Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by , with t = T/Tc. Knowing Hc2*(T) implies that Jc(T) is also known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from T up to about 80% of the maximum Hc2 can be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain () dependence is introduced through a temperature and strain dependent Hc2*(T,) and Ginzburg–Landau (GL) parameter κ1(T,) and a strain dependent critical temperature Tc(). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependences on Hc2*(T) and Hc2*(). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkably simple relation , where C is a constant, s() represents the normalized strain dependence of Hc2*(0) and h = H/Hc2*(T,). Finally, a new relation for s() is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues with respect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyse magnet performance from wire results.

/pdf/a-general-scaling-relation-for-the-critical-current-density-3o1ips6ain.pdf

A general scaling relation for the critical current density in Nb3Sn

This paper presents a topical review of the current state of the art in modelling the magnetization of bulk superconductors, including both (RE)BCO (where RE?=?rare earth or Y) and MgB2 materials. Such modelling is a powerful tool to understand the physical mechanisms of their magnetization, to assist in interpretation of experimental results, and to predict the performance of practical bulk superconductor-based devices, which is particularly important as many superconducting applications head towards the commercialization stage of their development in the coming years. In addition to the analytical and numerical techniques currently used by researchers for modelling such materials, the commonly used practical techniques to magnetize bulk superconductors are summarized with a particular focus on pulsed field magnetization (PFM), which is promising as a compact, mobile and relatively inexpensive magnetizing technique. A number of numerical models developed to analyse the issues related to PFM and optimise the technique are described in detail, including understanding the dynamics of the magnetic flux penetration and the influence of material inhomogeneities, thermal properties, pulse duration, magnitude and shape, and the shape of the magnetization coil(s). The effect of externally applied magnetic fields in different configurations on the attenuation of the trapped field is also discussed. A number of novel and hybrid bulk superconductor structures are described, including improved thermal conductivity structures and ferromagnet?superconductor structures, which have been designed to overcome some of the issues related to bulk superconductors and their magnetization and enhance the intrinsic properties of bulk superconductors acting as trapped field magnets. Finally, the use of hollow bulk cylinders/tubes for shielding is analysed.

/pdf/modelling-of-bulk-superconductor-magnetization-iet0fuf1ew.pdf

Modelling of bulk superconductor magnetization

The ITER magnet coils are wound from Cable-In-Conduit Conductors (CICC) made up of superconducting and copper strands assembled into a multistage, rope-type cable inserted into a conduit of butt-welded austenitic steel tubes. The conductors for the Toroidal Field (TF) and Central Solenoid (CS) coils require about 500 tons of Nb3Sn strands while the Poloidal Field (PF) and Correction Coil (CC) conductors need around 250 tons of Nb-Ti strands. The required amount of Nb3Sn strands far exceeds pre-existing industrial capacity and calls for a significant worldwide production scale up. After explaining the in-kind procurement sharing of the various conductor types among the six ITER Domestic Agencies (DA) involved: China, Europe, Japan, South Korea, Russia, and the United States, we detail the technical requirements defined by the ITER International Fusion Energy Organization (IO), and we present a brief status of ongoing productions. The most advanced production is that for the TF conductors, where all six DAs have qualified suppliers and about 50% of the required strands have been produced and registered into the web-based conductor database developed by the IO.

Status of ITER Conductor Development and Production

We review the scaling relations for the critical current density (Jc) in Nb3Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) = 1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from mu0H = 1 T up to about 80 percent of the maximum Hc2 can be described with Kramer's flux shear model, if non-linearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain (e) dependence is introduced through a temperature and strain dependent Hc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a strain dependent critical temperature Tc(e). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependencies on Hc2*(T) and Hc2*(e). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkable simple relation Jc(H,T,e)= (C/mu0H)s(e)(1-t1.52)(1-t2)h0.5(1-h)2, where C is a constant, s(e) represents the normalized strain dependence of Hc2*(0) andh = H/Hc2*(T,e). Finally, a new relation for s(e) is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues withrespect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyze magnet performance from wire results.

We have developed a model that describes the transverse load degradation in Nb3Sn CICCs, based on strand and cable properties, and that is capable of predicting how such degradation can be prevented. The Nb3Sn cable in conduit conductors (CICCs) for the International Thermonuclear Experimental Reactor (ITER) show a significant degradation in their performance with increasing electromagnetic load. Not only do the differences in the thermal contraction of the composite materials affect the critical current and temperature margin, but mostly electromagnetic forces cause significant transverse strand contact and bending strain in the Nb3Sn layers. Here, we present the model for transverse electro-magnetic load optimization (TEMLOP) and report the first results of computations for the ITER type of conductors, based on the measured properties of the internal tin strand used for the toroidal field model coil (TFMC). As input, the model uses data describing the behaviour of single strands under periodic bending and contact loads, measured with the TARSIS set-up, enabling a discrimination in performance reduction per specific load and strand type. The most important conclusion of the model computations is that the problem of the severe degradation of large CICCs can be drastically and straightforwardly improved by increasing the pitch length of subsequent cabling stages. It is the first time that an increase of the pitches has been proposed and no experimental data are available yet to confirm this beneficial outcome of the TEMLOP model. Larger pitch lengths will result in a more homogeneous distribution of the stresses and strains in the cable by significantly moderating the local peak stresses associated with the intermediate-length twist pitches. The twist pitch scheme of the present conductor layout turns out to be unfortunately close to a worst-case scenario. The model also makes clear that strand bending is the dominant mechanism causing degradation. The transverse load on strand crossings and line contacts, abbreviated as contact load, can locally reach 90 MPa but this occurs in the low field area of the conductor and does not play a significant role in the observed critical current degradation. The model gives an accurate description for the mechanical response of the strands to a transverse load, from layer to layer in the cable, in agreement with mechanical experiments performed on cables. It is possible to improve the ITER conductor design or the operation margin, mainly by a change in the cabling scheme. We also find that a lower cable void fraction and larger strand stiffness add to a further improvement of the conductor performance.

https://iopscience.iop.org/article/10.1088/0953-2048/19/9/011/pdf

Transverse load optimization in Nb3Sn CICC design; influence of cabling, void fraction and strand stiffness

We have developed an instrument to study the behavior of the critical current density (Jc) in superconducting wires and tapes as a function of field (μ0H), temperature (T), and axial applied strain (ea). The apparatus is an improvement of similar devices that have been successfully used in our institute for over a decade. It encompasses specific advantages such as a simple sample layout, a well defined and homogeneous strain application, the possibility of investigating large compressive strains and the option of simple temperature variation, while improving the main drawback in our previous systems by increasing the investigated sample length by approximately a factor of 10. The increase in length is achieved via a design change from a straight beam section to an initially curved beam, placed perpendicular to the applied field axis in the limited diameter of a high field magnet bore. This article describes in detail the mechanical design of the device and its calibrations. Additionally initial Jc(ea) dat...

A device to investigate the axial strain dependence of the critical current density in superconductors

We have measured the critical current (Ic) of a high current density Nb3Sn strand subjected to spatial periodic bending, periodic contact stress and uniaxial strain. The strand is destined for the cable-in-conduit conductors (CICC) of the European dipole (EDIPO) 12.5 T superconducting magnet test facility. The spatial periodic bending was applied on the strand, using the bending wavelengths from 5 to 10 mm with a peak bending strain of 1.5%, a periodic contact stress with a periodicity of 4.7 mm and a stress level exceeding 250 MPa. For the uniaxial strain characterization, the voltage–current characteristics were measured with an applied axial strain from −0.9% to +0.3%, with a magnetic field from 6 to 14 T, temperature from 4.2 to 10 K and currents up to almost 900 A. In addition the axial stiffness was determined by a tensile axial stress–strain test. The characterization of the strand is essential for understanding the behaviour of the strand under mainly axial thermal stress variation during cool down and transverse electromagnetic forces during charging, which is essential for the design of the CICC for the dipole magnet. The strand appears to be fully reversible in the compressive regime during the axial strain testing, while in the tensile regime, the behaviour is already irreversibly degraded when reaching the maximum in the critical current versus strain characteristic. The degradation is accentuated by an immediate decrease of the n value by a factor of 2. The parameters for the improved deviatoric strain description are derived from the Ic data, giving the accuracy of the scaling with a standard deviation of 4 A, which is by far within the expected deviation for the large scale strand production of such a high Jc strand. The Ic versus the applied bending strain follows the low resistivity limit, indicative of full interfilament current transfer, while a strong decrease is observed at a peak bending strain of ~0.5%. For the periodic contact stress it appears that beyond 60 MPa, the Ic becomes noticeably irreversible. The n value, being a better indicator for the irreversible behaviour than the Ic, seems to indicate a somewhat lower level of the transverse stress irreversibility. Since the strand appears to be quite sensitive to the tensile strain, for the EDIPO CICC design, the tensile intrinsic axial strain in the filamentary region should stay well below zero (only compressive) and the contact stress sufficiently below 50 MPa. These requirements are feasible, in particular for a CICC design with steel conduit which would provide sufficient thermal compression, a sufficiently low void fraction and a cabling pattern that limits the peak bending strain during transverse load to about 0.3%.

https://iopscience.iop.org/article/10.1088/0953-2048/21/6/065001/pdf

Axial and transverse stress–strain characterization of the EU dipole high current density Nb3Sn strand

Change of interstrand contact resistance and coupling loss in various prototype ITER NbTi conductors with transverse loading in the Twente Cryogenic Cable Press up to 40,000 cycles

Knowledge of the influence of bending on the critical current (Ic) of Nb3Sn strands is essential for the understanding of the reduction in performance due to transverse electromagnetic load. In particular, for the large cable-in-conduit conductors (CICCs) meant for the international thermonuclear experimental reactor (ITER), we expect that bending is the dominant mechanism for this degradation. We have measured the Ic of a bronze, a powder-in-tube and an internal tin processed Nb3Sn strand when subjected to spatial periodic bending using bending wavelengths from 5 to 10 mm. Two of these strands were applied in model coils for the ITER. We found that the tested strands behave according to the so-called low interfilament resistivity limit, confirming full current transfer between the filaments. This is supported by AC coupling loss measurements giving an indication of the interfilament current transfer length. The reduction of Ic due to bending strain can then be simply derived from the bending amplitude and the Ic versus axial applied strain (e) relation. This Ic(e) sensitivity can vary for different strand types but since the electromagnetic force is the driving parameter for strand bending in a CICC, the stiffness of the strands definitively plays a key role, which is confirmed by the results presented

Critical current and strand stiffness of three types of Nb3Sn strand subjected to spatial periodic bending

The large currents in the cable-in-conduit conductors (CICC) destined for the high field magnets in the International Thermonuclear Experimental Reactor (ITER), cause huge transverse forces on the strands compressing the cable against one side of the conduit. This load causes transverse compressive strain in the strands at the crossovers contacts. Moreover, the strands are also subjected to bending and contact surfaces micro-sliding, which results into friction and anomalous contact resistance versus force behavior. Three Nb/sub 3/Sn central solenoid model coil (CSMC) conductors were tested previously in the Twente Cryogenic Cable Press up to 40 cycles with a transverse peak load of 650 kN/m. This press can transmit a variable (cyclic) transverse force directly to a cable section of 400 mm length at a temperature of 4.2 K (or higher). To explore life-time cycling, we tested a CSMC Nb/sub 3/Sn conductor up to 40,000 cycles. The coupling loss and the associated interstrand resistance between various strands and strand bundles are measured at various loads. The force on the cable and the displacement are monitored in order to determine the effective cable Young's modulus and the mechanical heat generation. Some aspects of strand deformation in CICC's are discussed. The test results are discussed in view of previous press results and data extracted from the ITER model coil tests.

Wouter Abbas

Papers

A device to investigate the axial strain dependence of the critical current density in superconductors

Axial and transverse stress–strain characterization of the EU dipole high current density Nb3Sn strand

Change of interstrand contact resistance and coupling loss in various prototype ITER NbTi conductors with transverse loading in the Twente Cryogenic Cable Press up to 40,000 cycles

Critical current and strand stiffness of three types of Nb3Sn strand subjected to spatial periodic bending

Performance of an ITER CS1 model coil conductor under transverse cyclic loading up to 40,000 cycles