REBCO-based dipole optimized for an ultimate-energy hadron collider
WWk2LPo1C-07
Submitted to IEEE Trans. Appl. Superconductivity,Proceedings of Applied Superconductivity Conference, Tallahassee, Oct. 24 – Nov. 7, 2020 REBCO-based dipole optimized for an ultimate-energy hadron collider
P.M. McIntyre
IEEE,
J.S. Rogers, and A. Sattarov
Abstract — REBCO tape has remarkable performance for super-conducting technology, but it is extremely expensive and it is a strongly anisotropic superconductor. The design of a 3.5 T collider dipole is presented in which all turns of the body winding are ori-ented so that the all turns of REBCO tape operate with maximum current density. Each turn within the winding contains a stack of Cu-clad REBCO tapes; all tapes within the turn are compressed to provide low-resistance Cu-Cu contact, but the successive turns are electrically isolated. Each turn is oriented so that the local magnetic field at the tapes is closely parallel to the tape surface. Sextupole is controlled using a current-programmed turn to provide excellent homogeneity over a 20:1 dynamic range. Issues of current re-distri-bution during ramping, quench stability, AC losses, synchrotron ra-diation, and cryogenics have been considered, and appear to provide favorable properties for an ultimate-energy hadron collider – 500 TeV.
Index Terms — Superconducting magnets; Superconducting coils; Stress control
I. I
NTRODUCTION
EBCO tape has remarkable properties for use in supercon-ducting magnets. It can operate with useful current density up to liquid nitrogen temperature, and can produce very high magnetic field at temperatures of 20-40 K. The manufactured tape is ready to use as supplied, and does not require a final heat treatment after winding into a magnet winding – an important benefit compared to Nb Sn and Bi-2212. But REBCO is extremely expensive, typically ~$90/m for a 6 mm wide tape capable of ~1000 A at 25 K. Also REBCO is a strongly anisotropic superconductor. Fig. 1 shows the de-pendence of the critical current I c in a 4 mm wide REBCO tape on the angle q between the magnetic field 𝐵"⃗ and the normal to the tape face when the tape is operating at 30 K temperature. The critical current 𝐼 ∥ when 𝐵"⃗ is oriented parallel to the tape surface ( q = 90 ° ) is ~3 times greater than the critical current 𝐼 ’ when 𝐵"⃗ is oriented normal to the tape surface ( q = 0 ° ). The tape must be oriented so that its face is oriented no more than Dq ~8 ° from the direction of 𝐵"⃗ at the tape location (the green zone in the figure), if it is to be capable of operating with I c >0.8 𝐼 ∥ . If one could orient the tapes of a winding so that the tape faces were everywhere aligned with the field, this excellent P.M. McIntyre is with the Accelerator Technology Lab, Texas A&M Univer-sity, College Station, TX 77845 USA and also with Accelerator Technology Corp. (e-mail: [email protected]). J.S. Rogers is with Accelerator Technology Lab, Texas A&M University, Cola performance could be realized. But in a dipole winding
𝐵"⃗ di-verges in the top/bottom regions of the body winding and eve-rywhere in the ends, so the winding current must be limited to ~ 𝐼 ’ . In what follows we will examine a strategy by which to actually operate a REBCO dipole winding with a current ~0.8 𝐼 ∥ . First, however, it is important to consider several aspects of current-sharing and inductive effects that complicate such a strategy. Quench protection is important in an accelerator dipole. In the event that a quench occurs, the rapid change in winding cur-rent produces an inductive voltage among the turns of the wind-ing. Since inductance is proportional to the square of the num-ber turns, the inductive voltage should be limited by choosing a smaller number of turns (and correspondingly larger winding current). But since a single REBCO tape can carry only <1 kA even in when it is oriented so that its face is parallel to 𝐵"⃗ , it is necessary to assemble 10 or more tapes as a cluster for the con-ductor of a low-inductance dipole winding. Clustering REBCO tapes has been used by several authors, including Roebel cable , Rutherford cable, CORC [1], cable-in-conduit [2], and stacked tapes [3]. In most cases REBCO tapes are stacked in a face-on cluster and then transposed by twisting
A. Sattarov is with Commonweath Fusion Systems, Boston, MA USA (e-mail: [email protected]) Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier will be inserted here upon acceptance. R Fig. 1. Dependence of I c on the angle between the tape face normal and the magnetic field, for various field strengths (30 K temperature). the overall cluster. The property of transposition is used in many superconducting winding designs to eliminate inductive coupling among the tapes of a cluster in each turn of the wind-ing. To understand this effect, consider a cluster of tapes, in face-face resistive contact with one another within the cluster, carrying an overall current I that is distributed among the tapes as shown in Fig. 2. When current is made to flow within a segment of length 𝐿"⃗ in the winding, a Lorentz force 𝐹⃗ acts upon the current in a di-rection to shift the current outwards from the vertical mid-plane of the winding. The current I in the innermost tape would expe-rience an outward-directed force 𝐹⃗ * """⃗ = 𝐼 * 𝐿"⃗ × 𝐵"⃗"⃗ that would transfer that current to the next tape (through the resistive cop-per cladding), and so forth, so that current concentrate in the outermost tape. As cable current were increased, the current I in the outermost tape would reach its critical current limit prem-aturely and quench before significant current was flowing in the inner tapes. Inductive forces on the currents among the tapes of a cable also produce AC losses as cable current is ramped up or down. If a tape is oriented normal to the magnetic field at the tape, increasing or decreasing the magnetic field induces an electro-motive force ℇ that would drive a loop current within the plane of the tape, reducing the tape’s superconducting current capac-ity. Inductive forces on the currents in neighboring tapes like-wise produce ℇ between neighboring tapes that drives current through the normal-conducting copper layers between them. In the above-mentioned uses of transposition in REBCO-based windings, the cluster of tapes is twisted along the length of the winding, so that each tape transposes from an inside lo-cation to an outside location as it traverses each twist pitch in the winding, so the inductive effects are mitigated. Transposi-tion has the consequence, however, that the current in every tape is limited to ~ 𝐼 ’ . II. C ONFORMAL WINDINGS
A conformal winding is made by orienting the tapes in a tape-cluster winding so that all tape faces within each tape cluster are closely parallel to
𝐵"⃗"⃗ at its location. The tape cluster is not transposed – the orientation of each tape in its local magnetic field is sustained in the parallel orientation that yields maximum superconducting current capacity. Consider the 4 T dual dipole shown in Fig. 3, which is de-signed as a sector dipole for an ultimate-energy (500 TeV) had-ron collider to be housed in a 2000 km circular pipeline sup-ported in neutral buoyancy at a depth of 100 m in the Gulf of Mexico [4]. The winding of each bore comprises a single layer of 10 turns of REBCO tape-cluster cable. Fig. 4 shows a detailed cross-section of the dipole winding and shows how each turn is oriented so that its face is parallel to its local magnetic field. The current capacity of the n th tape in each cluster can be estimated by extracting the local sheet current density K n (x) , adding it up for the entire tape width: 𝐼 ./ = ∫ 𝐾 / (𝑥)𝑑𝑥 . Using this method, for the particular dipole design shown, the cable critical current is ~80% 𝐼 ∥ . The con-formal winding thus requires three times less REBCO tape as would a winding in which all tape clusters were oriented verti-cally, or one utilizing a transposed cable as in prior art. Two versions of the design have been prepared and opti-mized: one with N =18 tapes in the tape-stack cable to produce 3.5 T bore field at short-sample limit; the other with N =28 tapes in the tape-stack cable to produce 4.5 T bore field. Both ver-sions have been optimized to produce approximately homoge-neous field distribution in the bore. III. C URRENT - SHARING IN A TAPE - STACK CABLE
As the dipole is ramped to increase the bore field from its value B i at injection energy to B c at collision energy, the current Fig. 2. Schematic model of a single-turn dipole winding of a 10-tape cable. Fig. 3. 4 T dual dipole, in which the winding of each bore comprises 10 turns of REBCO tape cluster cable.
Fig. 4. Detailed view of the conformal winding of the dual dipole, showing the orientation of each tape cluster in the magnetic field at its location. within each tape-cluster cable is increased proportionately. As in the preceding discussion, the magnetic field at each cable produces a Lorentz force 𝐹⃗ that pushes current flowing within each tape-cluster cable away from the dipole bore. Thus, even if current were injected so that it was initially distributed equally among all tapes within a first turn of cable, the Lorentz force would re-distribute current to the outermost tapes within the winding. It would therefore seem that as coil current were increased the outermost tape would quench when the overall cable current was still only a fraction of the desired current! But REBCO can operate at 30 K, where the heat capacity of the tape (~T ), and the conduction to remove heat ~(T hot -T) are both much greater, so it is possible to operate a cable of stacked non-insulated tapes without transposition and rely upon the ‘soft’ approach to quench in each tape to force re-distribution of current within the cable as the cable current is further in-creased. This strategy has been used to good effect in ‘no-insu-lator’ (NI) pancake windings for high-field solenoids [5]. We now analyze the dynamics of quasi-equilibrium current-sharing among the ~10 tapes within a non-transposed cable, the ap-proach of Noguchi [6] [7]. The REBCO layer within each exhibits a retarding electric field E that is current dependent: 𝐸 = 𝐸 (𝐼 𝐼 . ⁄ ) / (1) where E = 10 -6 V/m is the quench criterion, I c is the quench current for the conditions ( B,T, q ) for that tape, and n =24 is the index that characterizes the power-law dependence of the su-perconductor-normal transition for REBCO. The dynamics is analogous to the Hall effect in which the superconducting transport is acted upon by the transvers Lo-rentz force, and by a transverse electric field produced by the potential difference between neighboring tapes when they carry different currents, and by a contact resistance R c between adja-cent tapes through which current is displaced by Lorentz forces. Following Ref. 6, the time dependent distribution of current in a tape-stack cable can be estimated in a simple model in which the full length of one half-turn of the tape-stack cable is treated as a series-parallel L/R network. Each tape within a half-turn of one cable has a self-inductance per unit length (2) and a power-law series resistance (3) where w=6 mm is the tape width, g=10 cm is the vertical gap in the steel flux return, and x~10 cm is the horizontal width of the tape loop. Lu et al . [8] measured the dependence of the contact re-sistance R c upon the compression among the tapes in the stack, shown in Fig. 5a. As shown in Fig. 5b, each turn of tape-cluster cable in the conformal winding is supported by a laminar spring that pro-vides ~1 MPa uniform compression within the tape-cluster, cor-responding to contact resistance R c ~35 µ W -cm . The parallel resistance of a length ℒ of a tape to each of its neighbors is 𝑅 = = > ? ℒ6 = (7.ABC∙E)F (4) From these quantities, we can extract two results that char-acterize the scale of current-sharing. First, the scale length l over which this homogenization operates is the winding length for which R p ~R s : 𝜆 = H > ? J = 29𝑚 N OO ? P Q**.R (5) l is much longer than any reasonable winding length, so the current distribution would relax uniformly along the winding. Second, we can estimate the time constant with which a dif-ference in current between successive tapes in a tape-stack ca-ble relaxes to an equilibrium governed by the Lorentz force and the 2-D distribution of resistance within a tape-stack cable. The change in inductance along one winding length ℒ between one tape and the next is (6) Current-sharing poses a further challenge for field homoge-neity, however. At injection field, the current in each tape clus-ter is located mainly n the outermost tape; at collision field, the current is ~equally shared, so the ‘current position’ for that ca-ble turn is shifted inwards by half the cluster width. The multi-poles have been evaluated for the magnetic design of Figure 5 for these two limiting cases. The difference in the calculated multipoles is D b n <0.5x10 -4 for all multipoles! This result might seem remarkable, but it is actually a consequence of the confor-mal design strategy: because each tape cluster is oriented so that the tape faces are closely parallel to the field at conductor, the field distribution is insensitive to the horizontal position of the ‘current center position’ of that cluster. IV. SUPPRESSION OF PERSISTENT - CURRENT MULTIPOLES
In the conformal winding, all tape-stack cables are oriented so that tape faces are closely parallel to the magnetic field at the tape. As the winding current is ramped up or down, there is no induced emf in the plane of any tape, so persistent-current loops are strongly suppressed. This is a unique property of the con-formal winding of tape-stacks, not true for any other geometry of wire or cable. The multipoles from persistent-currents are a significant challenge for beam dynamics at injection field for colliders, and conformal windings naturally suppress them.
Fig. 5. a) Contact resistance between two copper-clad REBCO tapes as a func-tion of compression; b) structural assembly of a conformal winding showing the support of each tape-stack cable and compression by a laminar spring. inner structure ou t e r s t r u c t u r e laminar springs bore tube aperture steel flux return V. E ND WINDING
At each end of a dipole winding, the magnetic field flares outward both vertically and horizontally and returns to the sur-rounding steel flux return, as shown in Fig. 6. In the end region of the dipole, each turn of tape-stack cable must be formed along a catenary curve that connects one turn of the body winding from one side to the other and flares out of the mid-plane to provide clearance for the beam tube of the dipole. Provision is made to interweave additional tape segments between the tapes within the flared-end region of each tape-stack cable. The reinforced region can accommodate current transfer among the tapes of the tape-stack cable and the reinforcing tapes to provide twice the current-carrying capacity in the end winding region. VI. .C ONFORMAL SUB - WINDINGS FOR A HIGH - FIELD DIPOLE
Fig. 7 shows a 2-layer conformal sub-winding of REBCO tape-cluster in an 18 T hybrid dual dipole designed for the re-quirements of a 100 TeV hadron collider in a 100 km tunnel. The dipole was originally designed using a Nb Sn outer sub- [1] D.C. VanDerLaan, ‘Multiphase coaxial superconducting cables and CORC degaussing system’, Patent WO2015006350A3 (2015). [2] 银顺 , 阚 常涛 , 薛 济 萍 , 吴姜 , 姜喆 , 袁茜 ‘A kind of cable-in-conduit conductor based on ReBCO isotropism superconducting strands’, Patent CN107564623A (2018). [3] Y. Iwasa, J. Bascuñán, and S. Hahn, ‘High-temperature superconducting high-current devices compensated for anisotropic effects’ Patent US10079092B2 (2018). [4] S. Assadi et al ., ‘Cable-in-conduit dipoles to enable a future hadron col-lider’, IEEE Trans. Appl. Superconduct. , 4, 4004005 (2017). DOI: 10.1109/TASC.2017.2656157 . [5] S. Choi et al ., ‘A Study on the no insulation winding method of the HTS coil’, IEEE Trans. Appl. Superconduct. , 3, 4904004 (2012). https://iee-explore.ieee.org/document/6080707 winding and a Bi-2212 inner sub-winding (shown in left half of the quadrant), each composed of SuperCIC round cable [9]. The right half of the quadrant shows replacement of the Bi-2212 winding by a conformal REBCO tape-stack winding. The field homogeneity was preserved, the quantity of superconductor was reduced by half (although it is still prohibitively expen-sive!). By the above arguments, persistent-current multipoles from the REBCO sub-winding should be significantly reduced by the conformal geometry. This final example illustrates the power of the conformal winding strategy to get the maximum performance from a REBCO winding, and correspondingly to reduce the quantity of expensive superconductor for a given ap-plication. R EFERENCES [6] S. Noguchi, ‘Electromagnetic, thermal, and mechanical quench simula-tion of NI REBCO pancake coils for high magnetic field generation’, IEEE Trans. Appl. Supercond. , 5, 4602607 (2019). https://ieeex-plore.ieee.org/document/8664631 [7] R.C. Mateira et al ., ‘Finite-element modeling of no-insulation HTS coils using rotated anisotropic resistivity’, Supercond. Sci. Technol. , 08LT01 (2020). https://iopscience.iop.org/article/10.1088/1361-6668/ab9688 [8] J. Lu et al ., ‘Contact resistance between two REBCO tapes under load and load-cycles’, https://arxiv.org/ftp/arxiv/papers/1701/1701.00447.pdf [9] J. Breitschopf et al .), ‘>16 T hybrid dipole for an LHC Energy Doubler’, IEEE Trans. Appl. Superconduct (2020) 4901906. Fig. 7. 18 T hybrid dual dipole for a 100 TeV hadron collider. The winding comprises an outer Nb3