Zlobin, A

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DEVELOPMENT OF COS-THETA Nb3Sn DIPOLE MAGNETS FOR VLHC*A.V. Zlobin†, G. Ambrosio, N. Andreev, E. Barzi, D. Chichili, V.V. Kashikhin,P.J. Limon, I. Terechkine, S. Yadav, R. Yamada, FNAL, Batavia, IL 60510, USAAbstractThis paper describes the double aperture dipolemagnets developed for a VLHC based on Nb3Snsuperconductor, a cos-theta coil, cold and warm ironyokes, and the wind-and-react fabrication technique.Status of the model R&D program, strand and cable andother major component development are also discussed.1 INTRODUCTIONA feasibility study performed recently at Fermilab for apost-LHC Very Large Hadron Collider (VLHC) adopted astaged scenario with low and high field rings in the 233km tunnel [1]. The stage 2 (VLHC-2) ring with 10 TNb3Sn magnets will collide protons with a center of massenergy of 175 TeV. In order to provide both flat and roundbeam optics in the interaction regions, magnets with avertical bore arrangement are required. A Nb3Sn dipolebased on the common coil design and the react-and-windfabrication technique was, therefore, chosen as thebaseline arc dipole magnet. This approach is regarded asthe most innovative and cost effective.An alternative approach is based on Nb3Sn cos-thetacoils that need a smaller coil cross-section with respect toblock-type coils with the same aperture and field. Inaddition, these coils allow both horizontal and verticalbore arrangements and a smaller distance between theapertures, thereby reducing yoke and magnet size, weightand cost. However, due to the small bending radii, cos-theta coils are required to use the wind-and-reacttechnique in order to avoid a large degradation of thecable critical current during coil winding.Both design approaches are being studied at Fermilab inorder to provide a solid justification for the magnet designfor VLHC-2 [2]. This paper presents the results of adesign study of double-aperture dipole magnets based onthe Nb3Sn cos-theta coil.2 MAGNET DESIGNThe coil cross section is shown in Fig. 1. The borediameter is 43.5 mm, but it can be easily varied within the40-50 mm range with small cross-section adjustment.Each half-coil consists of two layers with 24 turns, andhas two pole inserts and eight wedges, which allowminimizing low order field harmonics.0 10Rel. field errors0     2    4     6     8    10   12   14   16   18   20(x10E-5)Figure 1: Coil geometry and field quality.The coil utilizes a keystone Rutherford-type cable madeof 28 Nb3Sn strands 1 mm in diameter. The width of thebare cable is 14.24 mm, the thickness is 1.800 mm, thekeystone angle is 0.91 degree and the packing factor is88%. The thickness of the cable insulation is 0.25 mm.Both inner and outer layers are wound from one piece ofcable without an inter-layer splice.The cross sections of the double bore dipole magnetsbased on the cos-theta Nb3Sn coils described above, withcold and warm iron yokes and with horizontal and verticalbore arrangements are shown in Figure 2.In design (a) the two coils are placed side by side in acold iron yoke with an aperture separation of 180 mm.This parameter can be varied within the 160-200 mmrange for the same iron OD without noticeable effect onthe field quality. The yoke is vertically split into threepieces to allow assembly of two coils in the commonyoke. The coil prestress is provided by the yoke and the          Figure 2: Double bore dipole magnets based on the cos-theta Nb3Sn coil, cold (a, c) and warm (b) iron yokewith horizontal (a, b) and vertical (c) bore arrangement._________________________* Work supported by the U.S. Department of Energy.† zlobin@fnal.gova) b) c)0-7803-7191-7/01/$10.00 ©2001 IEEE. 3427Proceedings of the 2001 Particle Accelerator Conference, Chicagostainless steel skin. Since two horizontal components ofthe Lorentz force acting on the left and right sides of bothcoils are compensated inside the cold mass, a 10 mm thickskin is sufficient to provide an effective coil support. Anopen gap minimizes the reduction of coil prestress aftercool down. In order to reduce the effect of gap variationon the field quality, the yoke split is partially parallel tothe flux lines so that it crosses only a small amount ofperipheral lines in the vertical plane. The iron saturationeffect is suppressed by introducing special holes and byoptimizing the yoke outer diameter.In design (b) the warm iron is remote from the coils farenough to accommodate such cryostat elements as thesupport system, the thermal shield and the vacuum vessel.The two coils are placed inside the cylindrical yoke withan aperture separation of 180 mm as in design (a). Thethick aluminum rings and stainless steel inserts providethe coil prestress and mechanical support. The cold massskin is thin since it is not a part of the coil supportstructure. The yoke inner radius and thickness wereoptimized with respect to field quality, fringe fields, ironcross-section and considerations related to the cryostatdesign. The iron saturation effect in the warm yoke designis small. A magnetic coupling between the two coilsresults in a large quadrupole component of the field. It iscompensated in each aperture by the geometricalquadrupole component of opposite sign generated byintroducing a small left-right asymmetry in coil blockposition.In design (c) the two coils are placed inside the coldyoke one on top of the other. To reduce the negativemagnetic coupling between them to an acceptable level aminimum aperture separation of 266 mm is required. Inorder to minimize the size of the cold mass, the yoke isdivided in two parts – cold and warm (the latter is notshown in Figure 2c). The cold part of the yoke isvertically split in two pieces for assembly and pre-stressing the coils. The coil prestress is provided by theyoke and the 20-mm thick stainless steel skin.  The skinthickness is a factor of two thicker than in design (a) sincethe horizontal components of Lorentz force acting on eachcoil are not compensated but added. In order to minimizeprestress reduction after cool down, the gap stays open.The warm part of the yoke is remote in order toaccommodate the cryostat elements as in design (b). Theiron saturation effect in this design is suppressed usingholes in the iron, and optimizing the cold and warm yokeinner and outer radii.Designs (b) and (c) require a proper alignment of thecold mass inside the warm yoke to reduce the forceimbalance and the effect on the field quality. Analysisshows that the alignment requirements are quite modestand can be easily met.The mechanical analysis shows [3] that in all the abovedesigns the coil is under compression, but that the stressnever exceeds 150 MPa, still acceptable for a strainsensitive Nb3Sn cable. The coil bore deformations aresmall, less than 100 µm, and all structural elements workin the elastic regime.3 MAGNET PARAMETERSThe main parameters of the dipole magnets describedabove are summarized in Table I.  All the designs meetthe VLHC-2 requirements. The magnet designs withwarm yoke allow a significant reduction in size withoutnoticeable degradation in performance.Table I: Calculated magnet parameters.Bore arrangement Horizontal Vertical Yoke design Cold Warm Cold+Warm Aperture, mm 43.5 43.5 43.5 Aperture separation, mm 180 180 266 Iron yoke OD, mm 520 580 564+710 Iron yoke area, cm2 1722 679 1378+327 Bmax, T 12.05 11.34 11.59 Imax, kA 21.9 24.0 22.3 B/I @11T, T/kA 0.56 0.47 0.52 Stored energy @11T, kJ/m 2×260 2×294 2×277 Inductance @11T, mH/m 2×1.34 2×1.08 2×1.23The values of Bmax and Imax were calculated for Nb3Snstrands with Cu/nonCu=0.85:1 and Jc=2.0 kA/mm2 at 12Tand 4.2K. Assuming a 10% Ic degradation these designscan provide Bmax~10-11.5 T using present Nb3Sn strand.A Bnom~10-11 T with 10-15% margin will be achievedusing R&D strands with Jc=3.0 kA/mm2 andCu/nonCu=1.2, which is required for quench protection.The calculated geometrical harmonics and RMS spreadfor ±50 µm random displacements of coil blocks aresummarized in Table II.Table II: Geometrical Harmonics at 1 cm radius, 10-4.Horizontal VerticalHar-monic#Cold yoke,bnWarm yokebnCold yokebnRMS(σa,b)2 - 0.000 - 1.1983 0.000 0.000 0.000 0.5644 - 0.000 - 0.2795 0.000 0.001 -0.000 0.1036 - -0.012 - 0.0477 0.000 -0.011 -0.006 0.0218 - 0.031 - 0.0089 -0.091 -0.130 -0.067 0.00510 - -0.011 - 0.001The iron saturation effect on the low order harmonics inthe operating field range 1-10 T is effectively suppresseddown to ±0.5 units by optimizing the yoke and correctionhole sizes. The coil magnetization effect at low fields islarge (b3=–20-25 units at B=1 T) with present Nb3Snstrands having a large effective filament diameter deff~100µm [4]. It can be reduced by a factor of seven using asimple passive correction based on iron strips [5]. Furtherreduction could be achieved by reducing the deff in Nb3Snstrands. Eddy current effects will be minimized usingstrands with a small filament twist pitch and optimizingthe crossover resistance in the cable.3428Proceedings of the 2001 Particle Accelerator Conference, Chicago4 MAGNET DEVELOPMENT STATUSShort model R&D. A Nb3Sn cos-theta coil is the keyelement of all the designs. Coil fabrication technologyuses the wind-and-react approach to avoid a largedegradation of the cable critical current during winding.In order to simplify the technology and reduce the cost,new features were introduced in the fabrication process.Each half-coil is impregnated with a liquid ceramic binderand cured at 120C after winding to pre-form coils beforereaction.  Then the two half-coils are assembled, reactedand epoxy impregnated together. It allows easy coilhandling, coil size and field quality control before thefinal magnet assembly, thereby avoiding expensive collarsand a delicate collaring procedure.To validate and optimize the coil and magnet designs, amodel magnet program has been undertaken. It startedwith single-bore cold-yoke models [6] and later will beexpended to double bore models. A first 1-m long modelmagnet was recently fabricated (see Figure 3) and now isbeing tested at Fermilab [7].Figure 3: Short model 3D view and assembled cold mass.Strand and cable. To reach the VLHC-2 nominal field,Nb3Sn strands and cables must meet specificrequirements.  Nb3Sn strands produced using Internal Tin(IT), Modified Jelly Roll (MJR), and Powder-in-Tube(PIT) processes were purchased and tested at Fermilab.The critical current density, Jc, of these strands wasmeasured to be within 1900-2200 A/mm2. It is controlledby the volumetric fraction of Nb3Sn phase, the heattreatment schedule, and the flux pinning mechanisms. Allthese parameters are presently studied and optimized inorder to reach the required Jc of 3000 kA/mm2.The strand magnetization and stability are driven by Jcand deff. For the strands produced using the most costeffective technologies such as IT or MJR, deff is ~100 µm.The PIT process provides it on the level of ~50 µm, butwith a significant increase in the strand cost [4]. Anoptimization of the strand design and technology aimingat the reduction of deff in the high Jc strands is underway.Strand plastic deformation during cabling, and reactedcable compression in the coil during magnet assembly andoperation causes Ic degradation and variation ofinterstrand resistance. Cables with different packingfactors were fabricated with and without a stainless steelcore and short samples of virgin and extracted strandswere tested. The studies show significant progress indeveloping of Nb3Sn cables for accelerator magnets withIc degradation less than 10% and high crossoverresistance [8].Insulation. The react-and-wind technique imposesdemanding requirements on the coil insulation. Theinsulation must withstand a long heat treatment at hightemperature (~700C) under high compression. Theceramic insulation meets these requirements and is beingused in the short models with ceramic binder (CTD Inc.)which improves the insulation performance during coilmanufacturing [6]. However, it is still rather expensive.An alternative is to use S-2 fiberglass, which is affordablebut involves a lot of pre-processing. Both insulationsystems are being extensively studied.End parts. Cos-theta Nb3Sn magnets use complicated3D end parts that must withstand the heat treatment cyclewithout deformation and match the cable shape in theends to avoid shorts. An optimization method for metallicend parts was developed and successfully tested [6].Rapid prototyping techniques reduce time and cost of theoptimization process for such end parts. Emergingtechnologies, such as water jet machining, promise asignificant reduction of the end part cost by a factor of 2.5and of the manufacturing time by a factor of 10.5 CONCLUSIONThe magnetic and mechanical designs of doubleaperture dipole magnets for a VLHC-2 based on a Nb3Sncos-theta coil with cold and warm iron yoke andhorizontal and vertical bore arrangement were developed.All magnets meet the target requirements. A nominal fieldof 10 T with 15% margin will be achieved using futureNb3Sn R&D strand. The accelerator field quality isprovided in the entire field range of 1-10 T. The operatingfield range can be further expanded by reducing deff inNb3Sn strands and using simple passive correction. Thechosen mechanical designs and the coil prestress levelprovides the coil mechanical stability in the fields up to11-12 T. The first single-bore dipole model was fabricatedand is being tested at Fermilab.6 REFERENCES[1] Design Study for a Staged Very Large HadronCollider, Fermilab-TM-2149, June 4, 2001.[2] V.V. Kashikhin, A.V. Zlobin, IEEE Trans. on AppliedSuperconductivity, v.11, No.1, March 2001, p. 2176.[3] D.R. Chichili et al., IEEE Trans. on AppliedSuperconductivity, v.11, No.1, March 2001, p. 2288.[4] E. Barzi et al., IEEE Trans. on AppliedSuperconductivity, v.11, No.1, March 2001, p.[5] V.V. Kashikhin, A.V. Zlobin, IEEE Trans. on AppliedSuperconductivity, v.11, No.1, March 2001, p. 2058.[6] D.R. Chichili, et al., IEEE Trans. on AppliedSuperconductivity, v.10, No.1, March 2000, p.2160.[7] N. Andreev et al., “Field Quality of the FermilabNB3SN High Field Dipole model”, this conference.[8] E. Barzi et al., IEEE Trans. on AppliedSuperconductivity, v.11, No.1, March 2001, p. 2134.3429Proceedings of the 2001 Particle Accelerator Conference, Chicago

Development of Cos-Theta \Nb_{3}Sn Dipole Magnets for VLHC

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