Conceptual Design of an HTS Dipole Insert Based on Bi2212 Rutherford Cable

The U.S. Magnet Development Program (US-MDP) is aimed at developing high field accelerator magnets with magnetic fields beyond the limits of Nb$_3$Sn technology. Recent progress with composite wires and Rutherford cables based on the first generation high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ (Bi2212) allows considering them for this purpose. However, Bi2212 wires and cables are sensitive to transverse stresses and strains, which are large in high-field accelerator magnets. This requires magnet designs with stress management concepts to manage azimuthal and radial strains in the coil windings and prevent degradation of the current carrying capability of Bi2212 conductor or even its permanent damage. This paper describes a novel stress management approach, which was developed at Fermilab for high-field large-aperture Nb$_3$Sn accelerator magnets, and is now being applied to high-field dipole inserts based on Bi2212 Rutherford cable. The insert conceptual design and main parameters, including the superconducting wire and cable, as well as the coil stress management structure, key technological steps and approaches, test configurations and their target parameters are presented and discussed.


Introduction
Progress with round Bi2Sr2CaCu2O8-x (Bi2212) composite wires, which can be used to produce Rutherford cables, makes them particularly suited for use in high-field accelerator magnets [1,2]. This work started in the U.S. several years ago within the U.S. Very High Field Superconducting Magnet Collaboration (VHFSMC) [3] and is now being performed in the framework of the U.S. Magnet Development Program (US-MDP) [4]. Whereas the LBNL group, in collaboration with ASC-NHMFL-FCU, pursues coil inserts based on a Canted Cosine Theta (CCT) coil concept [5], Fermilab is focused on coil inserts based on the traditional cos-theta coil concept with stress management elements [6].
Several challenges are to be addressed on the way. The composite Bi2212 wire with Ag matrix is a soft and very delicate material which needs stringent empirical laws for Rutherford cabling to minimize the wire internal damage. Once the cable is formed and used to wind a coil, the Bi2212 coil requires a multistage heat treatment in Oxygen atmosphere at maximum temperatures close to 900 o C to form the superconducting phase. Moreover, temperature homogeneity during the heat treatment has to meet strict gradient specifications. Similarly to Nb3Sn, Bi2212 wires and cables are sensitive to stress and strain [7][8][9]. Although Bi-2212 is universally made with the Powder-in-Tube (PIT) technique, it appears that stress/strain behavior depends on the specific details of the technological processes used by each manufacturer. Pressure transverse to the cable face is one of the main stress components in accelerator magnets. Whereas very accurate measurements on tensile strain can be found in literature, more data on Bi2212 performance sensitivity to cable loading are needed. It is already certain, however, that stress management concepts will need to be applied to insert coils' designs when aiming at large magnetic fields.
The first step in developing a Bi2212 dipole insert, i.e. design studies, is complete. The Fermilab's insert is based on a 2-layer coil concept with small aperture. It uses Bi2212 Rutherford cable, which was available at LBNL. The coil fits into 60 mm aperture dipole coils available at Fermilab. The coil is wound inside a support structure. All parts for the coil support structure have been designed and will be fabricated by 3D sintering technology. As a first step, a practice coil using "dummy" Nb3Sn or Cu cable and 3D printed plastic parts will be wound, impregnated with epoxy and cut to examine the turn position in various parts of the coil. After winding, the real coil will be heat treated (reacted to form Bi2212 stoichiometry) at 50 bar in a furnace at NHMFL, and shipped back for impregnation with epoxy, instrumentation and cold testing at FNAL. This paper describe the insert conceptual design and main parameters, including properties of the superconducting wire and cable, as well as the coil stress management structure, key technological steps and approaches, test configurations and their target parameters. In preparation for this and future inserts, cable development and characterization, including transport properties of extracted strands, cable at field, and cable under pressure will be performed. Some of these steps to be used for the first Bi2212 insert coil are reviewed in the paper.

2D Magnetic Design and Parameters
The design concept of the Bi2212 insert is based on a two-layer cos-theta coil with stress management concept which was developed at Fermilab for high-field large-aperture Nb3Sn accelerator magnets [6]. The coil uses a Rutherford cable with rectangular cross-section 7.8 mm wide and 1.44 mm thick, wrapped with 0.15 mm thick insulation [10].
This insert coil is designed to be tested inside 60-mm aperture Nb3Sn dipole coils developed at Fermilab [6,11]. Thus, the coil outer diameter is limited to 59 mm, leaving 0.5 mm of radial space for the insulation between the Bi2212 and Nb3Sn coils. The coil inner surface is slightly elliptical with a minimal radius of 8.5 mm. There is ~2.4 mm of radial space outside of each coil layer for the mechanical support structure and inter-layer insulation. The coil consists of 15 turns, 5 turns in the inner layer and 10 turns in the outer layer. Each coil layer is split into 3 blocks, with the number of turns approximately following the cos-theta distribution. Each coil layer has a pole block, 2 inter-blocks and a small mid-plane spacers per quadrant, which ensure the radial turn position in the coil and minimize the low order geometrical harmonics.
The coil magnetic optimization was done using ROXIE [12] for a cylindrical iron yoke with inner diameter of 100 mm and constant iron magnetic permeability of 1000. The optimized coil cross-section is shown in Fig. 1. The coil geometrical parameters are summarized in Table 1.   Stored energy at coil current of 6 kA, kJ/m 6.99 The calculated design parameters of the Bi2212 dipole insert are presented in Table 2. The length of the coil is limited by the available cable length of 15 m. It is estimated that the coil straight section will be ~300 mm long and the total length of coil winding will be ~450 mm, or approximately half of the Nb3Sn coil length. Due to the small insert size, the coil cross-section area as well as the coil inductance, stored energy and Lorentz forces in this design are relatively small.

Field Quality
The induction of magnetic field B(x,y) in the aperture of accelerator magnets is represented in terms of harmonic coefficients defined in a series expansion using the following complex functions: where Bx(x,y) and By(x,y) are the horizontal and vertical field components, bn and an are the normal and skew harmonic coefficients, B1 is the main dipole component, and Rref is the reference radius. For this insert Rref = 5 mm, which corresponds to ~60% of the insert aperture radius.
The design low-order harmonics for the dipole central field, assuming an iron yoke permeability of 1000, are reported in Table 3. The cross-section of the insert coil, with the field uniformity diagram in the aperture and the field distribution in the coil cross-section at a current of 6 kA, is shown in Fig. 2. Whereas it was possible to reduce b3, b9 and b11 harmonic coefficients below 1 unit, the other two low-order geometrical harmonics, b5 and b7, are relatively large, due to restrictions in turn positioning in this design. However, since they have opposite signs, the good quality field area, where dB/B1 is smaller than 3 units, is round and close to 10 mm in diameter. It is shown as the dark-blue area in the aperture in Fig. 2. bn, 10 -4 -0.76 -9.6 3.43 -0.23 0.03 Figure 2. Cross-section of the insert coil with the field uniformity diagram in the aperture and the magnetic field distribution in the coil cross-section at a current of 6 kA.

Coil Support Structure
The Lorentz force values and directions in the coil blocks without any external field applied are shown in Fig. 3. At a coil current of 6 kA, the horizontal Lorentz force component Fx = 97.5 kN/m/quadrant and the vertical one Fy = -62.2 kN/m/quadrant. The Lorentz forces in the inner layer are practically horizontal, whereas in the outer layer there are both force components. Since the Lorentz force FL per unit length is a vector product of the current I and the field induction B, or FL=I×B, the horizontal component of the Lorentz force in an external dipole field will proportionally increase, whereas the vertical one will not change.   A 3D view of the coil turns in the non-lead end is shown in Fig. 5. Due to the very small aperture, the width of the inner-layer pole in this design is relatively small (~7.3 mm), which is quite challenging for the inner-layer pole-turn bending in the coil end areas. This important question will be addressed and optimized during practice coil winding.

Wire and Cable Parameters and Technology
Cross-sections of the Bi2212 wire and the Rutherford cable are shown in Fig. 6. Their main parameters are summarized in Table 4. The Bi2212 wire was produced by Bruker OST LLC using precursor Bi powder provided by nGimat (now Engi-Mat). The cable was made and insulated at LBNL. The cable insulation consists of 0.15 mm thick mullite braided sleeve chemically compatible with the Bi2212 heat treatment process. The length of the insulated cable is ~15 m.   Bi2212 is a copper-oxide high temperature superconductor (HTS), which in addition to much higher critical temperature also have higher irreversibile magnetic field compared to low temperature superconductors. Bi2212 is the only copper-oxide material which can be easily melt processed and, thus, to be produced in a wide variety of shapes, including isotropic round multifilamentary wire. To achieve this so-called partial melt processing, a multistage heat treatment in Oxygen atmosphere at very uniform high temperatures up to 900 o C is required. Bi2212 is made with the Powder-in-Tube (PIT) technique. Whereas the matrix embedding the filaments requires using pure Ag, the wire fabrication process typically uses an outer sheath made of Ag0.2%Mg alloy which is dispersion strengthened by oxidation of the Mg during wire heat treatment.
Significant progress was made in the development and industrialization of Bi2212 composite wires. Km-length quantities of Bi2212 round wires have been commercially produced since the 1990s. The critical current density Jc and the engineering wire current density Je at 20 T and 4.2 K of the round wire increased from 1500 A/mm 2 and 400 A/mm 2 or less respectively in the 2000s, to the Je values shown in Fig. 7 today [10]. The range of the engineering wire current density for the wire used in the Rutherford cable provided by LBNL at 5 T is shown in the plot by the red double arrow, which is consistent with the parameters of the 2015 generation Bi2212 wire. The two main factors that led to the Bi2212 wire improvement are a) the removal of the 30% porosity in as-drawn Bi2212 wires by an overpressure processing heat treatment (OPHT), and b) the introduction of a new chemical powder technology by nGimat (now Engi-Mat), which produces highly homogenous Bi2212 precursor powders with very good composition control. Fig. 8 gives an example of a typical heat treatment cycle, which is used for the partial melt processing at 1 bar of gas pressure. The gas is either pure Oxigen (O2) or a mixture of Oxigen and Argon (O2/Ar) with Oxigen partial pressure of 1 bar. The OPHT process uses 98% Ar and 2% O2 with a total gas pressure at 50 bar, with the O2 partial pressure still at 1 bar. Whereas the best wire performance is usually obtained by O2 pre-annealing of the Ag0.2%Mg sheathed strand, the hardened sheath which results from this pre-anneal severely restricts the diameter around which the wire can be bent without cracking. To enable cabling of Bi2212 round stands, specific O2 anneal processes have to be used. Then Bi2212 wires that pass a nominal bending test can be used to fabricate of Rutherford-type cables. Cable development is performed by designing and fabricating samples of different geometries using state-of-the-art wires, with the purpose of studying the effect of cable parameters and processing on their performance. This includes for instance the sensitivity of electrical properties (such as critical current Ic, residual resistivity ratio RRR) and internal structure (architecture, filament shape and spacing, sheath composition) to cable compaction, measurements of cable

Coil Structural Materials and Technology
For the first insert coil, the coil materials and the current procedures developed at LBNL [10,14] and at Fermilab will be used. The mandrel and the parts of the coil structure will be made of Aluminum-bronze-954 or Inconel-600, which is more expensive and challenging to machine, or some other appropriate material which can accept the high-temperature heat treatment in Oxigen atmosphere. The coil parts will be produced using precise 3D sintering technology. Every former part is pre-oxidized before the Bi2212 heat treatment, in order to create an Al3O3 oxidation layer that prevents the material from absorbing Oxygen from the environment during the coil heat treatment. The Bi-2212 Rutherford cable is insulated with mullite braided sleeve, i.e. ceramic braid 2 Al2O3:SiO2. After winding and reaction the coil will be impregnated with epoxy. Whereas at LBNL, Mix-61 from NHMFL is used for this purpose, at Fermilab it will be done either using traditional CTD101K epoxy or some other tested impregnating materials under study at Fermilab, with their corresponding procedures. Coil materials and technologies are being carefully analysed and optimized for the coils of this series.
Unfortunately, the Bi2212 leaks that were observed at 1 bar reaction in Oxigen do not desist when performing the 50 bar heat treatment. Spots or discolorations form where Bi2212 liquid leaks through the encasing Ag alloy metal at high temperatures and reacts with surrounding materials, including the insulation [10]. Most leakages in small racetracks produced at LBNL occur at the Rutherford cable edges, and they degrade the Je locally. An example of leaks in Rutherford cables and their composition can be found in [15]. After reaction, the surface of all cables under study showed black spots embedded in the Ag coating as in Fig. 9, left and center. When tested at 4.2 K and self-fields of 0.1 to 0.3 T, an Ic degradation of about 50% was found for all these cables. This current reduction on the cables was significantly and systematically larger than that of their extracted strands.
SEM/EDS analysis performed on the surface of a cable showed that the composition of this black material was very close to that of Bi-2212 (Spectrum 1 in Table of Fig. 9, at right). In a small crater at the edge of the sample, analysis showed several oxide phases, with specific shapes and morphologies, such as Bi-2212 (needle like grains), Bi-2201 (step like grains), (1,0) phase (spherical grains) and others. However, because no leaks were observed on the extracted strands, which performed well, the hypothesis was made that this problem is not as much related to the strand ability to withstand deformation as to the heat treatment of the cables itself.

2
To reduce Bi2212 leaks, before insulating the Rutherford cable with the mullite sleeve, the cable is brushed with a thin layer of TiO2-polymer slurry, i.e. TiO2 powder mixed with ethanol. Once this is done, this coating is also applied to the insulated cable onto the mullite sleeve [10,14]. This method does not eliminate leaks, but at least reduces their number.

Effect of transverse pressure
As previously shown, the main stress components on the conductor in the coil are transverse to the Rutherford cable axis. Transverse stress is the largest stress component in accelerator magnets, and can therefore damage brittle Bi2212 coils. To determine Ic 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 Rutherford cable or wire samples and testing their transport current at several magnetic fields. Strain sensitivity increases with magnetic field.
There are two components of the critical current reduction: 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 Ic after unloading the sample. The Ic degradation should strongly depends, as previously mentioned, on the Bi2212 wire technology.
The only data found in literature for transverse pressure testing of Bi2212 Rutherford cables are presented in [9]. The tested cable had 20 strands from a Showa billet, a Ni-Cr 80 core covered with two-layer wrap of MgO paper, and after reaction had expanded from 2.240 mm to 2.348 mm in thickness and from 8.89 mm to 8.94 mm in width. It was insulated with S-glass, placed in 304 stainless steel test tooling, and vacuum impregnated with CTD-101 epoxy. The cable sample was confined horizontally. The measurements were made at NHMFL, in a split-pair solenoid with a piston of 130 mm diameter in the loading device which pushed on the center of the beam, displacing it into the cable loading fixture. For a load of 100 MPa, mechanical modeling produced a displacement into the cable package of 25 µm, i.e. a strain on the Bi2212 cable of about 0.5%. Assuming an irreversible strain limit of 0.3%, in [9] it was recommended to limit the transverse pressure load to 60 MPa.
The transverse stress limit will be further verified by tests planned at Fermilab. The Ic degradation should strongly depends, on the Bi2212 wire technology, but also on sample preparation and setup design. The former has an impact on possible stress concentrations; the latter determines the sample's actual stress-strain state. The Fermilab's Transverse Pressure Insert (TPI) measurement system is a device to test critical current sensitivity of impregnated superconducting cables to uniaxial (plane stress) transverse pressures up to about 200 MPa [13]. This device produces the effect of uni-axial and not multi-axial strain, since the experimental setup allows for the sample to expand laterally. This produces larger strain values on the cable sample than for instance on a laterally constrained one.

Coil insert testing
To test and optimize the Bi2212 coil design and technology, inserts will be tested independently and inside 60-mm aperture Nb3Sn dipole coils available at Fermilab.
The first single Bi2212 half-coil, described above, will be tested individually and in a background field of a 2-layer Nb3Sn coil that had been developed at Fermilab for the 11 T dipole for LHC [11]. The two coils will be placed inside the dipole mirror structure HFDM [16] as shown in Fig. 10.
Then the whole Bi2212 dipole insert will be tested inside a 4-layer 60-mm aperture dipole coil, which will feature stress management in the two outermost layers (see Fig. 11, left). This 6-layer hybrid coil will be placed inside a slightly modified 600 mm outer diameter structure (Fig. 11, right), which was developed and used at Fermilab for the MDPCT1 dipole [17]. The large-aperture coil with stress management has been developed [6] and is now being fabricated at Fermilab.  In both configurations, the Bi2212 coils will be powered individually and then connected in series with the Nb3Sn coil. Since additional Lorentz forces from the Bi2212 insert coil are much lower than the Lorentz forces of the Nb3Sn outsert coil, no modification of the structures shown in Figs. 10 and 11 is planned at the present time. Geometrical parameters of the hybrid test configurations discussed above are summarized in Table 5. The conductor limits of Bi2212 coils, made of two wire generations, inside the 4-layer and 6-layer hybrid configurations, were estimated using coil load lines and typical parameterizations for Bi2212 critical current Ic(B), such as the following: where Bc2 is 150 T and A is 11.12 and 17.79 A . T 0.2 for Bi2212-2015 and Bi2212-2017 wires respectively. Ic(B) curves of two Bi2212 wire generations and of the Nb3Sn cable used in outserts, and maximum field load lines of the Bi2212 (1-4) and Nb3Sn (5-6) coils are plotted in Fig. 12. The insert current and field limits for operation without and with external field from Nb3Sn coils are defined by the intersection of the corresponding cable Ic(B) curves with the insert load lines.
The maximum field in Bi2212 coils in various test configurations for two Bi2212 types of wires at various levels (from 30% to zero) of cable Ic degradation is summarized in Table 6. The first coil made of Bi2212-2015 wire will be assembled and tested as a 4-layer hybrid mirror and powered independently and then in series with the Nb3Sn coil outsert. For conductor degradation within 10-30%, the maximum field of the individually powered Bi2212 coil will vary within 3.3-4.1 T, and in the 4-layer hybrid mirror within 6.9-8.1 T. The whole Bi2212 dipole insert with the Bi2212-2015 wire tested as a 6-layer dipole, as seen from Table 5, could achieve a maximum field range of 9.9-12 T.   It is expected that the next Bi2212 coils will use Bi2212-2017 wire. These coils could be assembled and tested in both the 4-layer hybrid mirror and in the 6-layer hybrid dipole configurations. The maximum field of the individually powered Bi2212 coil in the mirror will vary within 4.8-5.8 T. In the 4-layer hybrid mirror with the Bi2212 coil connected in series with the Nb3Sn coil, the maximum field will increase to 9.2-10.7 T for conductor degradation within 10-30%. The maximum field in the Bi2212 dipole insert, powered individually and in series with the 4-layer Nb3Sn outer coils as a 6-layer hybrid dipole, will reach 5.0-6.1 T and 14.2-17.2 T respectively for the same conductor degradation range.
As can be seen from Fig. 12, the critical current of the Nb3Sn coil in the 6-layer dipole is close but still higher than the critical current of Bi2212 coil. In the mirror configurations, the Nb3Sn coil has larger critical current than the Bi2212 coils. Notice also that the maximum field ranges of individually powered Bi2212 coils in the 4-layer mirror and in the 6-layer dipole configurations are very close since the load lines 1 and 2 in Fig. 12 are very close. This is not surprising since the field level produced by Bi2212 coils is relatively small and, thus, the iron saturation effect in the mirror is not large and the iron works as an ideal magnetic mirror.

Conclusions
The 2-layer dipole coil design, described above, allows extensive and cost-effective ways of developing and testing the technology of HTS inserts based on Bi2212 cable and the cos-theta coil geometry. With existing Bi2212 composite wires, there is the potential of reaching a maximum field in Bi2212 coils up to 16-17 T using a 6-layer hybrid dipole design. The maximum field in the coil bore will be ~2% lower, or within 15.7-16.6 T.
The presented insert design concept, as well as the basic technological solutions, will be studied experimentally on a series of short coils. The development of the Bi2212 coil engineering design is in progress. Tests of the first Bi2212 coil in dipole mirror configuration could start by end of 2021.