Optimisation of Roebel cable for HTS accelerator magnets Jerome Fleiter and Amalia Ballarino on the behalf of EuCARD2 WP10.2 EuCARD-2 is co-funded by the partners and the European Commission under Capacities 7th Framework Programme, Grant Agreement 312453

Outline Introduction Roebel cable Conclusions geometry and performance transverse stress sensitivity windability transposition pitch Conclusions Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Context We need a high current and high current density YBCO cable In circular collider: Further particle discovery => higher energy => higher dipolar field Maximum dipolar field of superconducting coils: Nb-Ti 9 T, Nb3Sn 16 T, YBCO >20T YBCO very promising but in form of tape Requirements for YBCO accelerator dipole: 5-7 T in 10-15 T background, Jce >600 A/mm2 (4.2 K) Large stored energy=> High current cable (~10 kA) We need a high current and high current density YBCO cable Ebeam[TeV] ≈0.3 B0 [T] Rb [km] 4-12 mm 0.1 mm Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Roebel cable geometry Need for a high current transposed cable but YBCO tapes difficult to bent in the plane 2006:Roebel cable made of pre-shaped YBCO tapes Typical cable geometry: Cable width (W): 4-12 mm Cable thickness (t): 1-2 mm Transposition pitch (Tp): 126-300 mm Crossing angle (α) :30 deg Picture from GCS Drawing from C. Barth Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Roebel cable electrical performances at 4.2 K and 10 T Measurements at CERN in FRESCA test station in  and // fields Cables from KIT: 126 mm pitch, 9, 10 and 16 strands Cables from GCS: 300 mm pitch 15 strands Additional 5-12 mm2 cooper shunt Segregated Distributed Good quench performances No impregnation Vtaps on each strand Low joint resistance ~1 nΩ B// :Ic>11 kA and Jce > 1.1 kA/mm2 * *Not including shunt 1 strand= 1 YBCO Copper 12 mm <1 mm Optimisation of Roebel cable for HTS magnets J. Fleiter et al., Electrical characterization of REBCO Roebel cables Supercond. Sci. Technol. 26 (2013) EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Roebel cable transverse stress sensitivity Transverse stress of 100-200 MPa on Roebel cable in high field magnet coils YBCO resilience to transverse stress > 600 MPa Roebel cable resilience ~10-50 MPa =>Uneven transverse stress distribution To distribute the transverse stress in Roebel cable: Epoxy impregnation Optimization of cable geometry Impregnation helps to distribute stress but cable design still has to be optimised Cable geometry optimization required to distribute transverse stress Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

The transverse effective section (Es) of Roebel cable Definition: section that experiences the transverse stress/ projected section (in prints: red/ (grey+red)) Effective section in dry cables depends on: Strand geometry Number of strands Classical tape geometry: Es =2%-50 % => Model developed and validated vs. measurements used to optimize the strand geometry. Es -> 100% (in dry cables) to minimize peak stress Red=thicker spots =>stress Grey =thinner spots =>no stress J. Fleiter et al., IEEE Trans. Appl. Supercond. , vol. 25, no. 3, June. 2015 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Optimized design for meander tapes Classical design (α=30°):Reproduce the bending of a coated conductor of a constant width that is cabled Low Es (~0-12%) in even configuration Medium Es (~2-40%) in odd Square wave design: Additional winglet in the crossing segment of the classical design Add current margin at crossing segments Enhance the transverse stress effective section No reduction of the longitudinal mechanical resilience =>Even square wave design :large Es and small pitch=>interesting for accelerator magnets J. Fleiter, C. Lorin and A. Ballarino “On Roebel Cable Geometry for Accelerator Magnet ”, CERN ACC- Note, 2015-003, EDMS Nr: 1455142 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Windability of Roebel cable Modulation (+/- t/2) of the bending radius of strands in coil heads =>differential developed length differential length induces a shift of the strands with respect to each other (no friction) If strand shifting > inter strand gap => strand buckling Strand shifts depends on cable and coil geometry => Minimization of strand shift since it is detrimental to both windability and transverse effective section Picture from J.V. Nugteren wc’ Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Strand shift during winding Coil geometry considered as a pancake Coil inner radius R constrained by coil aperture and costs Number of turns (n) constrained by magnetic design Short section length (SS) could be tuned Strands bending radius: Strand shift between tapes (i,j) in the nth half-turn : Strand shift ∝ to Tp, t and depends on SS (trough strand phase φ) => Small strand shift = short Tp and optimization of SS t cable thickness 𝜑 𝑛𝑖 strand phase N number of strands ∆ 𝐿 𝑖,𝑗,𝑛−1 differential Tp cable pitch length at the end Rm mean radius of n-1 turn 𝑅 𝑠,𝑖 𝜃 = 𝑅 𝑚 + 𝑡 2 cos 2𝜃𝜋 𝑅 𝑚 𝑇 𝑝 + 𝜑 𝑖 ∆ 𝐿 𝑖,𝑗,𝑛 𝜃 = 𝑇 𝑝 𝑡 2𝜋 𝑅 𝑚,𝑛 g(𝜃)𝑓( 𝜑 𝑛,𝑖 , 𝜑 𝑛,𝑗 ) +∆ 𝐿 𝑖,𝑗,𝑛−1 J. Fleiter, C. Lorin and A. Ballarino “On Roebel Cable Geometry for Accelerator Magnet ”, CERN ACC- Note, 2015-003, EDMS Nr: 1455142 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Impact of straight section on strand shift 3 specific straight section lengths considered here: Phase continuity (SS=m x Tp): safe case Strands in Anti-phase (𝑆𝑆= 2𝑚+1 2 𝑇 𝑝 −𝜋 𝑅 𝑚 ):good case but unstable Strands in Phase (𝑆𝑆= 𝑚 𝑇 𝑝 − 𝜋 𝑅 𝑚 ): bad case Phase continuity: safe case: limited amplitude and dump Phase continuity Strands in Anti-phase Strands in Phase J. Fleiter, C. Lorin and A. Ballarino “On Roebel Cable Geometry for Accelerator Magnet ”, CERN ACC- Note, 2015-003, EDMS Nr: 1455142 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Impact of strands shift on Es Strand shifts reduce critical number of strands Nc Es drops to 0 at reduced number of strands (for a given Tp) Es is unchanged for even configurations The Es of even configuration is more stable vs. strands shift Distributed +/1 mm shift Plot for +/- 2mm shift J. Fleiter, C. Lorin and A. Ballarino “On Roebel Cable Geometry for Accelerator Magnet ”, CERN ACC- Note, 2015-003, EDMS Nr: 1455142 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Quest of short transposition pitch Field quality and strand shifting reasons => smallest transposition pitch Cables made of even number of square wave strands have the lowest Tp and highest Es (~100%) Straight section =m x Tp From coil geometry we know strands shift amplitude Longitudinal gap should not close: We add some margins for strands alignment and manufacturing tolerances Smallest pitches (Es~100%) are obtained with Roebel cable made of square wave meander tapes with even number of strands 𝑇 𝑝 𝑡 𝜋𝑅 sin 𝜋 𝑁 𝑇 𝑝,𝑚𝑖𝑛 ≥ 𝑁 𝑤 𝑐 ′ 1− 𝑁𝑡 𝜋𝑅 sin 𝜋 𝑁 Small cable pitch Small strand shift Small inter strands gaps J. Fleiter, C. Lorin and A. Ballarino “On Roebel Cable Geometry for Accelerator Magnet ”, CERN ACC- Note, 2015-003, EDMS Nr: 1455142 Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

Conclusions Roebel cables meet the requirements of large current and current densities for HTS accelerator magnets Roebel cables sensitive to transverse stress Optimization of strand geometry: effective to distribute the transverse stress Strand shifts during winding of Roebel may be limited using short Tp and adapted coil straight section length Impact of strand shift on transverse stress distribution : NO for cable made of even number of strands, STRONG for cables made of odd number of strands. Cable minimum pitch could be predicted with regards to coil geometry. Optimisation of Roebel cable for HTS magnets EuCARD2, 2nd annual meeting, Barcelona 22 April 2015