High-field Magnet Design Research Articles

Multiscale modelling and numerical homogenization of the coupled multiphysical behaviors of high-field high temperature superconducting magnets

Ensuring the safe and stable operation of the high temperature superconducting (HTS) magnet has become a key problem to be solved currently. In this paper, we developed a numerical homogenization scheme to simulate the coupled electromagnetic-thermal-mechanical behaviors of the REBCO (REBa2Cu3Ox, where RE = rare earth) high field magnets. The homogenized T-A formulation is adopted to model the electromagnetics of HTS tapes. The representative volume element (RVE) based on the micromechanics is created to predict the homogenization properties of the magnets. The field dependences of the critical current density of HTS tapes on the magnetic field, magnetic field angle, the temperature and the strain are considered. The effectiveness and efficiency of the proposed numerical scheme have been well validated through comparisons with experimental results. Moreover, the effects of the anisotropic plasticity on the mechanical behaviors of the HTS magnets are also evaluated. Our results show that compared with the Hill’s anisotropic model the commonly used isotropic von Mises plasticity model underestimates the plastic strain in the magnet. Under ultrahigh magnetic field, quench of the magnet is mainly triggered by the strain-induced degradation in the critical current of HTS tapes, which needs special attention in the design of high field magnets.

Critical current degradation behaviour of various REBCO tapes under uniaxial strain

REBCO coated tapes have become one of the most practical superconducting materials, which have been considered in the design of high-field magnets for fusion in the future. At present, several manufacturers are able to produce commercial REBCO tapes. During the fabrication and operation of REBCO magnets, REBCO tapes are subjected to tension, compression, bending, and torsion loads, resulting in applied strains. However, the critical current (Ic) of REBCO tape is strain dependence. Therefore, the clear Ic performance of a single REBCO tape under applied uniaxial strain is required before designing REBCO conductors/magnets in order to help select an appropriate tape specification and manufacturer. In this paper, several measurements of Ic and n-value versus applied uniaxial strain were performed on different kinds of REBCO tapes, which were produced by Shanghai Superconductor Technology and Fujikura at 77 K with self-field on the U-spring device. The width of the REBCO tape is from 3 mm to 5 mm, and the thickness of the substrate is from 25 μm to 50 μm. The results show that the Ic of most of the tapes are reversible under applied uniaxial compressive strain. The width of the tape and the thickness of the substrate affects the irreversible tensile strain limit. The n-value of the REBCO tape hardly depends on the strain condition.

Predicting the superconducting transition temperature and relative resistance ratio in YBa[formula omitted]Cu[formula omitted]O[formula omitted] films

The increase in critical temperature, Tc, of high-temperature superconductors fulfills the needs of practical applications with liquid-helium-free refrigeration and a delay in magnet failure. The YBa2Cu3O7 (YBCO) superconductor exhibits Tc of greater than 90 K and an upper critical field of greater than 100 T, which is a promising candidate in high-field magnet design. Due to their large anisotropy in current transportation, YBCO superconductors are usually processed as thin films by pulsed-laser deposition. But the research requires significant manpower for materials synthesis, analysis, and quench detection, as well as costly equipment and facilities. In this work, we develop the multiple linear regression model to shed light on the relationship between pulsed laser deposition parameters and the superconducting transition temperature (Tc) and relative resistance ratio (rR) in the laser deposition of YBa2Cu3O7 films. The model is straightforward and simple and demonstrates a high degree of accuracy and stability, contributing to fast low-cost estimations of Tc and rR.

Study on screening current field of quasi-isotropic strand and directly stacked strand at different field orientations

REBCO tapes, the so-called second-generation high temperature superconductor, have wide application prospects in electrical engineering and high field magnets because of their high critical current density and superior mechanical and electromagnetic properties. However, a screening current field (SCF) can be induced by the perpendicular component of the magnetic field if the tapes are in a variable magnetic field since the width of the commercial tape is generally more than 2 mm. As a result, the SCF results in an uneven spatial distribution of the magnetic field. In this paper, the SCFs of the quasi-isotropic strand and the directly stacked strand, made of the REBCO tapes, are calculated at 77 K under different orientations of a 300 mT external magnetic field. Then, the experiments are conducted under the same conditions as the simulation. The experimental results are in good agreement with the calculated results. The conclusions of this paper are helpful to understand the SCFs of two kinds of strands and useful in the design of high field magnets in the future.

Intelligent design of large-size HTS magnets for SMES and high-field applications: using a self-programmed GUI tool

Different from many superconducting magnet designs based on the analytical algorithm and finite element method (FEM), this article presents an intelligent design of the SMES and high-field magnet using the self-programmed graphical user interface (GUI). As the important basis, the analytical solutions of SMES magnet are developed for calculating the magnetic field, inductance and critical current, whose accuracies are also verified by the experiment. Then, the analytical solutions are merged into the GUI tool with multi-window interface based on the MATLAB. The new platform is built to offer scientists and engineers a smart tool to design and optimize SMES magnets to reach the maximum energy capacity. After the structural optimization of a MJ-class SMES magnet, the critical current and energy capacity improve by 20.46% and 38.67%, respectively. Compared to previous superconducting magnet designs, this new platform for the SMES and high-field magnet design has the advantages of diverse HTS tape/magnet structure selections, user-friendly interface, automatic optimization, and fast speed.

Guiding future high-field magnet design by better predicting and mitigating screening current-induced stress and strain

Guiding future high-field magnet design by better predicting and mitigating screening current-induced stress and strain

Joint Resistance Characteristics in Ultrasonic Weld REBCO CC Tapes at Various Temperatures and Magnetic Fields

In coil and magnet manufacturing that requires long length 2G coated conductor (CC) tapes, the development of joining methods for CC tapes with zero or low resistance is necessary. Nowadays, although it is said that CC tapes with around 1-km length were produced, it is still inadequate to produce cables and coil windings. Therefore, the development of a stable and reliable joint for long CC tapes having a low joint resistance (R j ) and the understanding of the magnetic field and temperature dependence of R j is essential in the design of high field magnets and coils. In this study, the characteristics of joint resistance in REBCO CC tapes jointed using ultrasonic welding (UW) method were experimentally evaluated in various temperatures and magnetic field. The CC joints were also fabricated by hybrid welding, which incorporates soldering to the UW joint. The magnetic field and temperature dependencies of joint resistance of both types CC joints were measured. The acquired results showed that the joint resistance decreased with a decrease of temperature, and increased slightly as magnetic field applied increased.

The 77-K Stress and Strain Dependence of the Critical Current of YBCO Coated Conductors and Lap Joints

The electromechanical performance of commercially available YBCO high-temperature superconductor (HTS) is characterized in support of the 32T all-superconducting magnet program at the National High Magnetic Field Laboratory. Accurate characterization of the HTS coated conductors mechanical properties are essential for the aggressive high-field magnet design. Here, we report the 77-K stress-strain behavior of a series of conductors with varying thickness coatings of copper. The electromechanical performance of the conductors is determined in tests to measure the critical current as a function of applied axial strain, at 77-K in self field. Available conductor lengths necessitate a magnet design with soldered lap joints and the subsequent evaluation the lap joint performance reported here. Reports of low transverse strength and conductor delamination due transverse ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis) tensile stress prompted tests to measure the conductors' electrical performance in the presence of transverse stress that are also reported.

Florida electro-mechanical cable model ofNb3Sn CICCs for high-field magnet design

Performance degradation of Nb3Sn cable-in-conduit-conductors (CICCs) is a critical issue in large-scale magnet designsuch as in the International Thermonuclear Experimental Reactor (ITER) andthe series-connected hybrid (SCH) magnets currently under development at theNational High Magnetic Field Laboratory (NHMFL). The critical current Ic ofNb3Sn conductors is strongly affected by thermal pre-strain in strand filaments in a CICC fromdifferential thermal contraction between strands and conduit during cooling down afterheat treatment. Mitchell and Nijhuis recently introduced strand bending underlocally accumulated Lorentz force for the interpretation of observed transverseload degradation, defined as the Ic reduction due to strand bending and contactstress at strand crossing with respect to the expected Ic from strand data atthe thermal compressive strain. In this paper, a new numerical model of CICCperformance has been developed based upon earlier work by Mitchell and Nijhuis.The new model, called the Florida electro-mechanical cable model (FEMCAM),combines the thermal bending effects during cooling down and the electromagneticbending effects during magnet operation, as well as effects due to strand filamentfracture. We present the FEMCAM formulation and benchmark the results againstabout 40 conductor tests of first-cycle performance and 20 tests that include cyclicloading. We also consider the effects of different jacketing materials on CICCperformance. We conclude that FEMCAM can be a helpful tool for the design ofNb3Sn-basedCICCs and that both thermal bending and transverse bending play important roles in the performanceof Nb3Sn CICCs.

Modeling of the Performance of $\hbox{Nb}_{3}\hbox{Sn}$ CICCs for High Field Magnet Design

Accurate prediction of the performance of cable-in-conduit-conductors (CICCs) is challenging but critical for the design of high field magnets such as the series connected hybrid (SCH) magnet currently under development at the NHMFL. With various CICC tests performed for EFDA dipole magnet and ITER, we present the Florida electro-mechanical cable model (FEMCAM) and demonstrate that it is a self-consistent model incorporating important effects caused by differential thermal contraction and filament fracture to better predict CICC performance.

Magnet Technology Beyond 50 T

The unique opportunities high magnetic fields offer scientific research, and their use as a tool for science, have motivated many activities to expand their technological limits. Because of the Lorentz forces, the successful design of high field magnets is a challenge at the frontiers of magnet technology, and it is equally a stimulus for the materials scientist. The quest for higher fields translates into the urgent need for ultra-strong materials with higher Young's modulus and conductivity. High field magnets are an ideal test bed for materials and concepts. Fields above 50 T can be generated with continuous and pulsed fields. We describe the technologies, which have been developed, the achievements and the potential for future improvements. We focus mainly on the field region between 50 T and 100 T

Selected Composites for High Field Magnets

AbstractThe national high magnetic field laboratory builds and uses various high field magnets for fundamental research. In building high field magnets, a variety of high strength composites are required because of the Lorentz stresses generated by high field exceeding the strength of most of the materials, particular conductors. For example, a field of 60 T can generate a magnetic pressure that corresponds to a stress in the conductor of 1.5 GPa, which is at the limit of known conducting materials with conductivity higher than 70% International Annealed Copper Standard and sizes suitable for building high field magnets. The design of high field magnets is limited by these forces and, consequently, by the available materials. At the same time, the materials need to have excellent physical properties. For instance, the conductors need to have high electrical conductivity and high specific heat and the superconductors should have high critical current in field and low alternative current losses. This paper outlines our requirements and research on metal matrix composite materials for building high field magnets. The discussions include both the macrocomposite and microcomposite. The scales of the structures in the composites are from millimeters to nanometers.

Robust design of high field magnets through Monte Carlo analysis

An effective approach to the optimal design of electromagnetic devices should take into account the effect of mechanical tolerances on the actual devices performance. A possible approach could be to match a Pareto optimality study with a Monte Carlo analysis by randomly varying the constructive parameters. In this paper it is shown how such an analysis can be used to allow an expert designer to select among different Pareto optimal designs.

Shape optimization of high T/sub c/ superconducting magnets

The availability of new high-temperature superconducting (HTS) tapes makes it possible to realize high-field HTS magnets made of such tapes, wound in "pancake coils" shape. The critical current characteristics of HTS tapes are anisotropic, and specific criteria must be adopted in the optimal design of such HTS magnets, that imply a time-consuming analysis of the magnetic field map at each step of the optimization process. In this paper, a new optimization scheme, able to deal with the HTS high-field magnet design, is presented.

A high field magnet design for a future Hadron collider

US high energy physics community is exploring the possibilities of building a Very Large Hadron Collider (VLHC) after the completion of LHC. This paper presents a high field magnet option based on Nb/sub 3/Sn technology. A preliminary magnetic and mechanical of a 14-16 T, 2-in-1 dipole based on the common coil design approach is presented. The computer code ROXIE has been upgraded to perform the field quality optimization of magnets based on the racetrack coil geometry. A magnet R&D program to investigate the issues related to high field magnet designs is also outlined.

An approach to materials processing and selection for high-field magnet design

In this paper, the physical principles and design criteria for materials selection for high-field, pulsed magnets is discussed. Selection charts are developed based on the design constraints of minimizing ohmic heating and resisting Lorentz forces. Using the selection charts, the merits of various materials are compared. The effects of processing techniques on the material properties and, therefore, the performance of the magnet design are illustrated with the use of selection charts. This leads finally to a discussion of development vectors for composite winding materials.

Review of quasi-optical gyrotron development

There is currently a need for megawatt average power sources of 100–600 GHz radiation for electron cyclotron heating of fusion plasmas. One of the leading candidates for such a source, the conventional wave guide cavity gyrotron,(1) has produced impressive output powers and efficiencies at frequencies up to about 300 GHz. However, this gyrotron configuration is limited at high frequencies by high ohmic heating and problems with transverse mode competition due to the highly overmoded configuration, and with beam collection, since the beam must be collected along a section of the output waveguide. The quasi-optical gyrotron (QOG), first proposed in 1980 by Sprangle, Vomvoridis, and Manheimer,(3) features an open resonator formed by a pair of spherical mirrors instead of a waveguide resonator and has the potential for overcoming each of these limitations. The resonator mirrors can be well removed from the beam-wave interaction region, allowing a large volume for the interaction and low ohmic heating densities at the mirrors. The beam direction is transverse to the resonator so that beam collection is separate from the output waveguide. This geometry is particularly well suited to the use of a depressed collector for electron beam energy recovery. The QOG operates in the lowest-order transverse (TEMool) Guassian mode of the resonator, higher-order transverse modes being effectively suppressed by higher diffraction losses. This paper reviews recent progress toward the development of high-power quasi-optical gyrotrons for ECRH of fusion plasmas. It includes an overview of gyrotron theory in terms of normalized variables as they apply to the quasi-optical gyrotron for operation both in the fundamental and the higher harmonics. Scaling equations for the output power and resonator mirror heating by the RF are given. The design tradeoffs between annular and sheet electron beams are discussed as is the issue of beam space-charge depression in the open resonator. Recent advances in the analysis and design of QOG configurations capable of efficient and stable single-mode operation are discussed, showing the possibility of achieving 50% transverse efficiency in highly overmoded resonators. The application of a depressed collector is discussed as a means of recovering the energy in the axial motion of the spent electron beam and, thus, raising the output efficiency to near the transverse electronic efficiency. The problem of high field magnet design is addressed, for both fundamental and higher harmonic operations, the latter being necessary at very high frequencies. The design equations and tradeoffs are applied to the design of 1-MW, CW quasi-optical gyrotrons operating at 120 GHz, in the first and second harmonic at 280 GHz and in the second harmonic at 560 GHz. The output coupling for these 1 MW designs is 5–7% showing the potential for even higher powers per tube if sheet-beam electron guns can be developed. The estimated electronic efficiency of the fundamental harmonic designs is 23%, which leads to an output efficiency of 47% with the use of a depressed collector with a modest collection efficiency. The peak ohmic heating density is 500 kW/cm2 in all the designs. This leads to resonator mirror separations ranging from 127 cm for 120-GHz design, to 232 cm for the 560-GHz, second harmonic design. Finally, a simple output system composed of'elliptical and parabolic mirrors is described that converts the output radiation from the resonator into a parallel, quasi-Gaussian beam. Experimental programs are reviewed as well, including the recent experiment at the Naval Research Laboratory that produced frequencies ranging from 95–130 GHz and powers up to 150 kW. Operation in a single mode was observed at powers up to 125 kW despite the resonator being highly overmoded. Comparison is made with the theoretically-predicted region of single-mode operation. Recent progress in the experimental characterization of QOG resontors is summarized.

The initial filament strain state of cable-in-conduit superconductors and the relation of this strain to large-bore, high-field magnet design

Cable-in-conduit superconductors formed by enclosing a cable of MF-Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn/Cu composites in a strong steel sheath are a useful element in magnet design and construction. However, an important feature of this type conductor, which must be understood and accounted for in magnet design, is the initial strain state of the superconducting filaments. This initial strain state results from the differential cooldown strains of the various components of the cable-in-conduit system as this system is brought from the Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn formation temperature (∼1000 K) to the operation temperature (∼4 K). The resultant strain depends on the proportions and thermomechanical properties of the constituent materials. However, empirical data suggest that the initial strain state also depends on the void fraction in the cable. In this paper, we survey the literature to provide data for a simple model to describe the mechanical link between cable and sheath. We also report on new experiments devised to further clarify this link. In addition, we discuss using the initial superconductor strain state as a parameter in magnet design.

Long sample high sensitivity critical current measurements under strain

The extreme strain sensitivity of the critical current in Nb 3Sn superconductors at high fields is well known and must be taken into account in the design of high field magnets where strains up to 0.5% may be encountered. Current density/field measurements are relatively easy to perform but current density/strain measurements require fairly elaborate equipment and are time consuming in their execution. As a result commercial data is readily available for predicting current density at a particular field for a particular conductor but its measurement at a particular strain is less available. In this Paper an apparatus is described in which the sample is attached on the outside of the turns of a very thick spiral spring such that when one end of the spring is rotated with respect to the other the outer surface and, therefore, the sample is either stretched or even compressed. The sample geometry of six turns of 40 mm diameter over a length of 70 mm, is very similar to that typically used in current density/field measurements and using it strain tests can similarly be easily performed. Long samples can be tested in small bore ( ≈ 55 mm) solenoids where > 1–2% field variation can be achieved over the measured length and current transfer effects can be avoided so that unambiguous measurements can be obtained at a sensitivity of > 1.0 μV m −1. The strain sensitivity of the conductors used in this work increased between 3.6 and 5.4% per decade increase in electric field sensitivity at 11 T.

In situ formed multifilamentary composites part I: Coupling mechanisms, stress effects and flux pinning mechanisms

Recent developments on in situ formed multifilamentary composites are reviewed and their superconducting and mechanical properties discussed in terms of the underlying physical mechanisms. The evidence is presented for a strong size dependence of the strengthening, flux-pinning and coupling mechanisms and, in turn, the composite normal-state and superconducting transport properties. The importance of the composite microstructure and micro-geometry is illustrated with data on Cu-Nb, Cu-Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn and Cu-V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Ga conductors. In particular densely spaced interfaces are shown to interact effectively with both matrix crystal dislocations and flux-line lattice, resulting in strongly anisotropic material properties. The importance of the proximity-effect coupling is discussed for Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn-based composites below the microstructural percolation threshold where the self-field critical current densities (normalized to the filament volume fraction) reached values of 1.4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . At high fields, the performance of Cu-V <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Ga in situ composites is significantly better than that of Cu-Nb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> Sn conductors, with typical normalized values of J <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> of 1.4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> at 18 Tesla and 4.2 K. Possible use of Cu-Nb in situ composites in high-field magnet design is also discussed in view of their remarkable strength (up to 2.9 GPa at 77 K) and high normal-state conductivity.