1. 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

2. 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

3. 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 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

4. 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): 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

5. 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

6. Roebel cable transverse stress sensitivity
Transverse stress of 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

7. 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

8. 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, , EDMS Nr:
Optimisation of Roebel cable for HTS magnets
EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

9. 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

10. 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, , EDMS Nr:
Optimisation of Roebel cable for HTS magnets
EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

11. 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 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, , EDMS Nr:
Optimisation of Roebel cable for HTS magnets
EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

12. 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, , EDMS Nr:
Optimisation of Roebel cable for HTS magnets
EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

13. 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, , EDMS Nr:
Optimisation of Roebel cable for HTS magnets
EuCARD2, 2nd annual meeting, Barcelona 22 April 2015

14. 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