Nb 3 Sn Wires and Cables for High-Field Accelerator Magnets

Since the discovery of superconducting Nb 3 Sn in 1954, continuous developments have led to a strong improvement of its properties. This chapter describes the evolution of Nb 3 Sn fabrication techniques since the 1960s and the main properties of modern Nb 3 Sn composite wires and Rutherford cables.


Introduction
The intermetallic compound Nb 3 Sn, discovered by Matthias et al. (1954), is a type II superconductor having a stoichiometric composition ranging from 18-25 atomic percent (at.%) Sn.Its crystal structure is classified as A15 (also known as β-tungsten).The critical temperature T c0 is ~18 K, and the upper critical magnetic field B c20 can reach 30 T. As a comparison, the ductile alloy Nb-Ti has a T c0 of 9.8 K and a B c20 of 14.5 T, which makes Nb-Ti adequate only for operational magnetic fields of up to 8-9 T. Thanks to its larger critical current density J c , Nb 3 Sn enables operating fields in accelerator magnets above 10 T. This field is larger than any achieved with present Nb-Ti particle accelerator magnets.Some of the challenges with Nb 3 Sn are that it requires high-temperature processing to create the superconducting Nb 3 Sn phase.It is also a brittle material, which makes it strainsensitive, i.e., high strain on the sample may reduce or totally destroy its superconductivity (Foner and Schwartz 1981).
The first laboratory attempt to produce Nb 3 Sn wires was in 1961 at Bell Laboratories (Kunzler et al. 1961) by filling Nb tubes with crushed powders of Nb and Sn and drawing them into long wires.This primitive powder-in-tube (PIT) technique required reaction at very high temperatures, in the range of 1000-1400 C, to form the superconducting Nb 3 Sn phase.Nevertheless, that same year it was used to fabricate the first 6 T solenoid.An initial alternative to PIT wires and the first commercial production of Nb 3 Sn were tape conductors fabricated by either chemical vapor deposition (1963) or by surface (or liquid solute) diffusion of Sn into a Nb E. Barzi • A. V. Zlobin (*) Fermi National Accelerator Laboratory (FNAL), Batavia, IL, USA e-mail: barzi@fnal.gov;zlobin@fnal.govsubstrate (1964).Although successful in demonstrating the use of Nb 3 Sn in highfield magnets, none of these techniques were very practical.The large filaments in the case of the PIT wire, and the inherently large aspect ratio of the tape, invariably resulted in large trapped magnetization and flux jump instabilities.
A major step for practical Nb 3 Sn production occurred with the discovery of the solid-state diffusion process.It was demonstrated in 1970 that the superconducting Nb 3 Sn phase can be produced at the interface of Nb and a Cu-Sn alloy at lower temperatures compared to binary Nb and Sn couples.This principle allowed composite conductors to be formed in fine multifilamentary configurations by cold working, and before heat treatment.The bronze route (Howlett 1970;Kaufmann and Pickett 1971;Tachikawa 1971) was the first application of the above principles.To overcome the J c limits of the bronze method the internal tin (IT) process was introduced in 1974 (Hashimoto and Yoshizaki 1974).The PIT, bronze, and IT methods were further developed into multifilamentary composites, and practically all commercially available wires are now produced by one of these methods.
In the 1980s and early 1990s, the development of Nb 3 Sn conductor was mainly steered by fusion magnet programs.The Nb 3 Sn toroidal magnetic system of the Tokamak T-15 was built and tested in the USSR at the end of 1988.The construction of the T-15 motivated the use of Nb 3 Sn wires for the International Thermonuclear Experimental Reactor (ITER).The conductor-development programs for accelerator magnets were focused on Nb-Ti composite wires and were driven by the needs of accelerators such as the Tevatron, the Superconducting Super Collider (SSC), and the Large Hadron Collider (LHC).Since the late 1990s the high-energy physics (HEP) community has taken leadership in the development of Nb 3 Sn wires for post-LHC accelerators to be used in high-field accelerator magnet research and development (R&D).
In this chapter we describe the development of commercial Nb 3 Sn composite wires and tapes from the 1960s to the 1990s.We then illustrate the most important wire properties and their progress, as achieved in HEP by 2010.Finally, Rutherford cables are touched upon.These developments on wires and cables were crucial for the first reproducible accelerator-quality Nb 3 Sn dipole and quadrupole magnets and their scale-up in the 2000s to the 2010s.Definitions of key wire and cable parameters are presented in Appendix 1. Properties and fabrication methods for Nb 3 Sn composite wires and Rutherford cables have also been reviewed elsewhere (Dietderich and Godeke 2008;Bottura and Godeke 2012;Barzi and Zlobin 2016).
2.2 Development of Nb 3 Sn from the 1960s to the 1990s

Nb 3 Sn Development from the 1960s to the 1970s
The very first commercial Nb 3 Sn composite conductor, which was used for accelerator magnet models in the period from the 1960s to the 1970s, was in the form of a flexible tape (also called a ribbon).A schematic of a Nb 3 Sn ribbon is shown in Fig. 2.1.
Tape conductors had been fabricated by chemical vapor deposition since 1963, and by surface diffusion of Sn into a Nb substrate since 1964.The latter process, also called Liquid Solute Diffusion, consisted of the introduction of a thin Nb tape into a molten Sn bath.The Sn-coated tape was then heated to ~1000 C in a vacuum or inert atmosphere to form Nb 3 Sn on both sides of the substrate.The tape was then Cu-cladded or Cu-plated for electrical stabilization.This technique was readily developed for long length production of ~500 m, and was first available in 1964 from the National Research Corporation in Massachusetts.Next, in 1965 the Compagnie Générale de Télégraphie sans Fil in France commercially produced a tape that was double the width and half the thickness, to allow for coil bending around smaller radii.In the same year, General Electric (GE) at Schenectady, NY, produced wide tapes with currents of 150 A, 300 A, and 600 A at 10 T. This was possible by fabricating tapes with a double substrate.GE also provided stainlesssteel cladding, in addition to the Cu cladding option.And finally, in 1968 the Plessey Company in England introduced a diffusion-type Nb 3 Sn narrow ribbon, which was Cu-cladded on one or both sides.
In parallel, chemical vapor deposition was developed, which is accomplished by hydrogen reduction of a mixture of chlorides of the constituent elements.By passing chloride over the metallic elements at ~1000 C, gaseous chlorides such as SnCl 2 and NbCl 4 are produced.The chlorides are reduced by hydrogen and helium gasses, and the Sn and the Nb are deposited in the proper proportions onto substrates such as stainless steel.The A15 layer thickness was controlled by the rate at which the substrate was passed through the reaction chamber.Following deposition of Nb 3 Sn, the ribbon was electroplated with a thin layer of nickel and then clad with silver or copper.The sole commercial producer of this material since 1963 had been the Radio Corporation of America (RCA), at Harrison, New Jersey, offering wide tape at current ratings of 300 A, 600 A, 900 A, and 1200 A at 10 T. It is to be noted that the vapor-deposited ribbon had a critical temperature of only 15 K, compared to 18 K for the diffusion process material.Whereas the commercial diffusion-type tapes were offered either bare or insulated with varnish, the vapor-deposited ribbon was just offered bare.
Conductor testing at that time included critical current and resistive critical temperature measurements of short samples, as well as continuous testing of the ribbon magnetization when passed through a 5 T field and measured with pick-up coils.This latter method produced the diamagnetic strength of the superconducting layer and allowed the detection of defects both in the superconductor and at the interface between superconductor and conducting metal.Unfortunately, information on the performance of these ribbons is limited.The best engineering current density of 500 A/mm2 at 4.2 K and 12 T was obtained in a small-bore solenoid coil wound with RCA tape.The lowest current density of 270 A/mm 2 at 4.2 K and 2 T was seen in a 0.6 m long quadrupole with a large aperture.It is interesting that, at that time, instabilities had already been recognized as a challenge.Ribbons had anisotropic properties and suffered from flux jumps in magnetic fields perpendicular to the tapes' wide face.In solenoidal coils, flux jump instabilities already occurred in magnetic fields below 8-10 T. Flux jumping was observed as voltage spikes much larger than expected by magnet inductance when ramping the current up and down.An experiment showed that by doubling the purity of the normal Cu conductor the current limits increased, but were still not at the short sample limit (SSL).When coils were instead used as inserts into a magnet and operated in background fields, the short sample limit was more likely to be achieved.
Requirements for superconductor stability with respect to magnetic flux jumps and superconductor protection in case of transition to the normal state led to the concept of composite superconducting wire, in which thin superconducting filaments are distributed in a normal low-resistance matrix.This matrix provides several important functions.It conducts heat away from the surface of the superconducting filaments because of high thermal conductivity, absorbs a substantial fraction of heat due to its high specific heat, and decreases Joule heating when the superconductor becomes normally conducting.To reduce eddy currents induced by varying external fields and improve the stability of composite wires to flux jumps, these filaments are twisted along the wire axis.
Multifilamentary Nb 3 Sn composite wires were possible through the discovery of the solid-state diffusion process and by finding that Nb 3 Sn can be produced at the interface of Nb and a Cu-Sn alloy at lower temperatures than for binary Nb-Sn couples.The formation of the brittle compound could be therefore postponed until the desired geometrical configurations for conductors (such as a multifilamentary wire) were achieved.
In the binary Nb-Sn system, single-phase Nb 3 Sn is formed by solid-state diffusion above ~930 C, where the only stable phase is Nb 3 Sn.At temperatures below 845 C, the two non-superconducting phases NbSn 2 and Nb 6 Sn 5 are also stable, and all three phases will grow at the interface, with NbSn 2 most rapidly formed and Nb 3 Sn being the slowest.In the ternary system (Nb-Cu-Sn), however, the only relevant stable phase is Nb 3 Sn, even at lower temperatures.The diffusion path from the Cu-Sn solid solution to the Nb-Sn solid solution passes through the A15 phase field alone, preventing formation of the non-superconductive phases.In short, the addition of Cu strongly lowers the A15 formation temperature from well above 930 C to practical values in industrial wires of ~650 C, thereby also limiting grain growth and retaining a higher grain boundary density, as required for flux pinning.
This principle was used to fabricate multifilamentary Nb 3 Sn composite wires by the so-called bronze route, which is still today one of the leading techniques for manufacturing Nb 3 Sn wires for various applications.The bronze process is based on a large number of thin Nb filaments dispersed in a Sn-rich bronze matrix (Fig. 2.2).
The initial billet is made of hundreds of Nb rods, and it is drawn into a hexagonal element of intermediate size.The rods are then cut and assembled in a second billet, which is extruded, annealed, and drawn to the final wire size.The bronze core is surrounded by a high-purity Cu matrix that is separated by a thin Nb or Ta diffusion barrier.The composite is twisted to increase electromagnetic stability and reduce AC losses.The bronze route provides the smallest filament size (~2-3 μm), but has a relatively low critical current density J c due to the 13 wt% limited content of Sn in bronze.
The external diffusion process, a modification of the bronze method, was introduced in 1972.This process consists of extruding a Nb-Cu composite and drawing it to a final size.The wire is then coated with a layer of Sn before heating it to form a Cu-Sn alloy matrix and then Nb 3 Sn filaments.The main benefit of this variant was that the Sn in the matrix was not limited as in the case of the bronze process.Its primary difficulty was delamination of the outer layer of the wire for plated Sn layers thicker than 5 μm.The maximum wire size was therefore limited to 0.25 mm.
The IT diffusion process, another modification of the bronze method, was first reported in 1974.This process consists of assembling Cu-clad Nb bars and a Cu-clad Sn-Cu alloy rod in a Cu tubing such that the Sn-Cu rod is at the center (Fig. 2.3).The assembly is then cold-drawn to final size.By restacking a number of assemblies and redrawing the billet down, a larger number of filaments and reduced bundle sizes are obtained.The advantage over the external diffusion process was that the Cu stabilizer, and a Ta barrier to protect the Cu from Sn diffusion, could be placed either outside of a wire in a single barrier configuration (Fig. 2.3a), or around each filament bundle in a distributed barrier configuration (Fig. 2.3b).Another interesting method that was proposed in 1973 was the in situ process.It consisted of casting a Nb-Cu melt to form a dendritic network of Nb in Cu, and of drawing it to wire.Sn could be added in the initial melt or afterward before heat treatment.The most interesting aspect of this method was the great enhancement of the wire mechanical properties, due to the close proximity of the finely divided filaments.
Several companies were already active in producing commercial Nb 3 Sn wires by that time.US companies included Airco, Inc., Intermagnetics General Corporation (IGC), Supercon, Inc., and Teledyne Wah Chang Albany (TWCA).
Airco, Inc. had started to manufacture superconductors in the mid-1960s at their Central Research and Development Laboratories in Murray Hill, NJ.They moved their manufacturing plant to Carteret, NJ in 1979.Their standard bronze wire was based on a modular approach, which meant combining one of three first extrusions containing 19, 55, and 187 rods, respectively, into second extrusion billets.In the 1970s Airco supplied 14 kg of 0.3 mm diameter 30% Nb in situ wire, Sn-plated on a commercial plating line in Airco's plant, to Brookhaven National Laboratory (BNL) for Nb 3 Sn dipoles.In parallel, in cooperation with BNL, Airco developed a technique to wrap a multifilamentary Cu matrix conductor around a high-Sn Cu alloy core.The cable was then sheathed in Cu on a continuous tube mill to produce long lengths of finished wire.This was called the "distributed tin" process and reduced some of the problems encountered by external tinning.Airco also developed and brought to commercial maturity a high-rate magnetron sputtering process for producing Nb 3 Sn tape for transmission lines by a variation of the bronze process.
In the USSR, the collaboration between the Kurchatov and Bochvar institutes and several plants of the nuclear industry focused on the development and production of Nb 3 Sn wires for new thermonuclear facilities and for research magnets with high fields (Chernoplekov 1978).Studies of Nb 3 Sn tapes were also conducted from 1962 to 1972.Equipment for the industrial production of tape by tinning was manufactured and installed in industry, but the work was stopped after the discovery of the solid-phase diffusion method.In 1972, intensive testing of multifilamentary samples based on Nb 3 Sn composite wires began.The number of tests in subsequent years reached 3000 samples per year.These studies led to the Tokamak T-15 project with Nb 3 Sn toroidal coils (Chernoplekov 1981).For this project, in the 1980s the USSR industry produced 30 tons of 1.5 mm diameter Nb 3 Sn bronze wire with a Sn content of 10.5%.
Several Japanese companies also developed and produced Nb 3 Sn composite wires.Sumitomo Electric Industries developed Nb 3 Sn conductors in which the Nb 3 Sn layer is formed by solid-liquid reaction between Nb tubes and the Cu-Sn alloy core (Yamasaki and Kimura 1982).This simpler method was later called the "internal-tin tube" or "tube-type" method.Mitsubishi Electric Co. was working on the internal Sn diffusion process, and Toshiba R&D Center and Showa Electric Wire and Cable Co. developed a Nb tube method.Furukawa Electric Company was working on bronze Nb 3 Sn conductors with a large current capacity.Hitachi Ltd. and Hitachi Cable Co. focused on large-scale multifilamentary Nb 3 Sn composite wires.
By this time, critical current measurements of wires were performed within the bore of a solenoid on either straight samples a few centimeters long in a transverse field, or on a few turns wound around a 3.5-4 cm diameter barrel.The longer sample length allowed the use of a critical current criterion of 10 À14 Ω m (i.e., smaller resulting voltages) as opposed to an electrical field criterion of 1 μV/cm.Inductive critical temperature measurements of short samples were sometimes added to conductor characterization as a means to identify lower critical temperature T c regions in the material.The degradation of the critical current I c due to the bending of the wire was measured as function of the bending diameter.The critical current density at 4.2 K and 12 T in the non-Cu samples ranged from 500 to 700 A/mm 2 in round wires.

Nb 3 Sn Development from the 1980s to the 1990s
In 1980, TWCA proposed another innovative process called "jellyroll."In this process Nb foil was slit on a conventional slitter used to produce expanded mesh and rolled in a "jellyroll" together with bronze sheet.After wrapping with a diffusion barrier and a Cu stabilizer, the billet was compacted and then extruded and drawn in a conventional manner.
By the end of the 1990s, Oxford Superconducting Technology (OST), previously Airco, was fabricating Nb 3 Sn multifilamentary wires with a modified jellyroll (MJR) process.In this version of the IT process, thin Nb sheets (with a thickness from 50 to 500 μm) were slit and expanded with controlled interconnection distances of 5-150 mm.The expanded Nb sheet (45-85% open) was then rolled up with the desired matrix material (i.e., bronze, Cu, Al, etc.) in the fashion of a jellyroll, inserted into a Cu container, sealed, extruded, and processed as conventional wire.A diffusion barrier was inserted if needed.
To overcome some of the constraints of the MJR process, OST also worked in the early 2000s on an internal Sn strand made with a restacking process called hot extruded rod (HER) process (Parrell et al. 2002).In this method, small Sn rods were inserted into the washed-out salt holes after extrusion.This technique, which was successfully demonstrated for a 37 restack, resulted in better bonding and had the potential for economic production of large quantities of conductor, as is the case for Nb-Ti.It was later abandoned, however, due to the relatively large effective filament diameter, or D eff .
In September 1980, the Energy Research Foundation (ECN) from the Netherlands presented an alternative process that used both conventional and powder technologies.The core of a Nb tube was filled with fine grain size NbSn 2 powders inserted into a Cu tube and the resulting wire reacted at temperatures of 650-700 C to form a continuous Nb 3 Sn layer.The so-called PIT process was further optimized by the Shape Metal Innovation Company (SMI) (Lindenhovius et al. 1999) (Fig. 2.4).
By the end of the 1990s, the strand samples used for I c measurements were typically wound on grooved cylindrical Ti-alloy (Ti-6Al-4V) barrels, and held in place by two removable end rings.This method is still current today.After heat treatment, the Ti-alloy end rings are replaced by Cu rings, and voltage-current (V-I) characteristics are measured in boiling He at 4.2 K, in a transverse magnetic field provided by a solenoid.The voltage is measured along the sample by means of voltage taps placed 50 cm apart.The I c is determined from the V-I curve by either the 10 À14 Ω m resistivity or the 0.1 μV/cm electrical field criterion.The relative directions of the external magnetic field and the transport current are such as to generate an inward Lorentz force.Due to the latter and the differential thermal contraction between sample and barrel, the specimen is subject to a tensile strain of up to 0.05% at 12 T and 4.2 K.This strain leads to an overestimate of I c between 3% and 5%.The n-values are determined in the V(I c )-10V(I c ) range by fitting the V-I curve with the power law V ~In .Using this procedure, typical I c uncertainties can be as low as AE1% at 4.2 K and 12 T, and about AE5% for the n-values.Magnetization measurements are performed with either balanced coil or vibrating-sample magnetometers.
Another new type of characterization included measuring the I c of strands extracted from Rutherford-type cables.Plastic deformation during cabling affects the strand integrity.This phenomenon depends on the specific strand design and structure, and I c degradation after cabling can be an indicator of internal damage.

Target Parameters of Nb 3 Sn Wires for HEP
IT and PIT are the two Nb 3 Sn composite wire technologies, with sufficiently high J c and availability in large quantities from industry, that were used in magnets for HEP applications in the new millennium.Commercial Nb 3 Sn wires based on these two processes were further developed to meet the needs of accelerator magnets.
State-of-the-art PIT and IT wires benefited from at least two HEP-related conductor programs.The US Conductor Development Program (CDP) (Scanlan 2001) was started in 1999 by the US Department of Energy (DOE) as a collaborative effort of US industry, national laboratories, and universities with the goal of increasing the critical current density of Nb 3 Sn IT wires for HEP applications including high-field accelerator magnets.Parallel R&D started in the early 2000s in the European Union as part of the Next European Dipole (NED) program (Devred et al. 2004).The target Both programs had similar performance requirements in terms of J c and D eff , but NED was focused on the development of PIT composite Nb 3 Sn wires of larger diameter (up to 1.25 mm) for high-field magnet applications.The effort was later continued by CERN with Bruker-EAS for the High Luminosity LHC (HL-LHC) upgrades.
Development of Nb 3 Sn wires for high-field accelerator magnets continues.At present, properties are driven by the design studies of a Future Circular Collider (FCC) (Ballarino and Bottura 2015).The FCC Nb 3 Sn wire specifications are also shown in Table 2.1.They are focused on reaching higher J c at 16 T and on a significant reduction of conductor cost.The push for J c increase is a stimulus for improving flux pinning using artificial pinning centers (APC) and increasing the upper critical field B c2 of Nb 3 Sn.CERN is presently co-funding the R&D of several superconductor companies in Europe, Asia, and Russia to achieve the target parameters in commercial Nb 3 Sn wires and to involve a sufficient number of companies in the longer-term production of large conductor volumes.

PIT Nb 3 Sn Wires
The latest PIT process is based on stacking thick-wall round Nb tubes filled with fine NbSn 2 powder in a high-purity Cu matrix.The stacked assembly is drawn or extruded to the final wire size.This method allows an optimal combination of small filament size (<50 μm) and high J c comparable with the IT process.The current cost of PIT wire is, however, a factor of two to three higher than the cost of IT wire.
The PIT process, first developed by the Netherlands Energy Research Foundation (ECN), was further optimized by the Shape Metal Innovation Company (SMI).In 2006 Bruker-EAS in Germany purchased the "know-how" for the PIT technology from SMI to industrialize this type of conductor.Cross-sections of some PIT composite wires produced by SMI and later by Bruker-EAS are shown in Fig. 2.5.
The development of this technique has allowed the production of kilometer-long wires with 192 filaments.Shorter laboratory-scale wire samples with 504 and even 1332 filaments were also obtained.Wires were manufactured at Bruker-EAS in about 50 kg net production units.In 2008 the commercial PIT wire design started using round filaments instead of hexagonal ones to keep both the J c and residual resistivity ratio (RRR) high during heat treatment and to reduce cabling degradation.These positive effects had been first demonstrated by SMI and Fermi National Accelerator Laboratory (FNAL) in 2004.
In PIT wires the Nb 3 Sn A15 phase is formed in a solid-state diffusion reaction, typically after a few days at ~675 C. The Sn diffusion and Nb 3 Sn phase formation processes in the PIT route are described in detail elsewhere (Godeke et al. 2008)

IT Nb 3 Sn Wires
As mentioned above, the IT process includes several versions, which differ, for example, in the design of the Nb filaments, the diffusion barrier position, the Sn distribution in the composite cross-section, sub-element and billet processing.Their potentials and limitations in terms of performance and large-scale production vary widely.IT composite wires were produced by several companies.In the USA, first IGC (Outokumpu since 2000, Luvata since 2005), and later OST (Bruker-OST since 2016) worked on this process.The Restack Rod Process® (RRP®), which was developed by OST in the early 2000s, provided the best results for accelerator magnet applications until February 2019, when short samples of APC PIT wires achieved the FCC J c specifications shown in Table 2.1.
The IT RRP process is based on assembling a large number of Nb filaments and pure Sn or Sn-alloy rods in a Cu matrix (Parrell et al. 2004).The assembly is surrounded by a Nb barrier to prevent Sn diffusion into the high-purity Cu matrix, and it is then cold-drawn down to final size.Restacking of assemblies allows further reduction of the final sub-element size.Due to the fact that the diffusion barrier also reacts to form Nb 3 Sn (and contributes to the J c ), there is a balance between subelement size, metal ratios, heat treatment parameters, J c , and Cu purity, which must be considered and optimized for every strand design.
During heat treatment of IT wires, several Cu-Sn phases are created and eliminated in the course of the Cu-Sn diffusion and Nb 3 Sn formation processes.The presence of liquid phases in IT wires may cause motion of Nb filaments, allowing contact with adjacent ones; and the presence of voids may hinder the diffusion process.In addition, wire bursts can damage the wires.These problems were solved by using a three-step heat treatment cycle.
In the first step, temperature dwells below 227 C allow the formation of a thin layer of a higher melting point Cu-Sn phase (ε-phase) that works as a container for the liquid Sn above 227 C. A 1-3 day 210 C dwell followed by 1-2 days at 400 C provide appropriate Sn diffusion inside each sub-element, but also prevent Sn leaks through the Cu matrix, which is typically strongly deformed in the Rutherford cabling process.The superconducting Nb 3 Sn phase is formed during the third step of the heat treatment cycle between 620 C and 750 C.During this stage the optimal phase microstructure, critical for flux pinning, is also formed.The Nb 3 Sn microstructure is controlled by the temperature and the duration of this stage.Reactions at higher temperatures usually take the shortest time, but produce the largest grains.The choice of temperature and duration of the third stage is a compromise between an optimal pinning structure leading to high J c , and Sn diffusion through the barrier leading to Cu pollution and to an increase of the matrix electrical and thermal resistivity.
Since 2002, when the RRP process was commercially introduced for HEP applications, OST has produced tons of Nb 3 Sn wires.Cross-sections of some wire designs manufactured by OST for accelerator magnets are shown in Fig. 2.6.In a configuration with 54 superconducting elements in a 61-restack wire (also represented as 54/61) of 0.8 mm size, the sub-element diameter is ~80 μm.Because of the impact of D eff on conductor and magnet stability, OST focused on increasing the stack count in a billet to decrease the sub-element diameter.
As we will see below, in the Rutherford cables used in magnets, the Nb 3 Sn filaments coalesced with each other.This "merging" randomly produced locally some superconducting areas several times larger than the size of the individual undeformed filaments (i.e., as in the round wire).These enlarged superconducting areas, which in cables may be up to five to six times the size of the undeformed filaments, clearly increase magnetic instabilities in cables.In 2006, OST produced for FNAL a 60/61 RRP billet with extra Cu spacing between sub-elements to reduce sub-element merging during cabling.Studies at FNAL showed that the mechanism by which the extra Cu thickness in the new OST design is effective is by providing a barrier to merging during reaction (i.e., not as much during the deformation process itself).Shortly afterward a 108/127 stack billet was produced with the same concept, and in 2007 OST adopted the spaced-filaments design as standard for HEP wires.
The 127-stack design entered production in 2008, with several tons utilized in HEP at 0.7-0.8mm diameter and a D eff of 45-52 μm.A third-generation wire with a 169stack design followed in 2011.This wire has a D eff of 40-58 μm for sizes of 0.7-1 mm.Integrated volume production of 169-stack RRP billets at OST is approaching that of the 127-stack billets.The development of 217-stack billets still continues.
Another improvement that OST obtained in RRP wires was that of interspersing Ti rods among the Nb filaments inside the sub-elements instead of using Ta-doped Nb filaments.This kind of doping allowed lowering the wire optimal reaction The numbers represent the total number of superconducting sub-elements temperatures from ~695 C for Ta-doped wire to ~665 C for a Ti-doped wire, thereby increasing the wire J c at high fields, better preserving RRR, and also improving the irreversible strain limit (Cheggour et al. 2010).
In 2016, OST was purchased by Bruker, which recently stopped standard PIT production, making the RRP conductor a workhorse for Nb 3 Sn accelerator magnets.Bruker continues to use the PIT technology in R&D as a possible platform for future high-J c wires with APCs.Also, based on promising results in increasing the heat capacity of Nb 3 Sn composite wires for improved stability (Xu et al. 2019), Bruker-OST is implementing hexagonal copper rods filled with mixed powder of rare earth oxides and copper in RRP re-stacks.The critical current density J c is a key parameter, which controls the current-carrying capability, stability, magnetization, and AC losses of a superconducting wire, and thus the design field and performance of superconducting magnets.Improvement of the critical current density at 12 T and 4.2 K in commercial IT and PIT composite wires since 1980, when the best J c for Nb 3 Sn wires reached 0.5-0.7 kA/mm 2 , is shown in Fig. 2 The J c of PIT Nb 3 Sn is affected by design parameters such as filament size, number of Nb tubes, use of binary Nb 3 Sn or ternary (NbTa) 3 Sn, and the quality and size of the NbSn 2 powder.During the 1980s the J c of PIT wires was increased by ECN to 1.7 kA/ mm 2 at 4.2 K and 12 T.The next step to ~2.3 kA/mm 2 was made by SMI in 2000.The maximum non-Cu J c at 12 T and 4.2 K in PIT reached ~2.7 kA/mm 2 in 1.25 mm wires with 288 filaments of 50 μm, developed by SMI for the NED program.In the most recent composite wire, produced by Hypertech Research Inc. in 2019 using PIT technology and APC, the J c in short samples approached to 1.5 kA/mm 2 at 16 T field, which corresponds to J c of ~3.6 kA/mm 2 at 12 T.For commercial PIT wire production at Bruker-EAS, the J c at 12 T 4.2 K was ~2.5 kA/mm 2 .

Main Properties of Nb 3 Sn Composite Wires
Optimization of the IT wire design and processing at OST from 1999 to 2006 produced fast progress in J c at 12 T and 4.2 K, from ~1.5 kA/mm 2 to more than 3 kA/ mm 2 .The record J c (12 T, 4.2 K) of 3.3 kA/mm 2 was achieved first in a RRP wire of 54/61 design and a diameter of 0.7 mm.The peak value of J c (12 T, 4.2 K) in RRP wire production has been essentially stable since 2005.A J c (12 T, 4.2 K) at or above 2.5 kA/mm 2 is routinely achieved in commercial wires.
The critical current density of Nb 3 Sn is a function of magnetic field B, temperature T, and strain ε.Several empirical scaling laws were proposed to parameterize the J c data (see Appendix 1).One of the practical purposes of parameterization is that of calculating the expected performance of a magnet from I c measurements of strand samples used as witnesses during coil reaction.The intersection of the critical surface of each coil at the various magnet test temperatures with the B peak load line of the magnet produces the expected coil SSL at that temperature.It is to be noted that SSL values for accelerator magnets typically have very little sensitivity (<0.3%) to the scaling law that is used.voltage-current transition, whereas open symbols denote the maximum current I q reached before a premature quench due to instabilities.An I c (B,T ) parameterization curve is shown by the solid line.

Flux Jump Instabilities
Flux jumps in Nb 3 Sn composite wires, predicted by stability criteria at fields below certain levels (Wilson 1983), are observed in critical current and magnetization measurements.In critical current measurements the flux jumps are recorded as large voltage spikes and premature quenches below the superconductor critical surface I c (B,T) during either V-I or V-H measurements.An example of flux jump instabilities in critical current measurements of RRP wires is shown in Fig. 2.8.In magnetization measurements they are seen as a sawtooth pattern at the low fields (Fig. 2.9).Flux jump instabilities may cause magnet premature quenches and also complicate quench detection in magnets.

Nb 3 Sn Wire Magnetization
Magnetization of a composite wire plays an important role in superconducting accelerator magnets, which have demanding requirements on field uniformity.Magnetization loops measured at low field ramp rates (dB/dt < 0.02 T/s) for IT (IGC), RRP, and PIT wires are shown in Fig. 2.9 per non-Cu volume.
The magnetization of a composite superconducting wire has eddy current and hysteretic components (see Appendix 1).The eddy current component of magnetization in Nb 3 Sn composite wires is suppressed by using a small wire twist pitch l p .For l p < 15 mm and a rather low matrix transverse resistivity ρ ~10 À10 Ω m, the eddy current As expected for the hysteretic component, the magnetization loop width is larger for wires with higher J c and larger D eff .Due to the larger J c and D eff , the level of wire magnetization as well as the range of wire re-magnetization when dB/dt changes sign are more than an order of magnitude larger than for Nb-Ti wires used in accelerator magnets.A large magnetization leads to field quality deterioration.Flux jumps also produce field fluctuations from cycle to cycle in accelerator magnets at low fields.

Cu Matrix RRR
RRR is a measure of Cu matrix purity, which is important for strand stabilization and magnet quench protection.It is defined as the ratio of the Cu matrix resistivity at room temperature R 300 to its residual resistivity R 4.2 at T ¼ 4.2 K.When measuring the RRR of the Nb 3 Sn wire matrix, T ¼ 19 K.A low RRR indicates damage of the internal structure of the strand and Sn leakage into the Cu matrix.
RRR depends on the type of Cu used, on the amount of Sn in the billet, on the diffusion barrier thickness, and on the heat treatment cycle.For instance, when using the same heat treatment cycle for IT wires, RRR values ranging from about 20, to 60, to 160 were obtained for barrier thicknesses of 3 μm, 4.2 μm, and 6 μm, respectively.
Typical RRR values for the latest PIT and RRP round wires are about 200 to 300.Bruker-OST uses Cu 101 with a RRR rating of 300 for a majority of their billets.To maintain a good RRR, OST had also been working on optimizing the Sn fraction in the billet, as well as the diffusion barrier thickness.It is to be noted, however, that RRR, using as numerator the Cu matrix resistivity value at room temperature and zero magnetic field, reduces because of the magnetoresistivity effect, i.e., its value strongly decreases with increasing magnetic field.The same can be expressed in a so-called reduced Kohler plot, where the normalized magnetoresistance increase is shown against the magnetic field multiplied by the resistance ratio at 294 K over 19 K.
The magnetoresistivity effect is stronger for a higher purity Cu matrix, thereby reducing the importance of high RRR at larger fields.

Cable Design and Fabrication
Accelerator magnets use high-current, multi-strand superconducting cables to reduce the number of turns in the coils, and thus magnet inductance.The Rutherford cable, developed at the Rutherford Appleton Laboratory (RAL) in the early 1970s (Gallagher-Daggit 1973), has played a crucial role in establishing Nb-Ti accelerator magnet technology due to its excellent mechanical, electrical and thermal properties.Rutherford cables are produced using special cabling machines, with single-pass and multi-pass approaches.In the former case, the cable is formed into its final crosssection in one single step, i.e., through the largest plastic deformation.In the multipass case, a cable with intermediate cross-sections with respect to its final geometry is produced first, which imparts plastic deformation more gradually.This method allows the use of an annealing heat treatment between cabling steps to release tension in the cable.
During cabling, quality monitoring includes checking for strand crossovers, when two adjacent strands alternate their position in the cable by crossing over each other during cable fabrication, and for sharp edges.Crossovers are deleterious to cable performance, and sharp edges are dangerous for the insulation, as shorts may be created.Cable width and thickness are measured periodically or continuously to keep their values within the required tolerances, which are usually of AE6 μm for thickness and of AE25 μm for width.
The Rutherford cable geometry is characterized by a cable aspect ratio, a geometrical cross-section area, a pitch angle, a packing factor (PF) and, if applicable, a keystone angle.Commonly used definitions of these parameters are summarized in Appendix 1.Large strand-plastic deformations, which were acceptable for a ductile superconductor like Nb-Ti, are not suitable for the more delicate Nb 3 Sn strand structure.Examples of RRP strand cross-sections, as deformed after cabling, are shown in Fig. 2.11.Local sub-element deformations due to barrier breakage and merging are shown.
It was found that RRP and PIT strands behave differently under plastic deformation.Despite relative filament deformation being similar for the two, at increasing deformations RRP wires manifest some breaking, but also increasing merging between sub-elements, whereas PIT tubes show only some breaking under shearing.In both keystoned and rectangular cables the largest deformation values are found in the strands at the cable edges.The average strand deformation is lower in a lesscompacted cable.Deformation of strand cross-sections in cables also causes deformation of the sub-elements, which depends on the cable packing factor PF.
The small edge deformation in Nb 3 Sn keystoned cables should be larger than 0.85, and the width deformation should be slightly larger than 1.0, typically between 1.0 and 1.03, to avoid excessive strand deformation at the cable's thin edge.The limits on small edge deformation and cable width define a value for the optimal keystone angle of the cable cross-section.
The nominal cable PF for Nb 3 Sn cables is within 84-87%.This PF range allows keeping the critical current degradation of Nb 3 Sn Rutherford cables sufficiently low and at the same time provides adequate cable compaction to achieve the mechanical stability that is needed for coil winding.

Cable Size Changes after Reaction
A precise cable cross-section is important for achieving the required field quality in accelerator magnets.It is known that Nb-Sn composite strands expand after reaction due to formation of the superconducting Nb 3 Sn A15 phase.In round wires this expansion is isotropic.For Nb 3 Sn Rutherford cables, however, an anisotropic volume increase was observed.It was found that the plastic deformation imparted during cabling releases itself through heat treatment, and therefore the thickness expansion is always larger than the width expansion.The volume expansion of a round wire increases with the Nb-Sn content, varying from 2 to 3% for both PIT and RRP wires.
The change in dimensions before and after reaction was measured for keystoned cables based on RRP strands.The average width expansion was 2.6%, the average mid-thickness expansion was 3.9%, and the average length decrease was 0.3%.Some cable samples were reacted under two different conditions, i.e., "unconfined" and "confined" in the transverse direction within a special fixture.The unconfined cable tests showed a clear longitudinal contraction by 0.1-0.2% for the cable made in two passes, and by 0.2-0.3% for the one-pass cable.The thickness and the width expansions in this case were 4% and 2%, respectively.When transversally confined to the unreacted cable cross-section, the cables elongated by ~0.4% and the thickness increased by only ~2%.The unconfined cables made of PIT strands with a Cu/non-Cu ratio of 1.2-1.3showed a thickness expansion after reaction of 3-3.6% and a width expansion of ~1.5%.It was also reported that the cable width and thickness expansions were affected by the insulation.Braided insulation increased cable thickness expansion while simultaneously reducing the cable width expansion.
Cable thickness expansion after reaction is an important parameter for cables to be used in a magnet, and is therefore an important part of a magnet development plan.For magnetic design optimization, it is the reacted thickness and width values that are used as cable dimensions.The coil dimensions in the winding and curing tooling are determined by the unreacted cable cross-section, whereas the coil dimensions in the reaction and impregnation tooling are based on the reacted cross-section.

Cable Performance Parameters
The most important parameters that define the performance of a Rutherford cable in a magnet include the critical current I c and average critical current density J a , the Cu/non-Cu ratio, cable RRR, and interstrand resistances R c and R a , where R c is the resistance between strands from the two cable layers and R a is the resistance between adjacent strands within a layer.The parameters of the heat treatment cycle affect I c , RRR, and contact resistances R c and R a .

Cable Critical Current I c and Flux Jump Instabilities
The critical current I c evaluation of Rutherford cables is performed by either testing short cable samples or individually extracted strands.The good correlation usually found between cable and extracted strand test results at high fields, as shown for instance in Fig. 2.12, confirms the validity of both approaches.As in Fig. 2.8, closed symbols represent I c data measured in a smooth voltage-current transition, whereas open symbols denote the maximum current I q as reached before an abrupt quench due to instabilities.The solid line represents an I c (B) parameterization.A good correlation between extracted strand and cable test results also reveals a small variation of strand properties within the billets used in the cable, and is consistent with a uniform transport current distribution.
The effect of flux jump instabilities observed at low fields in Nb 3 Sn wires was also seen in tests of short cable samples (see Fig. 2.12).Analysis and comparison of flux jump instabilities in Rutherford cables and their corresponding round wires show that these instabilities are larger in cables, due to sub-element deformation and possible sub-element merging (Fig. 2.11a), which in both cases lead to an increase of the local D eff .The reduction of local RRR after cabling also increases flux jump instabilities in cables with respect to virgin wires.

Effect of Strand Plastic Deformation in Cables
Cable degradation studies and optimization are an important part of the magnet development process.The effect of cable plastic deformation on the critical current I c , minimal stability current I S and matrix RRR was studied using strands extracted from cables with different PFs.The results of I c measurements made on extracted strands were compared with those made on the round wire from billets used in the cables.The cable I c and critical current density J a per cable cross-section area at 4.2 K and 12 T normalized to the I c0 and J a0 of a cable made of undeformed round strands (PF ¼ 78.5%), respectively, are plotted in Fig. 2  decreases with increasing PF, the normalized critical current density J a in compacted cables is larger than in the undeformed cable, since the I c degradation is less than the reduction of cable geometrical cross-section.Some early IT wires demonstrated a relative I c degradation of up to 80% at PFs above 84%.A large I c degradation of up to 60% was also observed in early PIT strands.In 2004, however, SMI and FNAL found that by using round filaments in PIT wires, the I c degradation could be reduced to 15% or less at PFs up to 94%.At a PF between 84% and 87%, which is typical for Nb 3 Sn Rutherford cables, the I c degradation in well-optimized cables is usually ~5% or less.Similar measurements performed at CERN on cables made with modern RRP and PIT strands are consistent with these data.
The effect of strand plastic deformation due to cabling on the stability current I S and on the RRR is much stronger than on the I c due to sub-element damage, and merging and Cu matrix contamination.It was also found that RRP strands with extra spacing between sub-elements were able to maintain a higher I S in the higher PF range (above 90%).
Based on the results of I c degradation in Nb 3 Sn Rutherford cables, high PF values of 92-95% provide the highest J a .Large I S and RRR degradation values due to large deformations and possible damage and merging of the delicate sub-elements, however, impose an optimal PF within 84-87%.

Cable RRR
Due to the larger strand deformation at the cable edges, it was expected that RRR would vary along a strand.The first resistivity measurements made on extracted strands from high-edge compacted cables showed significant RRR degradation from an RRR % 120 measured on strand segments on the cable faces.On the edges the results were an order of magnitude smaller, i.e., RRR % 13, consistent with local Sn leakages through the diffusion barriers caused by the plastic deformation at the cable edges.Since this reduction is local, the average RRR value was still large, around 81.Such a large RRR degradation at the edges is often found even in cables with low packing factors.Recent measurements were performed at CERN on optimized cables made out of RRP132/169 wires with high RRR (between 100 and 250) for the 11 T dipole.The RRR reduction on the small edge was between 40% and 50%, and that on the large edge between 70% and 75% of the maximum values obtained on the cable flat parts.

Effect of Transverse Pressure
Transverse stress is the largest stress component in accelerator magnets, and can therefore damage brittle Nb 3 Sn coils.To determine I c sensitivity to transverse pressure, electro-mechanical tests are typically performed on either cables or encased wires.Transverse pressure studies are made by applying pressure to impregnated cable or wire samples and testing their transport current at several magnetic fields.
Strain sensitivity, as previously indicated, increases with magnetic field.There are two components of the critical current degradation: a reversible component, which is fully recovered when removing the load, and an irreversible component.The latter is permanent.The irreversible limit is defined as the pressure leading to a 95% recovery of the initial I c , or I c0 , after unloading the sample.Institutions where transverse pressure measurements are performed include FNAL, the University of Twente, the National High Magnetic Field Laboratory, CERN, and the University of Genève.The I c degradation strongly depends on conductor technology, but also on sample preparation and setup design.The former has an impact on possible stress concentration; the latter determines the sample's actual stress-strain state.
Figure 2.14 shows the total I c degradation at 4.2 K and 12 T (unless otherwise indicated in figure caption), at transverse pressures up to ~200 MPa, of epoxyimpregnated Rutherford cables and encased wires made of PIT and RRP.Most of the load in this plot was applied cold.Older data (not shown) indicate that cables made of low-J c strands are less sensitive to transverse pressure than those made with stateof-the-art, high-J c strands.In some cases a stainless-steel core inside the cable also reduced pressure sensitivity.
In reference to magnet assembly and operation, it is important to distinguish the areas with maximum stress from those with maximum field, as well as the actual temperature conditions of the load application.Recent experiments performed at FRESCA to measure the irreversible component with the load applied warm showed that the irreversible component is negligible at least up to 150 MPa.It is important that these studies continue.

Interstrand Resistance
Contact resistances between adjacent strands inside each layer, R a , and between strands from different layers, R c , control eddy current magnetization and AC losses, as well as current and heat sharing between strands in a Rutherford cable.To reduce eddy current effects without compromising cable electrical stability, one needs to increase R c while keeping R a low.Calculations show that for field ramp rates up to 0.1 T/s, R c has to be larger than ~10 μΩ, and R a larger than ~0.1 μΩ.In this case, the eddy current effect will be negligible with respect to the persistent current effect.
Direct measurements of R c and R a contact resistances performed under transverse pressures of 10-100 MPa gave R c ¼ 1.1-1.4μΩ and R a ¼ 8-16 μΩ for Nb 3 Sn cables without a core, and R c ¼ 150-275 μΩ and R a ¼ 1.5-1.9μΩ for cables with a 25 μm stainless-steel core.Very low R c values of ~0.1-0.4 μΩ were measured in Nb 3 Sn Rutherford cables without a core reacted in coils under pressure.In cables with a full-width stainless-steel core, a high R c of 246 μΩ was found based on AC loss measurements.For comparison, in the LHC Nb-Ti cables, typical R c values under pressure are ~20 μΩ, i.e., an order of magnitude larger than in a Nb 3 Sn cable without a resistive core, and an order of magnitude lower than in a Nb 3 Sn cable with resistive core.Typical R a values for Nb-Ti cables are ~170 μΩ.Since the R a limit is much smaller than the actual R a data, their large variations will not affect magnet field quality or AC losses, whereas low values and large variations of R c data in cables without a core will produce a large impact on magnet field quality and quench performance.Studies of interstrand contact resistances in Nb 3 Sn Rutherford cables have shown that using a stainless-steel core is very efficient in reducing the level of eddy current effects (magnetization, AC loss) in cables.This approach is simpler than using a resistive coating, such as chromium, on individual strands.Resistive coating increases both R c and R a to 100 μΩ and higher, and may negatively impact the cable's electrical stability.

Conclusion
High-performance composite wires and Rutherford cables are key components of superconducting accelerator magnets.Whereas Nb-Ti has been the workhorse for HEP applications for almost 50 years, in the past 25 years Nb 3 Sn wires and cables have made steady progress in wire fabrication techniques, understanding of their properties, and large-scale commercial production.They have now approached the necessary maturity to be used in accelerator magnets.Coupled with innovative development in the Nb 3 Sn magnet technology itself, conductor progress has made it possible for accelerator magnets to achieve magnetic fields above 10 T, which is beyond the reach of Nb-Ti technology.In 2010, Nb 3 Sn was adopted as the baseline conductor for the HL-LHC at CERN.Still, the potential of Nb 3 Sn wires and cables is not fully apprehended.Work on Nb 3 Sn composite wires for accelerator magnets continues, focusing on a better understanding and optimization of their technical performance and of their market parameters.

Cable Edge and Width Deformations R e , R w
The critical current degradation is determined mainly by the amount of cable crosssection deformation.The deformations of cable edge R e and width R w are defined as where D is the strand diameter, N is the number of strands in the cable (N ¼ N + 1 in the case of odd N ), and θ is the cable transposition angle.They can also be expressed as edge c t and width c w compactions (Bottura and Godeke 2012), which are related to R e and R w as

Critical Current Density
Critical current density is a key parameter, which controls the current carrying capability, stability, magnetization, and AC losses of a superconducting wire, and thus the performance of superconducting magnets.Parameterizations of the critical current density as a function of magnetic field B, temperature T and strain ε, can be generally expressed as Parameters m, n, p, q, and ν as well as functions C(t,ε), T c0 (ε), k(t), and B * c20 (0,ε) are usually determined by fitting experimental data of Nb 3 Sn wires.For the practical strain range of À1 < ε < 0.5, the experimental data are well fitted with m ¼ n ¼ q ¼ 2, p ¼ 0.5, ν ¼ 1.7-2, and C(t,ε) ¼ C(ε).
Due to electromagnetic coupling between strands, the Rutherford cable magnetization and AC loss power include additional eddy current contributions, which depend on the cable geometry and interstrand contact resistances as where 4L is the cable transposition pitch, α is the cable aspect ratio, B ⊥ and B || are the perpendicular and parallel components of the magnetic field to the cable wide surface, and ρ c and ρ a are the effective cable resistivity between cable layers and within a layer, respectively.The first term in both formulae provides the main contribution due to the large value of α.The parameters ρ c and ρ a are related to the measurable contact resistances R c and R a as where R c is the contact resistance of two crossing strands and R a is the resistance per unit length of two adjacent strands in a cable.

Fig. 2 . 1
Fig. 2.1 Schematic of a cross-section of a Nb 3 Sn ribbon

Fig. 2 . 4
Fig. 2.4 Schematics of Nb 3 Sn composite wire based on the powder-in-tube process.(Courtesy Peter Lee, FSU) . The NbSn 2 powder turns first into Nb 6 Sn 5 and then into the Nb 3 Sn phase.After 16 h, the initial Nb 6 Sn 5 phase is converted into large grains.The void fraction in these regions is attributed to the reduced volume of Nb in Nb 3 Sn, relative to the Nb 6 Sn 5 phase.The Nb 3 Sn phase formation ends after about 64 h at 675 C, due to Sn depletion of the core-A15 interface region.Thus, a longer reaction does not increase the Nb 3 Sn fraction.The outer boundary of the Nb 3 Sn area is controlled to prevent Sn diffusion into the high-purity Cu matrix, and the resulting decrease in RRR.The heat treatment of commercial PIT composite wires without a diffusion barrier was optimized with respect to the area of reacted Nb to provide good RRR values.Most recently, PIT binary and ternary, mono and multi-filamentary wire configurations were successfully used at Hypertech Research Inc. to implement ZrO 2 precipitates as artificial pinning centers (APC) in the Nb 3 Sn by means of internal oxidation of Nb-Zr.

Fig. 2 . 5
Fig. 2.5 Cross-sections of PIT wires of different designs (Courtesy of SMI and Bruker-EAS).The numbers represent the total number of superconducting tubes

Fig. 2 . 6
Fig. 2.6 Cross-sections of some commercial RRP wires (Courtesy of OST).The numbers represent the total number of superconducting sub-elements 2.3.4.1 Critical Current Density J c and Critical Current I c Fig. 2.7 J c (12 T, 4.2 K) progress of IT and PIT composite wires

Figure 2 .Fig
Fig. 2.8 Critical current of a Nb 3 Sn wire vs. magnetic field measured at 4.2 K

Fig. 2 . 9
Fig. 2.9 Nb 3 Sn wire magnetization per non-Cu volume It is also widely used in Nb 3 Sn magnets.Examples of Nb 3 Sn Rutherford cables are shown in Fig.2.10.

Fig. 2 .
Fig. 2.10 Nb 3 Sn Rutherford cables: (a) large face view of cable with stainless-steel (SS) core; (b) cross-sections of 40-strand cable; and (c) 28-strand cable with SS core

Fig. 2 .
Fig. 2.11 Examples of: (a) a deformed RRP strand in a cable with local sub-element damage and merging; and (b) tube breakage in PIT wires

Fig. 2 .
Fig. 2.12 Maximum current vs. magnetic field of a 40-strand Nb 3 Sn cable with RRP strands.The solid line represents an I c (B) parameterization PIT wire, U.Genève PIT rolled wire, U.Genève

Fig. 2 .
Fig. 2.14 Normalized I c at 4.2 K vs. transverse pressure on Rutherford cable face or on encased wire for epoxy impregnated samples.All the Ic data correspond to 12 T, except for the PIT round and rolled wires which were measured by U. Genève at 19 T

Table 2 .
1 CDP, NED, and FCC Nb 3 Sn wire target parameters Parameter .13 vs. cable PF.Whereas I c