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.

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.

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.

An improved analysis method for assessing the nuclear-heating impact on the stability of toroidal field magnets in fusion reactors

The superconducting magnet system of a fusion reactor plays a vital role in plasma confinement,a process that can be dis-rupted by various operational factors.A critical parameter for evaluating the temperature margin of superconducting magnets during normal operation is the nuclear heating caused by D-T neutrons.This study investigates the impact of nuclear heat-ing on a superconducting magnet system by employing an improved analysis method that combines neutronics and thermal hydraulics.In the magnet system,toroidal field(TF)magnets are positioned closest to the plasma and bear the highest nuclear-heat load,making them prime candidates for evaluating the influence of nuclear heating on stability.To enhance the modeling accuracy and facilitate design modifications,a parametric TF model that incorporates heterogeneity is established to expedite the optimization design process and enhance the accuracy of the computations.A comparative analysis with a homogeneous TF model reveals that the heterogeneous model improves accuracy by over 12%.Considering factors such as heat load,magnetic-field strength,and cooling conditions,the cooling circuit facing the most severe conditions is selected to calculate the temperature of the superconductor.This selection streamlines the workload associated with thermal-hydraulic analysis.This approach enables a more efficient and precise evaluation of the temperature margin of TF magnets.Moreover,it offers insights that can guide the optimization of both the structure and cooling strategy of superconducting magnet systems.

Explaining Pomeranchuk Effect by Parity of Magnetic Moments of Leptons and Hadrons for Superconductivity in 3He and Graphene*

The mystery of superconductivity has intrigued scientists for 110 years now. The author in 2014 specifically predicted the superconductivity in carbon, sulfur and hydrogen compounds and generally predicted carbonaceous, hydrogeneous and sulfurous compounds in 2005 with reference to scattering to asymmetric orbital motions and associated spin and orbital exchanges between nuclei and electrons. The emphasis was in 2005 upon stronger electron and nuclear interactions and electron-phonon effects. But here the author develops more the un-gerade parity of the p and f orbitals and their contributions to the superconductivity at lower pressures and higher temperatures. On the bases of such, the role of parity from the origin and inflation of the Universe is noted and dark and bright energies and matters in the mature Universe are reasoned. Moreover, the superconductors are all reasoned by positive and negative nuclear magnetic moments (NMMs) with availability of un-gerade parities of p and f subshells and their orbitals. In addition to superconductivity, such positive and negative NMMs by Little Effect is presented for explaining Pomeranchuk Effect and thereby further explaining superconductivity and superfluidity of 3He. On the bases of successes of Little Effect via positive and negative NMMs, in particular negative NMMs of 3He, the superconductivity in twisted graphene is explained and also its recently discovered Pomeranchuk Effect.

Development of 5 T NbTi Superconducting Magnet with 160 mm Warm Bore for Magnetic Separation

A wide-bore 5 T NbTi superconducting magnet, for magnetic separator, with an operational current of 106 A is designed and fabricated. This magnet with a Ф60 mm roomtemperature bore is installed in a vacuum cryostat and immersed in liquid helium. A two-stage 4 K Gifford-McMahon （GM） cryocooler is used to maintain the cooling shield at 70 K and the condenser at 4 K in order to achieve the zero vaporization loss of liquid helium. The cooling power of the GM cryocooler is 1.5 W. In this paper, the design, heat leakage, stress analysis, quench protection characteristics and preliminary test results are presented.

Study on a Highly Stabilized Power Supply for Hybrid-Magnet Superconducting Outsert

The superconducting outsert of the 40 T hybrid-magnet in High Magnetic Field Laboratory （HMFL） of Chinese Academy of Sciences （CAS） requires a highly stabilized power supply. In this paper, two kinds of power supply design are briefly presented and both advantages and disadvantages are analyzed. In order to overcome the drawbacks of switching power supply, a series regulated active filter is adopted and a new design is proposed which ensures cooperative relationship between the feedback control loops of the switching converter and the series regulated active filter. Besides, unlike the traditional switching power supply, which can generate positive voltage only, this new design can also generate negative voltage which is needed in the quench protection for the superconducting magnet. In order to demonstrate the effectiveness of the methodology, a low-power prototype has been accomplished. The simulation and experiment results show that the power supply achieves high precision under the combined action of two feedback control loops. The peak-to-peak amplitude of the output ripple voltage of the prototype is 0.063%, while the peak-to-peak amplitude of the output ripple current is 120 ppm.

Innovative pre-concentration technology for recovering ultrafine ilmenite using superconducting high gradient magnetic separator

To achieve the utilization of the abandoned ultrafine ilmenite(-20 μm) produced in the titanium magnetite processing plant in Panzhihua,the superconducting high-gradient magnetic separation(SMS) technology was proposed in this study.After optimizing the conditions of magnetic intensity,feeding and pulsation,an SMS concentrate with TiO_(2) grade of 16.03% and TiO_(2) recovery of 66.39% was obtained through one roughing-one cleaning pre-concentration flowsheet.The specific magnetic force and magnetic force were calculated and analysed to illustrate the pre-concentration mechanism,and the results revealed that the combination of high magnetic field and strong pulsating resulted in the effective preconcentration of the ultrafine ilmenite in the SMS process.In addition,the magnetic force analysis indicated that the high magnetic intensity and high magnetic gradient are the key factors of the SMS technology.Furthermore,the EDS-Mapping detection certified that the ultrafine ilmenite was concentrated from the gangue minerals using SMS technology.

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.

Present Status of the KSTAR Superconducting Magnet System Development

The mission of Korea Superconducting Tokamak Advanced Research (KSTAR)project is to develop an advanced steady-state superconducting tokamak for establishing a scientificand technological basis for an attractive fusion reactor. Because one of the KSTAR mission is toachieve a steady-state operation, the use of superconducting coils is an obvious choice for themagnet system. The KSTAR superconducting magnet system consists of 16 Toroidal Field (TF) coils and14 Poloidal Field (PF) coils. Internally-cooled Cable-In-Conduit Conductors (CICC) are put into usein both the TF and PF coil systems. The TF coil system provides a field of 3.5 T at the plasmacenter and the PF coil system is able to provide a flux swing of 17 V-sec. The major achievement inKSTAR magnet-system development includes the development of CICC, the development of a full-size TFmodel coil, the development of a coil system for background magnetic-field generation , theconstruction of a large-scale superconducting magnet and CICC test facility. TF and PF coils are inthe stage of fabrication to pave the way for the scheduled completion of KSTAR by the end of 2006.

Mechanical Analysis and Measurements of a Multicomponent NbTi/Cu Superconducting Magnets Structure for the Fully Superconducting Electron Cyclotron Resonance Ion Source

A fully superconducting electron cyclotron resonance （ECR） ion source （SECRAL ID is currently being built in the Institute of Modern Physics, Chinese Academy of Sciences. Its key components are three superconducting solenoids （Nb-Ti/Cu） and six superconducting sextupoles （Nb-Ti/Cu）. Different from the conventional supercon- ducting ECR magnetic structure, the SEC17AL Ⅱ includes three superconducting solenoid coils＇ that are located inside the superconducting sextupoles. The SECRAL Ⅱ can significantly reduce the interaction forces between the sextupole and the solenoids, and the magnets can also be more compact in size. For this multi-component SECRAL Ⅱ generating its self field of -8 T and being often exposed to the high self field, the mechanical analysis has become the main issue to keep their stress at 〈200 MPa on coils. The analytical and experimental results in mechanics are presented in the SECRAL Ⅱ structure. To improve the accuracy and efficiency of analysis, according to the composite rule of micromechanics, the equivalent uniform windings are used to simulate the epoxy-impregnated Nb-Ti/Cu coils. In addition, using low temperature strain gauges and a wireless fast strain acquisition system, a fundamental experiment on the based on our analysis, the stresses and deformations optimized. strains developments of a sextupole is reported. Finally, for its assembly of each SECRAL Ⅱ coil will be further

The Test Facility for the EAST Superconducting Magnets

A large facility for testing superconducting magnets has been in operation at the Institute of Plasma Physics of the Chinese Academy of Sciences since the completion of its construction that began in 1999. A helium refrigerator is used to cool the magnets and liquefy helium which can provide 3.8 K-4.5 K, 1.8 bar-5 bar, 20g/s-40g/s supercritical helium for the coils or a 150 L/h liquefying helium capacity. Other major parts include a large vacuum vessel （3.5 m in diameter and 6.1 m in height） with a liquid nitrogen temperature shield, two pairs of current lead, three sets of 14.5 kA-50 kA power supply with a fast dump quench protection circuitry, a data acquisition and control system, a vacuum pumping system, and a gas tightness inspecting devise. The primary goal of the test facility is to test the EAST TF and PF magnets in relation to their electromagnetic, stability, thermal, hydraulic, and mechanical performance. The construction of this facility was completed in 2002, followed by a series of systematic coil testing. By now ten TF magnets, a central solenoid model coil, a central solenoid prototype coil, and a model coil of the PF large coil have been successfully tested in the facility.

Optimal Design for Open MRI Superconducting Magnet with Active Shielding

The optimal design method for an open Magnetic Resonance Imaging （MRI） superconducting magnet with an active shielding configuration is proposed. Firstly, three pairs of current rings are employed as seed coils. By optimizing the homogeneity of Diameter Sphere Voltnne （DSV）, the positions and currents of the seed coils will be obtained. Secondly, according to the positions and currents of the seed coils, the current density of superconducting wires is determined, and then the original sections for the coils can be achieved. An optimization for the homogeneity based on the constrained nonlincar optimization method is employed to determine the coils with good homogeneity. Thirdly, the magnetic field generated by previous coils is set as the background field, then add two coils with reverse current, and optimize the stray field line of 5 Gauss in a certain scope. Finally, a further optimization for the homogeneity is used to get Final coils. This method can also be used in the design of other axisynmaetfic superconducting MRI magnets.

Angular Dependence of Lateral and Levitation Forces in Asymmetric Small Magnet/Superconducting Systems

The dipole-dipole interaction model is used to calculate the angular dependence of lateral and levitation forces on a small permanent magnet and a cylindrical superconductor in the Meissner state lying laterally off the symmetric axis of the cylinder. Under the assumption that the lateral displacement of the magnet is small compared with the physical dimensions of the system, we obtain analytical expressions for the lateral and levitation forces as functions of geometrical parameters of the superconductor as well as the height, the lateral displacement and the orientation of magnetic moment of the magnet. The effect of thickness and radius of the superconductor on the levitation force is similar to that for a symmetric magnet/superconducting cylinder system, but within the range of lateral displacement. The splitting in the levitation force increases with the increasing angle of orientation of the magnetic moment of the magnet. For a given lateral displacement of the magnet, the lateral force vanishes when the magnetic moment is perpendicular to the surface of the superconductor and has a maximum value when the moment is parallel to the surface. For a given orientation of the magnetic moment, the lateral force has a linear relationship with the lateral displacement. The stability of the magnet above the superconducting cylinder is discussed in detail.

Preliminary Engineering Design of Toroidal Field Magnet System for Superconducting Tokamak HT-7U

HT7U is a large fusion experimental device. It will be built in the Institute of Plasma Physics of Chinese Academy of Sciences. The mission of HT-7U is to develop the scientific basis for a continuously operating tokama-k fusion reactor. This paper describes only a toroidal field (TF) superconducting magnet system of HT7U. In this paper, design criteria of conductor and stability analysis, coil winding and support structure design of magnet system, mechanical calculation and stress analysis, heat load evaluation are given.

The 5.8 T Cryogen-Free Gyrotron Superconducting Magnet System on HL-2A

A 5.8 T cryogen-free superconducting magnet （SCM） system with a warm bore hole of 160 mm in diameter, used for gyrotrons operating in the frequency range from 68 GHz to 140 GHz, is installed on the site of the HL-2A tokamak. The SCM consists of two separate solenoidal magnetic coils connected in series, a 4.2 K Gifford-McMahon （GM） refrigerator, a com- pressor, a coil power supply and two temperature monitors. The performance, test and preliminary experimental results of this SCM system are described in this paper. The magnetic field distribu- tion was measured along the axis, and a dummy tube was used for adjusting the magnet system. Finally, the magnet was used for the operation of a 68 GHz/500 kW gyrotron, which is part of an electron cyclotron resonance heating （ECRH） system. With an additional auxiliary coil and after adjusting tile magnet system, a maximum output power for the ECRH system of up to 400 kW was achieved.

A novel transient rotor current control scheme of a doubly-fed induction generator equipped with superconducting magnetic energy storage for voltage and frequency support

A novel transient rotor current control scheme is proposed in this paper for a doubly-fed induction generator（DFIG）equipped with a superconducting magnetic energy storage（SMES） device to enhance its transient voltage and frequency support capacity during grid faults. The SMES connected to the DC-link capacitor of the DFIG is controlled to regulate the transient dc-link voltage so that the whole capacity of the grid side converter（GSC） is dedicated to injecting reactive power to the grid for the transient voltage support. However, the rotor-side converter（RSC） has different control tasks for different periods of the grid fault. Firstly, for Period I, the RSC injects the demagnetizing current to ensure the controllability of the rotor voltage. Then, since the dc stator flux degenerates rapidly in Period II, the required demagnetizing current is low in Period II and the RSC uses the spare capacity to additionally generate the reactive（priority） and active current so that the transient voltage capability is corroborated and the DFIG also positively responds to the system frequency dynamic at the earliest time. Finally, a small amount of demagnetizing current is provided after the fault clearance. Most of the RSC capacity is used to inject the active current to further support the frequency recovery of the system. Simulations are carried out on a simple power system with a wind farm. Comparisons with other commonly used control methods are performed to validate the proposed control method.

Development of Experimental Superconducting Magnet for the Collector Ring of FAIR Project

A pool cooled experimental magnet based on the copper stabilized NbTi supercon- ducting wire was designed, fabricated and tested, in order to evaluate the engineering design of the dipole superconducting magnet for the collector ring （CR） of the facility for antiproton and ion research （FAIR） project. In this paper, the experimental setup including quench protection system was presented. Performance of the liquid helium pool cooled test was introduced. All of the results indicate both the performance of conductor and the experimental superconducting magnet under low temperature is stable, which suggests the engineering design are feasible for the formal magnet in CR of the FAIR project.

Early Studies of Superconductive Materials and Superconducting Magnet in China(1962～1966)

On the basis of the published literature and the interviews with some participants,this paper introduces the early history of the studies of superconductive materials and superconducting magnet during 1962～ 1966 in China,narrates the achievements of other relevant experimental and theoretical studies of superconductivity in that period briefly,and tries to give the authors' comments on that history.