Analytical computation of magnetic field in coil-dominated superconducting quadrupole magnets based on racetrack coils

Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.

Integrated multi-scale approach combining global homogenization and local refinement for multi-field analysis of high-temperature superconducting composite magnets

Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.

Gradient coil design with enhanced shielding constraint for a cryogen-free superconducting MRI system

The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems.In this study,we present an enhanced shielding method incorporating a regionalized stray field constraining strategy.By optimizing the constraint parameters,we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half.In real measurement in an integrated MRI system,the developed gradient assembly demonstrated good performance and supported to output images of excellent quality.Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.

A 3–5μm broadband YBCO high-temperature superconducting photonic crystal

Photonic crystal structures have excellent optical properties,so they are widely studied in conventional optical materials.Recent research shows that high-temperature superconducting periodic structures have natural photonic crystal features and they are favourable candidates for single-photon detection.Considering that superconductors have completely different properties from conventional optical materials,we study the energy level diagram and mid-infrared 3μm–5μm transmission spectrum of two-dimensional superconducting photonic crystals in both superconducting and quenched states with the finite element method.The energy level diagram of the circular crystal column superconducting structure shows that the structure has a large band gap width in both states.At the same fill factor,the circular crystal column superconducting structure has a larger band gap width than the others structures.For lattice structures,the zero transmission point of the square lattice structure is robust to the incident angle and environmental temperature.Our research has guiding significance for the design of new material photonic crystals,photon modulation and detection.

Transient multi-physics behavior of an insert high temperature superconducting no-insulation coil in hybrid superconducting magnets with inductive coupling

A transient multi-physics model incorporated with an electromagneto-thermomechanical coupling is developed to capture the multi-field behavior of a single-pancake(SP)insert no-insulation(NI)coil in a hybrid magnet during the charging and discharging processes.The coupled problem is resolved by means of the finite element method(FEM)for the magneto-thermo-elastic behaviors and the Runge-Kutta method for the transient responses of the electrical circuits of the hybrid superconducting magnet system.The results reveal that the transient multi-physics responses of the insert NI coil primarily depend on the charging/discharging procedure of the hybrid magnet.Moreover,a reverse azimuthal current and a compressive hoop stress are induced in the insert NI coil during the charging process,while a forward azimuthal current and a tensile hoop stress are observed during the discharging process.The induced voltages in the insert NI coil can drive the currents flowing across the radial turns where the contact resistance exists.Therefore,it brings forth significant Joule heat,causing a temperature rise and a uniform distribution of this heat in the coil turns.Accordingly,a thermally/mechanically unstable or quenching event may be encountered when a high operating current is flowing in the insert NI coil.It is numerically predicted that a quick charging will induce a compressive hoop stress which may bring a risk of buckling instability in the coil,while a discharging will not.The simulations provide an insight of hybrid superconducting magnets under transient start-up or shutdown phases which are inevitably encountered in practical applications.

A novel approach to designing cylindrical-surface shim coils for a superconducting magnet of magnetic resonance imaging

For a superconducting magnet of magnetic resonance imaging （MRI）, the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylin- drical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.

Calculation of AC Losses of CICC for Superconducting Outsert Coils in a Hybrid Magnet

This paper is devoted to predict AC loss of cable in conduit conductor （CICC） which is of importance in the design of conductors. The consideration for the conductor＇s design and main parameters for the magnets are introduced. In order to attain a good accuracy in the calculation of AC losses, the field distribution within superconducting outsert should be considered. Calculation of the AC losses, including hysteresis losses and coupling losses, is conducted. An emphasis is put on the hysteresis loss during the ramp up of the current to the operational current （15.3 kA） and the coupling loss of the conductor in a power-down condition for insert. The results are obtained to be 74.9 kJ and 950 J for 40 T hybrid magnets, respectively. Based on the calculation, a brief analysis of losses effect on the conductor design and the operation of magnet is given for the purpose that the capacity of the cryogenertor can be evaluated and the stability regime can be improved in our future work on the hybrid magnets.

New Development of VPI Process for Large Superconducting Coils

High vacuum is required for Vacuum Pressure Impregnation (VPI) process of large coils used in cryogenic. The defects such as dry spots and over rich resins should be minimized in large superconducting coils used. Both sealing problems associated with the mold and over rich resin problems are eliminated by using vacuum bag mold method with which we can simplify the design of vacuum mold.

Comparative Study of 10-MW High-Temperature Superconductor Wind Generator with Overlapped Field Coil Arrangement

The electromagnetic characteristics and iron loss of a high-temperature superconductor wind generator(HWG)equipped with an overlapped field coil arrangement(OFCA)are studied by comparing with the one equipped with the conventional field coil arrangement(CFCA).Through a quantitative analysis,it was found that HWG with OFCA exhibits better electromagnetic characteristics than HWG with CFCA and can reduce the iron loss by eliminating the magnetic flux sag caused by the adjacent field coil sides with the same current flow direction.In addition,the OFCA topology can further reduce the volume of the wind generator.

High-temperature superconducting filter using self-embedding asymmetric stepped impedance resonator with wide stopband performance and miniaturized size

In this study, a novel self-embedding asymmetric stepped impedance resonator （SE-ASIR） topology is proposed. By embedding asymmetric stepped impedance resonators in themselves, circuit sizes of ASIRs can be reduced effectively, while the ability to control spurious modes of ASIRs remains. Therefore, SE-ASIRs are suitable for being used to design filters with wide stopbands and miniaturized sizes. Furthermore, the construction process of the SE-ASIR is described in detail, and an equivalent model of the SE-ASIR is proposed. For demonstration, a high-temperature superconducting bandpass filter centered at 1112 MHz is designed and fabricated. The measured result agrees well with the simulation result and shows that the out-of-band rejection is better than 60 dB up to 4088 MHz, which is about 3.7 times the center frequency. The filter circuit size is 31 mm × 13 mm or 0.28λg × 0.12λg, where g is the guided wavelength at 1112 MHz.

High-Temperature Superconducting YBa_(2)Cu_(3)O_(7-δ)Josephson Junction Fabricated with a Focused Helium Ion Beam

As a newly developed method for fabricating Josephson junctions,a focused helium ion beam has the advantage of producing reliable and reproducible junctions.We fabricated Josephson junctions with a focused helium ion beam on our 50 nm YBa_(2)Cu_(3)O_(7-δ)(YBCO)thin films.We focused on the junction with irradiation doses ranging from 100 to 300 ions/nm and demonstrated that the junction barrier can be modulated by the ion dose and that within this dose range,the junctions behave like superconductor–normal conductor–superconductor junctions.The measurements of the I–V characteristics,Fraunhofer diffraction pattern,and Shapiro steps of the junctions clearly show AC and DC Josephson effects.Our findings demonstrate high reproducibility of junction fabrication using a focused helium ion beam and suggest that commercial devices based on this nanotechnology could operate at liquid nitrogen temperatures.

Correlated-Electron Systems and High-Temperature Superconductivity

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlomethod. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa2Cu3O7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability δ, δ~x, is satisfied in the lower doping region, as indicated by the variationalMonte Carlocalculations for the two-dimensional Hubbard model. A checkerboard-like charge-density modulation with a roughly period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t-t′-t″- U Hubbard model with a Bi-2212 type band structure and found that the period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantumMonte Carlomethod, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.

Collaborative Simulation and Testing of the Superconducting Dipole Prototype Magnet for the FAIR Project

The superconducting dipole prototype magnet of the collector ring for the Facility for Antiproton and Ion Research （FAIR） is an international cooperation project. The collaborative simulation and testing of the developed prototype magnet is presented in this paper. To evaluate the mechanical strength of the coil case during quench, a 3-dimensional （3D） electromagnetic （EM） model was developed based on the solid97 magnetic vector element in the ANSYS commercial software, which includes the air region, coil and yoke. EM analysis was carried out with a peak operating current at 278 A. Then, the solid97 element was transferred into the solid185 element, the coupled analysis was switched from electromagnetic to structural, and the finite element model for the coil case and glass-fiber reinforced composite （G10） spacers was established by the ANSYS Parametric Design Language based on the 3D model from the CATIA V5 software. However, to simulate the friction characteristics inside the coil case, the conta173 surface-to-surface contact element was established. The results for the coil case and G10 spacers show that they are safe and have sufficient strength, on the basis of testing in discharge and quench scenarios.

Compact high-order quint-band superconducting band-pass filter

In this paper, we present a compact quint-band superconducting filter operating at 2.4, 3.5, 4.7, 5.3, and 5.9 GHz.Matching junctions with different impedance branch lines are used to connect a dual-band sub-filter with a tri-band sub-filter and to reduce the channel interactions. The quint-band filter design is divided into two sections to determine the controllable frequencies and bandwidths, while ensuring compact size and reducing design complexity. The filter is fabricated on double-sided YBCO film deposited on an Mg O substrate with a size of 26 mm×19 mm. The measured results match well with the simulations.

Compact wide stopband superconducting bandpass filter using modified spiral resonators with interdigital structure

In this study, we propose a novel resonator that is composed of a modified spiral with an embedded interdigital capacitor. A large ratio of the first spurious frequency to the fundamental resonant frequency is obtained, which is suitable for the design of filters with wide stopbands, and the circuit size is considerably reduced by embedding the interdigital structure in the spiral. For demonstration, a compact four-pole high temperature superconducting（HTS） filter with a center frequency of 568 MHz is designed and fabricated on double-sided YBCO film with a size of 11.4 mm×8.0 mm. The filter measurement shows excellent performance with an out-of-band rejection level better than 60.9 dB up to 3863 MHz.

Compact superconducting single-and dual-band filter design using multimode stepped-impedance resonator

This study presents two multimode stepped-impedance structures to design single-and dual-band filters. Transmission zeroes are introduced for the single-band filter by using dual-mode stepped-impedance resonators. The single-band filter with high selectivity is centered at 6.02 GHz and has a fractional bandwidth （FBW） of 25.6%. Four stubs （two low frequency and two high frequency ones） are connected to the rectangular patch in the center to construct a quadruple-mode resonator. The independent conditions of the center frequencies of the high and low bands of the resonator are analyzed. A dual-band filter, which operates at 1.53 GHz and 2.44 GHz with FWBs of 12.1% and 14.1%, respectively is designed. The single-and dual-band filters are both fabricated with double-sided YBCO films and they can be used in mobile and satellite communications.

Ramping loss and mechanical response in a no-insulation high-temperature superconducting layer-wound coil and intra-layers no-insulation coil

The layer-wound coil has a great potential in nuclear magnetic resonance and magnetic resonance imaging owing to the better spatial homogeneity of the magnetic field.However,high-temperature superconducting(HTS)coil wound by no-insulation(NI)layer-wound technique has been verified with a long field delay time.A new method named the intra-layer no-insulation(LNI)winding technique has been proposed to reduce the charging delay time of the coil.This paper is mainly to study and compare the ramping loss and mechanical characteristics of the layer-wound coil and LNI coil.The results indicate that the total ramping loss can be significantly reduced by using the LNI winding method.The effects of the ramping rate of power supply current and the contact resistivity on the ramping loss are also discussed in the paper.Furthermore,the stress distributions in the layer-wound coil and LNI coil are compared,where the cooling process and Lorentz force are both considered.It can be found that the copper sheet of the LNI coil experiences relatively higher stress than its(RE)Ba;Cu;O;(REBCO)conductor layer.Meanwhile,the magnitude of stress generated in the REBCO conductor of the LNI coil is slightly different from that of the layer-wound coil.

合肥先进光源储存环超导纵向梯度弯铁样机研制

介绍了合肥先进光源储存环超导纵向梯度弯铁样机的研制工作,基于已发展的一种磁体结构参数优化方法,综合考虑磁场空间分布需求和超导线圈工作负载,完成了磁铁结构的设计和优化。为了验证磁体设计方案,应用一种矩形铌钛线材和DT4C电工纯铁材料,研制了一台纵向长度0.30 m、磁极间隙46 mm的磁体样机。并搭建了一套简易低温测试装置,对该磁体进行了励磁特性测量,经过10余次失超,测得磁体最大工作电流大于275 A。磁体纵向磁场分布测量结果表明,该磁体在约196 A工作电流下,纵向磁场积分值达到0.4 T·m,峰值磁场约4.5 T。测试结果与理论设计结果基本一致,表明该种超导磁体的设计是可行的。

Screening current in ultra-high-field non-insulated superconducting magnets

Screening current is recognized as one of the critical elements limiting the progression of superconducting magnets toward achieving higher magnetic fields. Currently, most non-insulated(NI) superconducting magnets consider the magnet as insulated when addressing the issue of screening current. However, the bypass current in the NI magnet can modify the actual history of magnetization, so the screening current in NI magnet will be different from that in the insulated magnet. This paper presents a novel method based on the homogenized T-A formulation(T is the current vector potential, and A is the magnetic vector potential), which enables real-time simulation of both the bypass current behavior and the implications of screening current in NI superconducting magnets, even when these magnets contain tens of thousands of turns. We have developed a 32 T NI hybrid superconducting magnet and validated the effectiveness of this method through experiments. Employing this efficacious method,we conducted a comprehensive calculation of screening current in NI magnets, comparing them with insulated magnets in terms of screening current-induced stress(SCIS), screening current-induced field(SCIF), and losses. The results indicate that in the NI insert coils, the sequential excitation of background coils and insert coils induces a reverse screening current, resulting in slightly lower SCIF and SCIS compared to those in the insulated magnets. The method and results can contribute to the enhancement of magnet design and provide valuable insights for the development of ultra-high fields(UHF) NI magnets.

Theoretical understanding of correlation between magnetic phase transition and the superconducting dome in high-Tc cuprates

Many issues concerning the origin of high-temperature superconductivity(HTS)are still under debate.For example,how the magnetic order varies with doping and its relationship with the superconducting temperature(Tc);and why Tcalways peaks near the quantum critical point.In this paper,taking hole-doped La_(2)CuO_(4)as a classical example,we employ the first-principles band structure and total energy calculations with Monte Carlo simulations to explore how the symmetry-breaking magnetic ground state evolves with hole doping and the origin of a dome-shaped superconductivity region in the phase diagram.We demonstrate that the local antiferromagnetic order and doping play key roles in determining the electron-phonon coupling,thus Tc.Initially,the La_(2)CuO_(4)possesses a checkerboard local antiferromagnetic ground state.As the hole doping increases,Tcincreases with the enhanced electron-phonon coupling strength.But as the doping increases further,the strength of the antiferromagnetic interaction weakens and spin fluctuation increases.At the critical doping level,a magnetic phase transition occurs that reduces the local antiferromagnetism-assisted electron-phonon coupling,thus diminishing the Tc.The superconductivity disappears in the heavily overdoped region when the ferromagnetic order dominates.These observations could account for why cuprates have a dome-shaped superconductivity region in the phase diagram.Our study,thus,contributes to a fundamental understanding of the correlation between doping,local magnetic order,and superconductivity of HTS.