HTS Coil by the Outer Corner Modification

In designing an HTS coil, it is necessary to secure the large magnetic field and/or the stored energy with shorter tape length. From this point of view, the transport current performance of the HTS coil needs to be improved. The critical current and value depends on the magnitude and direction of the traversing magnetic field against the Bi-2223/Ag tapes. The critical current and value of the tape was measured with various magnitude and direction of the traversing magnetic field. From this, the fitting equations of the critical current and value for any magnitude and direction of the traversing magnetic field were obtained. Considering this anisotropic property of the tape, we considered the analytical model to obtain the coil critical current. As an initial coil shape, the minimum volume coil derived from the Fabry Factor constant curve is taken, which is often employed in low temperature superconducting coils. The electric field distribution within the coil cross-section was calculated to examine its effect on a current carrying capability. It was clear that high electric field portions appear at the coil edges due to the inclined magnetic flux against the tapes. In this study, the external corner portions of the coil are displaced under the condition that the total coil volume is kept constant. As a result of this, the coil critical current increased and the stored energy was improved by 20%.

2D Magnetic Design and Optimization of a 88-mm Aperture 15 T Dipole for NED

The Next European Dipole (NED) activity supported by the European Union aims at the development of a high-performance Nb3Sn conductor (Jc = 1500 A/mm2 @ 15 T, 4.2 K) in collaboration with European industry and at the design of a high- field dipole magnet making use of this conductor. In the framework of the NED collaboration which coordinates the activity of several institutes, CERN has contributed to the electromagnetic design study of a cos - thetas, layer-type superconducting dipole with an 88 mm aperture that is able to reach 15 T at 4.2 K. Part of the optimization process was dedicated to the reduction of the multipole coefficients so as to improve field quality while keeping an efficient peak-field to main-field ratio. In this paper, we present the optimization of the coil cross-section and of the shape of the iron yoke to reduce saturation-induced field errors during ramp. The effects of persistent magnetization currents are also estimated and different methods to compensate persistent-current-induced field distortions are presented.

Improvement of Dynamic Characteristics for Symmetric-Type Slim Optical Pickup Actuator by Changing Coil Shape

As rotational speed and track density of disk media in optical disk drives increases, an optical pickup actuator must have a high servo bandwidth for its focusing and tracking control to follow disk fluctuations. In this paper, we propose an efficient method to improve control bandwidth of actuators through changing the shape of cross section of coils without redesigning structural parts

Study on cross section of high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field and/or a large stored energy with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle against tapes. From this point, the performance improvement of HTS coils is taken into account with an analytical model. The minimum volume coil derived from the Fabry Factor constant curve is taken concerning the original coil shape, which is often employed in low temperature superconducting coils. The coil critical current was analyzed in consideration of the anisotropic properties of the tape. The electric field of HTS tapes in the coil was calculated at the coil critical current and the high electric field portion were cut out. The optimal coil cross section is obtained by iterating this calculation process. As a result, the critical current and the stored energy density of the coil were improved. The stored energy density increased about 17% and the central magnetic field was almost kept constant regardless of 19% reduction of HTS tapes, as compared with the original coil with the rectangular cross section.

Slit Design Consideration on the Ferromagnetic RF Integrated Inductor

Five types of RF integrated spiral inductors were microfabricated and applied for the discussion of local anisotropy field distribution in the film and the local current distribution in the coil cross section, which strongly influences the frequency profile of the complex permeability, ferromagnetic resonance (FMR) frequency and inductance-capacitance (LC) resonance frequency. The shifted type inductor exhibited as high quality factor as 20.7 at 1.9 GHz because the local FMR frequency is the highest and the current distribution is most uniform among the test inductors

Numerical Study on AC Loss Characteristics of HTS Coils With Various Cross Sections and Methods of AC Loss Reduction

AC loss characteristics of high temperature superconducting coils wound by Bi2223/Ag tape with various cross sections are numerically investigated. The numerical results show that the smaller coil aspect ratio, the smaller AC losses in the HTS coil. It was considered from the numerical results that the coil aspect ratio giving the minimum coil volume is the better shape judging from the many aspects such as the required length of tape, the stored energy, the central magnetic field and the critical current together with the AC loss. It was also shown by the numerical study that the optimal coil design giving the reduced AC loss can be done by employing the stepped cross section coil and the turn number graded coil

A Non-Linear Finite Element Model for the LHC Main Dipole Coil Cross-Section

The production of the dipole magnets for the Large Hadron Collider is at its final stage. Nevertheless, some mechanical instabilities are still observed for which no clear explanation has been found yet. A FE modelization of the dipole cold mass cross-section had already been developed at CERN, mainly for magnetic analysis, taking into account conductor blocks and a frictionless behavior. This paper describes a new ANSYS model of the dipole coil cross-section, featuring individual turns inside conductor blocks, and implementing friction and the mechanical non-linear behavior of insulated cables. Preliminary results, comparison with measurements performed in industry and ongoing developments are discussed

General coil-shape in superconducting quadrupole magnets for generating the perfect field

It is well-known that a constant current in a coil configuration generated by two perpendicular intersecting ellipses produces the perfect quadrupole field. We have found that an ideal quadrupole field can be obtained with a variety of coil shapes and the intersecting ellipse shape is only a special form in that class. We have given the general form of the coil shape for generating the ideal quadrupole field. The shape parameters of the coil can be optimized to obtain the maximum possible gradient for a given coil cross-section and aperture.

Three-Dimensional Supramolecular Organization of Molecular Rods Depending on Coil Cross Section in Rod−Coil Molecules

Coil−rod−coil molecules were prepared to have identical coil volume fraction (f = 0.78) relative to mesogenic rod segment, but different coil segments, i.e., poly(propylene oxide) with DP = 13 and poly(ethylene oxide) with DP = 18. Their self-assembly behavior in the solid and liquid crystalline phases was investigated using optical polarized microscopy and small-angle X-ray scattering techniques. The coil−rod−coil molecule with the poly(propylene oxide) coils shows a 3-D body-centered tetragonal micellar structure in both solid and liquid crystalline phases. In contrast, the coil−rod−coil molecule with the poly(ethylene oxide) coils exhibits a 3-D honeycomb-like lamellar structure in both solid and liquid crystalline phases. These results demonstrate that the cross-sectional area of coil significantly influences the self-assembly behavior of rod segments even at constant coil volume fraction relative to rod segment and provides the way to fine-tune 3-D supramolecular structures in the rod−coil system.

Study on the optimum design of a high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field, a large stored energy, etc. with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle with respect to tapes. In view of this, the performance improvement of HTS coils is taken into account with an analytical model. As a coil shape, the minimum volume coil derived from the Fabry Factor constant curve is taken up, which is often employed at low temperature coils. The electric field distribution within a coil cross-section is calculated to examine effects on a current carrying capability. It is clear that high electric field portions appear at the coil edge region due primarily to inclined magnetic fluxes against HTS tapes. Considering this, a grade winding method of a coil is proposed, where the winding density of conductors is reduced at coil edge portions. With this coil winding structure, the critical current of an HTS coil is improved since the magnetic field is reduced at edge portions. The stored energy per HTS tape length and the central magnetic field of the coil can be remarkably increased by this kind of grade winding method.

Analysis of AC loss characteristics of HTS coils with various cross-sections

An analytical study of AC loss characteristics of a high temperature superconducting coil wound by a Bi2223/Ag tape is presented in this paper. The AC loss in the high temperature superconducting coil wound by Bi2223/Ag tape was numerically calculated by using the measured DC data of the tape. The calculated AC loss was compared with the measured AC loss in the Bi2223 HTS coil obtained in the previous study. For the comparison of the measured and calculated AC losses, the mechanical loss was subtracted from the measured total loss data. The calculated AC losses were compared with the measured AC losses in the coil, producing rather good agreements. The relation between the AC loss characteristics in the HTS coil and shape of coil cross-section was numerically studied. A possible way to reduce the AC loss in the HTS coil was also presented and discussed.