Fermilab is developing high field dipole magnets for post-LHC hadron colliders. Several designs with a nominal field of 10-12 T, coil bore size of 40-50 mm based on both shell-type and block-type coil geometry are currently under consideration. This paper presents a new approach to magnet design, based on simple and robust single-layer coils optimized for the maximum field, good field quality and minimum number of turns

Zlobin, Vadim V. Kashikhin and Alexander V.

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Fermilab FERMILAB-Conf-01/127  July 2001SINGLE-LAYER HIGH FIELD DIPOLE MAGNETS*Vadim V. Kashikhin† and Alexander V. Zlobin, FNAL, Batavia, IL 60510, USAAbstractFermilab is developing high field dipole magnets forpost-LHC hadron colliders. Several designs with anominal field of 10-12 T, coil bore size of 40-50 mmbased on both shell-type and block-type coil geometry arecurrently under consideration. This paper presents a newapproach to magnet design, based on simple and robustsingle-layer coils optimized for the maximum field, goodfield quality and minimum number of turns.1 INTRODUCTIONA large number of superconducting magnets requiredfor a future Very Large Hadron Collider (VLHC) [1]makes it vitally important to simplify the design anddevelop manufacturing technology of main magnets,aimed at high reproducibility of magnet parameters, costreduction, increasing their efficiency and reliability. Themost critical part in the conductor-dominatedsuperconducting magnets is a coil that serves as fluxdriving and field forming element.  Usually the coil issubdivided onto several layers and blocks, whose positionand size are optimized in order to achieve a required fieldand field quality in magnet aperture. It gives more freeparameters for field tuning and also reduces the magnetoperation current. On the other hand, it complicates thefabrication technology, increases fabrication time andcost, reduces accuracy of the turn/block position becauseof accumulation of many small errors, puts restrictions onthe magnet length due to quench protection problems, etc.Experience with the single-layer RHIC magnets [2]demonstrated significant technical and economicaladvantages of reducing a number of layers in coils.  Thisapproach was successfully used in the Nb3Sn single-layercommon coil dipole developed for VLHC [3,4].The approach described in this paper expend the single-layer concept to high filed accelerator magnets and, inaddition to a minimization of number of layers, alsoinvolve a minimization of number of blocks and turns inthe coil. Although a small number of turns will leads to ahigh magnet operating current, a recent progress in thesemiconductor technologies, HTS current leads andsuperconducting power transmission lines reduces theimportance of these limitations for modern and futureaccelerators [1].2 MAGNET DESIGNSThe design goals were reaching the field of 11-12 T in40-50 mm bore Nb3Sn dipole magnets with a single-layercoil and a minimal number of turns. The number of turnswas reduced to a value, required for achieving a desiredfield and field quality by increasing the cross-section areaof a single cable.Two types of single layer coils (cos-theta and block)were considered in this study and referred as design I anddesign II. The coil cross-section was optimized using theROXIE code [5] with round inner surface of the iron yokeand iron permeability µr=1000. The iron yoke designs andresults of their optimization are reported elsewhere [3].2.1 Coil cross-sectionFigure 1 presents the optimized coil cross-sections withthe field quality diagrams. Magnet parameters aresummarized in section 2.3.0 10 20 30 40 50Rel. field errors0     2    4     6     8    10   12   14   16   18   20(x10E-5)  0 10 20 30 40 50Rel. field errors0     2    4     6     8    10   12   14   16   18   20(x10E-5)Figure 1: Coil geometry and field quality:(design I – left, design II - right)The design I coil is based on the shell type (cos-theta)geometry with turns distributed azimuthally on a roundsurface forming the coil bore.  In order to approximate thecos-theta azimuthal current distribution minimum sixturns grouped in tree blocks per quadrant as shown inFigure 1 (left) are required.  The chosen coil borediameter of 45 mm and the target field of 12 T defines thecable thickness of 2.200 mm and width of 26.717 mm for0.25-mm thick insulation.  A rectangular cable was usedin this design based on the fabrication considerations thatwill be explained in the next section.  The azimuthal blockposition and block tilt angle were optimized for the bestfield quality in the bore. The slightly elliptical coil borehelps increasing the coil efficiency and also reachingbetter field quality with respect to the round bore.The design II coil is based on the block type geometrywith turns positioned horizontally and stacked in oneblock (see Figure 1, right). In order to approximate thecross-section area of two intersecting ellipses five turnswere chosen.  The chosen number of turns, the coil borediameter and the target field define the cable thickness of3.350 mm and width of 20.233 mm for 0.25 mm thickcable insulation. The horizontal shift of each turn wasoptimized for the best field quality in the bore.___________________________________________* Work was supported by the U.S. department of energy†vadim@fnal.gov, zlobin@fnal.gov2.2 Coil support structure and fabricationFigure 2 shows possible coil support structures for thedesign I and design II. Figure 2: Collared coil mechanical structures.The coil support structure for design I consists of collarlaminations with rectangular slots for each block similarto stators of electrical motors. These slots unsure thenominal position of turns. The parts of collar separatingthe coil blocks provide a stress management preventing anaccumulation and transfer of the azimuthal component ofLorentz force to the midplane blocks. In case of design IIcoil support structure consists of outer collar laminationsand an inner insert. The collars and inner insert haverectangular steps for placing of each turn in the coil intheir nominal position. The inner inserts also serves forthe reaction of the vertical component of Lorentz forcemaximum in the pole turns. The large horizontalcomponent of Lorentz forces will be reacted in bothdesigns by the iron yoke and thick outer skin.Due to small bending radii of turns in coil ends thedesign I is better suited for the wind & react fabricationtechnique. Each half-coil is wound directly into the coilsupport structure. After that, the two collared half-coilsare assembled around the mandrel and collars are lockedtogether by keys, providing some small radial prestress.All the gaps between turns and collar necessary for theeasy turn installation into the slots will be removed andsome small azimuthal prestress in each block can becreated due to the Nb3Sn cable expansion during reaction.After reaction the collared coil will be impregnated withepoxy and assembled with iron yoke.The horizontal turn orientation in design II coil makes itwell suited for the react & wind fabrication technique inthe common coil configuration. Two coils are woundsimultaneously into the coil support structure similar tothe technique developed for the single-layer common coildipole [4], slightly prestressed in vertical and horizontaldirections, impregnated with epoxy and assembled withiron yoke.2.3 Magnet parametersTable 1 presents the major magnet parameters. Theseparameters were calculated at 11 T bore field with a roundinner surface of the iron yoke and low constant ironpermeability µ~5 chosen to fit the finite element results.Table 1: Magnet parametersParameter Unit Design I Design IICoil bore in midplane mm 45.0 50.0Available round bore mm 45.0 45.0No. of turns/aperture 12 10Coil area/aperture cm2 22.6 22.8Iron yoke ID mm 120 110Bore quench field T 11.79 11.84Maximum current kA 81.36 92.28Transfer function T/kA 0.1352 0.1192Inductance/aperture mH/m 0.076 0.057Stored energy/aperture kJ/m 251.5 242.7Horiz. force/quadrant MN/m 2.62 2.62Vert. force/quadrant MN/m 1.07 1.10Minimum distance of 8 mm between the outer coil andthe inner yoke surface was the same as in the two-layershell-type dipole model [3].  The quench field wascalculated for Jc(12T,4.2K)=2000 A/mm2 andCu/nonCu=0.85:1.Both designs have nearly the same coil bore diameter,coil areas and quench fields.  These parameters are similarto the double-layer shell type magnet and exceed by 10-20% the corresponding parameters of the single-layercommon-coil magnet [3]. Minimum number of turns inboth designs result in low transfer functions and highercurrents, which is however less than the 100 kA – thenominal current of the first stage VLHC magnets [1].10.011.012.013.01500 1750 2000 2250 2500 2750 3000Jsc(12T,4.2K), A/mm2B0, TCu/Sc=0.85Cu/Sc=1.2Figure 3: Bore quench field as a function of criticalcurrent density in the coil at 12 T and 4.2 K.The maximum (quench) field in the magnet aperture at4.2 K vs. the critical current density of SC strands in thecoil is shown in Figure 3.  For the expected criticalcurrent density in Nb3Sn strands of 3000 A/mm2,Cu:nonCu=1.2:1 required for magnet quench protectionand critical current degradation in the coil ~10% for thedesign I (wind and react approach) and 15% for thedesign II (react and wind approach and common coilconfiguration) the maximum bore field is 12.2 T and 12.0T respectively.  It meets the VLHC stage II requirementsand provides 20% critical current margin.Table 2 summarizes the systematic and randomgeometrical field multipoles due to ±50µm random turndisplacements.Table 2: Relative field multipoles @ 1 cm in 10-4Design I Design IInbn σan/σbn bn σan/σbn1 10000 1.66/- 10000 2.05/-2 - 0.92/1.02 - 1.01/1.073 -0.0001 0.47/0.47 0.0005 0.49/0.474 - 0.21/0.22 - 0.18/0.195 0.0011 0.09/0.10 0.0003 0.07/0.086 - 0.04/0.04 - 0.03/0.037 0.0019 0.02/0.02 0.0005 0.01/0.018 - 0.01/0.01 - 0.00/0.009 -0.0035 0.00/0.00 0.0008 0.00/0.0010 - 0.00/0.00 - 0.00/0.0011 -0.0219 0.00/0.00 -0.0013 0.00/0.00Design II has better field quality and as a result a largergood field region (see Figure 1) than Design I due to thelarger number of free parameters available for adjustingthe low order harmonics (five vs. three in design I).Nevertheless, both of the designs have excellentgeometrical harmonics, better than previously developedNb3Sn magnets [3]. Possible restrictions of random turnmotion in the precise collar structure described aboveoffer a reduction of the harmonics RMS spread.2.4 Strands and CablesThe parameters of the Rutherford type cables used inthe design I and II are summarized in Table 3. Both cableshave small aspect ratio that unsure good cable mechanicalstability.  However, such cables require quite large strandsof 2-3.5 mm in diameter that is by factor of 2-3 largerthan currently used Nb3Sn strands. As a result, suchcables may have rather high mechanical rigidity that maycreate some problems during coil winding.  In case of thereact and wind technique the large strand diameter wouldrequire too large bending radii or lead to the large criticalcurrent degradation.Table 3: Cable parametersParameter Units Design I Design IIStrand diameter mm 2.200 3.350No. of strands 24 12Cable width mm 26.717 20.233Cable thickness mm 3.942 5.935Aspect ratio 6.78 3.41In order to avoid the above problems and decrease theNb3Sn strand diameter to the level convenient for themagnet fabrication, multistage cable with sub-strandsshown in Figure 4 can be used.   Using such strandsallows reducing Nb3Sn strand diameter to the level of 0.7-0.45 mm comfortable for the strand production, increasingthe cable mechanical flexibility and minimizing bendingdegradation. Combination of Nb3Sn strands with quitelow Cu:nonCu ratio and pure Cu strands allows achievinga Cu:nonCu ratio in final cable required for magnetquench protection and reducing the cable cost.      Figure 4: Examples of strand structure combined withcopper and Nb3Sn strands with low Cu:nonCu ratio.3 CONCLUSIONSHigh field dipoles based on the shell-type and block-type single-layer coils with minimum number of turnshave been developed.  Both designs achieves 11-12 Tfield level with Nb3Sn coil and provides the acceleratorfield quality. A simple single-layer coil geometry andminimum number of turns allow significant reduction ofmanufacturing time and cost that is essential for magnetmass production. The collar structures, used also as a coil-winding fixture, provide precise conductors positioningand support. It offers improving a reproducibility of thefield quality and quench performance.  Magnet designsare well suitable for both “wind and react” and “react andwind” techniques. A low coil inductance simplify theproblems related to the magnet quench protection.Since both coils are based on the cable with a smallaspect ratio, the cable width can be easy increased byfactors of 1.5-2 to achieve higher fields.  However, anincrease of maximum field from 12 T to 14 T requiresdoubling the coil area. Using the SSC-type NbTi strandswith a critical current density of 2750 A/mm2 at 5 T and4.2 K in these designs allow reaching the maximum borefield of ~7 T at 4.2 K, or ~10 T at 1.8 K.4 REFERENCES[1] Design Study for a Staged Very Large HadronCollider, Fermilab-TM-2149, June 4, 2001.[2] P. Wanderer et al., ”Construction and testing of arcdipoles and quadrupoles for the Relativistic Heavy IonCollider (RHIC) at BNL”, Proc. of the 1995 Particleaccelerator conference and International conference onHigh-Energy Accelerators, v. 2, p.1293, May 1995.[3] V.V. Kashikhin, A.V. Zlobin, “Magnetic designs of 2-in-1 Nb3Sn dipole magnets for VLHC”, IEEETransactions on Applied Superconductivity, Vol. 11,No. 1, 2176, March 2001.[4] I. Novitski et al., “Design and mechanical analysis of asingle layer common coil dipole for VLHC”, IEEETransactions on Applied Superconductivity, Vol. 11,No. 1, p. 2276, March 2001.[5] S. Russenchuck, “A Computer Program for the Designof Superconducting Accelerator Magnets”, CERNAT/95-39, LHC Note 354, Geneva, Switzerland, 26September 1995.CuNb3Sn

Single-layer high field dipole magnets

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Single-layer high field dipole magnets

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