cosϑ magnet design option - cern · 2015. 5. 5. · eucard-2 enhanced european coordination for...

1 EuCARD2 Work Package 10 “Future Magnets” Task 3 Magnet design

Cosϑ magnet design option

EuCARD-2 Enhanced European Coordination for Accelerator Research & Development


Lorin, C. (CEA)

15 April 2015

The EuCARD-2 Enhanced European Coordination for Accelerator Research & Development project is co-funded by the partners and the European Commission

under Capacities 7th Framework Programme, Grant Agreement 312453.

This work is part of EuCARD-2Work Package 10: Future Magnets (MAG).



Table of Contents I. Introduction ..................................................................................................................................... 3

II. 10-mm wide cable design ................................................................................................................ 3

A. Double-layer configuration in Fresca2 ........................................................................................ 3

1) 2D magnet designs .................................................................................................................. 3

2) 2D elastic mechanical model ................................................................................................... 5

III. 12-mm wide cable designs .......................................................................................................... 7

A. Single-layer configuration in Fresca2 .......................................................................................... 7

1) 2D magnet design .................................................................................................................... 7

2) 2D elastic mechanical model ................................................................................................... 9

3) 3D single layer model ............................................................................................................ 14

B. Double-shell configuration in D1 ............................................................................................... 21

1) 2D magnetic design ............................................................................................................... 22

2) 2D elastic mechanical model ................................................................................................. 24

3) 3D coil ends and layer jump .................................................................................................. 27

IV. Conclusion ................................................................................................................................. 28

V. References ..................................................................................................................................... 29

VI. Appendixes ................................................................................................................................ 30

Appendix 1 Bruker data .................................................................................................................... 30

Appendix 2 Transverse pressure ...................................................................................................... 31

Appendix 3 Magnet dimensions ....................................................................................................... 32



I. INTRODUCTION

In the near future, one has to know if High Temperature Superconductor (or High Field

Superconductors) technology is a viable option to build the next generation of particle accelerators,

such as the High Energy LHC [TOD1] or the Future Circular Collider [FCC1]. Therefore, in the

framework of the enhanced European Coordination for Accelerator Research and Development

project (EuCARD-2), the Work Package 10 (WP 10 - Future Magnets [ROS1]) focuses on the

development of HTS dipoles in a form of an accelerator quality 5 T dipole with a 20-mm radius

aperture to be later used as insert in Nb-Ti or Nb3Sn dipole magnets in order to hopefully raise their

magnetic field beyond 16 T. In sections II.A and III.A, the outsert is the Nb3Sn Fresca2 magnet [FER1,

MUN1] and in section III.B, the outsert is the Nb-Ti D1 dipole [XU1]. In the task 10.3 of the previously

mentioned WP 10, numerous layouts of HTS dipole inserts with accelerator field quality are under

investigation [KIR1, LOR1, NUG1]. They are made of ReBCO-Roebel cable or BSCCO-Rutherford cable.

This report deals with cosθ configuration and provides first development about the HTS dipole

magnet at CEA from January 2014 to January 2015.

II. 10-MM WIDE CABLE DESIGN

A. Double-layer configuration in Fresca2

Three options were initially foreseen for the cosine-theta magnet cable technology [BOT1]. Two

types of REBCO Roebel cables and one BSCCO-Rutherford cable were initially under investigation and

some features are reported in Table I. These cables were narrower that the ones used in the other

designs of the EuCARD2 WP10.3 project – 10-mm wide cables instead of 12-mm – in an attempt to

leave enough room for the mechanical structure. For the double winding shell configuration inserted

into Fresca2, the two layers of cables as well as the mechanical support have to fit inside a 30-mm-

thick circular ring squeezed in-between the 20-mm-radius aperture and the 50-mm-radius bore of

the Fresca2 outer magnet that will have to provide the background field. Based on the cable

characteristics, various 2D magnet cross-sections are designed by means of the Cern-made Roxie

code and described in section II.A.

TABLE I

GEOMETRICAL DIMENSIONS OF INITIAL COS-Θ DESIGN CABLE OPTIONS

Material and cable

technology

BSCCO

Rutherford

REBCO

Roebel #1

REBCO

Roebel #2

Number of tapes/strands 22* 8+ 15+

Thickness (thin/thick edges) 1.39/1.52 mm 0.6 mm 1.2 mm

Width 9.5 mm 10 mm 10 mm

Transposition length 65 mm 126 mm 226 mm *0.8 mm strand diameter +4.5 mm wide meander tape

1) 2D magnet designs

A design has been generated (Figure 1) for each bare cable of Table I. A 100-µm-thick fiber glass

sleeve is taken into account as insulation. Each magnet consists of two layers of conductors and has a

central field of 5 T when surrounded by a 60 to 65 mm-wide iron yoke. The engineering current

densities Je are less than 470 A/mm2. The peak field Bpeak is about 5.3 T for all designs. A good

geometric field quality is obtained for all of the designs: the first four odd field harmonics b3 to b9

are below one unit at two thirds of the aperture. The results with Roebel cables must be considered

as preliminary ones since Roebel cables are not properly modeled in Roxie, while Rutheford cables



are (the current flow is modeled by line currents in the position of superconducting strands in the

cable). In addition, dynamic effects in Roebel cables can heavily modify the current distribution. And

finally, the use of YBCO Roebel cable can impact the 2D cross section of the design. Indeed the

allowable bending radius of YBCO Roebel cable is pretty large in comparison to Nb-Ti Rutherford

cable and can lead to a non-optimal position of the upper block in terms of field harmonics as shown

later for the single layer configuration which has been investigated more deeply.

Figure 1. Magnetic flux density in windings surrounded by a yoke not displayed. Left: Five block cos-θ design made of a BSCCO

Rutherford cable. Central: Seven block design made of a “thin” 0.6-mm REBCO Roebel. Right: Six block design made of a “thick” 1.2-mm

REBCO Roebel cable.

Figure 2. Six-block design inserted in Fresca2 facility. Left: Magnetic flux density in windings. Right: Magnetic flux density in iron parts.

Cos-θ end design can benefit from the constant perimeter profile criteria [RAN1], nevertheless, as

previously written the upper block of the inner layer will suffer from a small bending radius of

4.5 mm smaller than values given in the literature on Roebel cable (10-11 mm in [GOL1]) and, even,

out of the 5.5 to 6 mm specifications for REBCO tapes [BRU1, SUP1]. Measurements are foreseen at

the Karlsruhe Institute of Technology to precisely set a softway bending radius limit for Roebel cable

[KAR1]. The bending radius can be slightly increased resulting in field quality degradation as shown

later on in the single-layer configuration section (III.A).

In figure 2, the six-block design was simulated inside the 13 T background field (@ 4.2 K) of the

Nb3Sn block-coil Fresca2 magnet to work out the Lorentz forces exerted on the coils and perform a

2D mechanical analysis.

50mm

0 mm

1

2

3

4

5

6

x

y



2) 2D elastic mechanical model

A mechanical model of the six-block magnet was developed using the CEA in-house finite element

code cast3m [CAS1] (Figure 3). The code computes the initial pre-stress at 293 K, the stress induced

by the cooling to 4.2 K, and the deformation caused by coil powering in one fourth of the magnet.

The geometry is shown in figure 3: windings (purple), wedges (red), insulation (green) are glued all

together and named the coil block; a collar acting as filler (yellow) can slide on the coil block along

the polar plane with a gap that can open as well as along the arc-line with a closed gap (RELRA

subroutine in cast3m). The same kind of sliding contact with a closed gap is used between the collar

and the external tube (blue). The mechanical properties of the components are defined in Table II. It

is worth noticing that impregnated Nb3Sn properties are used for the windings since no mechanical

data regarding impregnated Roebel cables has been measured so far. To represent the symmetry

conditions both the collar and the external tube are free to slide along the vertical symmetry axis. In

the horizontal plane the collar is free to move in any direction, the coil block can only slide along the

horizontal plane as the external tube to which an additional displacement in the vertical direction can

be added to simulate a prestress.

Due to the large stability margin of HTS the assembly philosophy may differ from the manufacturing

of LTS magnets. The latter ones need to be pre-stressed to avoid mechanical movements of the cable

and long training. In HTS, the stability is higher and could lead to a change of paradigm in magnet

margin and conception: “HTS means higher stability, even at 4.2 K: how we use this characteristic?

Are we ready to re-discuss margins and other categories? Mantras are not good for accommodate

novelties” [ROS3]. In Table III the third row defined whether or not a pre-stress is applied to the

structure.

The main results are summarized in Table III: results in standalone mode (5 T field) and insert mode

(16.78 T field) are displayed for the peak azimuthal stress that occurs in block 1, which is the most

sensitive block in regards to stress due to pinching effect. The maximal thickness of the external tube

in the double-layer configuration inserted in Fresca2 is 8-mm (30-mm-ring space filled by two 10-mm

cables and the thickness of both insulation and collar/protection sheet). Without any pre-stress one

ends up with 600 MPa on the cable which is too high for a Roebel cable. A thicker external tube of 20

mm that would not fit inside the Fresca2 facility would lead to more reasonable – still high – value of

250 MPa. These results are very important and show that a double-layer cosine theta configuration is

not a viable solution for the dipolar magnet insert if Fresca2 is used as background field magnet.



Figure 3. Mechanical 2D model boundary conditions: symmetries, contacts, initial displacement. Windings (6 purple blocks), wedges (5

red blocks) and insulation surrounding them form the coil block. The collar (yellow) is actually a filler and the external tube (blue) is taking

all the forces.

TABLE II

Material properties of the mechanical model

Magnet

component

Colour

(Figure 3)

Young modulus

[GPa]

ILTEC*

[mm/m]

Material

Insulation Green 4 6.0 Epoxy**

Wedge Red 110 3.6 Copper

Winding Purple 30@293K [email protected] 3.9 Impregnated Roebel**

Collar/Filler Yellow 210 2.9 Steel

External tube Blue 210 2.9 Steel *Integrated Linear Thermal Expansion Coefficient: 300 K to 4.2 K **Measurements on impregnated Nb3Sn [DUR1,DUR2]

TABLE III

Azimuthal peak stress in coil block number 1 (Figure 2)

depending on field, external tube thickness and pre-stress

In order to keep on working on the cosϑ configuration, it has been decided to design a single layer

magnet to save enough space for the mechanical structure (see section III.A). This single layer design

has to be built with a slightly wider 12-mm cable initially dedicated to the block design [KIR1, NUG1],

this allows for a higher field than what could be achieved with a 10-mm wide single layer design and

spare time on cable development: one cable geometry for all magnet designs.

Sliding

contacts

Initial displacement to simulate the

prestress due to the press + welding

Collar extremity free displacement

X

Y

Symmetry :

-vertical: collar + yoke

-horizontal: coil only

Contact :

-glued: coil + wedges + insulation (coil block)

-sliding: collar with yoke or coil block



Another exotic option is the use of the D1 dipole magnet to generate the background field [XU1] (see

section III.B). The advantage of D1 is a larger aperture of 150 mm in diameter giving enough space for

a double layer with a 12-mm wide Roebel cable. However, D1 is a Nb-Ti magnet that can produce no

more than 6 T which would limit the total field that would be created by the whole system:

background field + insert magnets (~ 10 T).

III. 12-MM WIDE CABLE DESIGNS

A. Single-layer configuration in Fresca2

Since two layers of cable with a proper mechanical structure cannot fit in the Fresca2 aperture a

one-layer magnet configuration is investigated. Based on data currently available [KAR2], great care

is given to the Roebel cable minimal bending radius which is still unknown so far [KAR1].

1) 2D magnet design

In the design shown in Figure 4, the gap in-between the upper blocks of the design is kept as wide as

possible to try to end up with a bending radius deemed acceptable in the magnet 3D ends (gap = 2 x

9.89 mm, see figure 4). This should avoid any degradation of the carrying capability of the Roebel

cable during the winding. Nevertheless, reaching a wide gap between the upper blocks has a cost.

First, the aperture radius is increased from 20 mm to 22 mm: therefore current density, peak field

and forces are slightly increased. Secondly, the upper block ideally seating at about 70° of angular

position is set at 63° ([see Table III in [ROS2]). With an angle of 70°, the minimal bending radius

would be around 4.5-5 mm (below the tape limit! [SUP1]), with an angle of 63° the minimal bending

radius is about 7.6 mm as shown in section III.A.3. Such an adjustment of the upper block position

leads to a degradation of the field quality especially on b7. Field magnitudes and harmonics are

reported in Table III. Magnet dimensions are given in the appendix 3.

Figure 4. Magnetic field density [T] in the windings of the single-layer cosine-theta magnet for a transport current of 11 680 A.

For the single-layer design, the slightly bigger 12-mm wide cable under development for the aligned

block design at Cern [KIR1, NUG1] is used in order to try to reach the 5 T magnetic field target in

standalone mode. The magnet, shown in figure 4, can reach 5 T central field when powered with a

9.89 mm



current of 11 680 A and surrounded by a 50-mm inner radius iron yoke of 62 mm in thickness that

means a tape engineering current density of 944 A/mm² with the actual cable geometry (15 tapes of

0.15 mm in thickness and 5.5 mm in width). Based on tape producer data available at the time of the

report, the tape engineering current density with a 20 % margin on the loadline is around 850 A/mm²

(figure 5 Left) [CAR1]. Associated to the actual cable geometry the total current flowing through the

cable would only reach 10 500 A. Actually tape with higher performance are under development at

BHTS-Bruker HTS who is a collaborator of the EUCARD2 project [USO1] (Appendix 1).

A fit of the critical surface of HTS tapes has been developed at CERN by Fleiter for Fujikura material

[FLE1]. This fit can be slightly modified in order to catch the Bruker tape performance, i. e.

1740 A/mm² at 5 T, 4.2 K, B//c and 725 A/mm² at 18 T, 4.2 K, B//c, data reported in appendix 1

[USO1]. Since data from Bruker are only available in perpendicular field (B//c), the fit is changed by

tuning the coefficient αc directly related to the magnitude of the current density under perpendicular

field. Indeed, if αc = 4.22 [MAT/mm²] instead of 1.86 [MAT/mm²] – as in the initial fit of Fujikura

material – keeping the same other parameters current densities very close to Bruker ones can be

reached: 1802 A/mm² at 5 T, 4.2 K, B//c and 724 A/mm² at 18 T, 4.2 K, B//c. Now, according to the fit

of Bruker data, one could fairly assess that a tape engineering current density of 944 A/mm² that

would allow for a magnetic field of 5 T (~6 T peak field on the loadline) with a significant margin

(28.75 %) is now at our fingertips (figure 5 Right):

1325 A/mm² x 5.5 mm x 0.15 mm x 15 tapes x 71.25% = 11680 A (= 5 T central field)

To summarize, in stand-alone mode the tape engineering current density is 944 A/mm², the cable

engineering current density is 811 A/mm² and the overall current density is 684 A/mm².

Figure 5. Left: 12-mm wide tape engineering current density of worldwide manufacturers at 4.2 K under perpendicular field [CAR1]. Right:

Loadline of the single-layer design and critical surface from Fleiter’s fit applied to Bruker data.

In insert mode in Fresca2 operating at 13 T (@4.2 K), in order to have a 20% margin on the loadline

(Figure 6), the tape engineering current density is set at 620 A/mm² (7 670 A) and in Fresca2

operating at 15 T (@1.9 K), the tape engineering current density is 572 A/mm² (7 078 A) (Table III). It

is worth noticing that the previous fit is used with a temperature of 4.2 K in both cases since it is not

working at 1.9 K according to [FLE1]: “The fit has been optimized to be accurate over the field range

0 2 4 6 8 10 12 14 16 18 20

100

1000

10000

@4.2K, B//c

J eng [

A/m

m2]

B [T]

SuperPower

Fujikura

SuNAM

AMSC

BHTS T191

BHTS T002

SuperOx

Tap

e e

ngi

nee

rin

g cr

itic

alcu

rren

td

en

sity

J eng

[A/m

m²]

Bpeak [T]

Fujikura fit withαc = 4.22 [MAT/mm²]to fit Bruker dataT = 4.2 K, B//c

944 A/mm²

1325 A/mm²

~30% margin



from 0.5 T to 17 T, the temperature range from 4.2 K to 77 K and angular range from 0 to 2π.”. An

important point is that the peak field does not occur at a location where the magnetic field is

perpendicular to the conductors. Therefore, the results should be conservative since the load-line

represents the variation of the peak field versus the engineering current density in the cable tapes

and the blue curve represents the 4.2 K slice of the critical surface in a perpendicular field (B//c).

Figure 6. Loadlines of the single-layer operating inside Fresca2 with 20% margin and critical surface of the tape engineering current density.

TABLE III

Geometrical field harmonics at a radius of 13.34 mm in stand-alone mode

as well as inside Fresca2 operating @4.2 K, 13 T or @1.9 K, 15 T Operating mode Stand-alone in Fresca2

4.2 K, 13 T

in Fresca2

1.9 K, 15 T

Current [A] 11 680 7 670 7 078

Central field [T] 5.01 15.52 17.33

Peak field [T] 5.72 15.79 12.94* 17.78 15.05**

b3 0.16 6.19 8.52

b5 -0.36 -0.47 -0.48

b7 30.76 6.51 5.38

b9 -3.26 -0.69 -0.57 *13.13 T peak field in Fresca2 cable without insert at 10 660 A in Fresca 2 cable. **15.21 T peak field in Fresca2 cable without insert at 12 600 A in Fresca 2 cable.


A similar finite element model as previously described in figure 3 was developed. The mechanical

structure with the windings is shown in Figure 7. The external tube is 14 mm thick – to be compared

Tap

e en

gin

eeri

ng

crit

ical

curr

ent

den

sity

J en

g[A

/mm

²]

Bpeak [T]

Fujikura fit with αc = 4.22 [MAT/mm²]to fit Bruker data, T = 4.2 K, B//c

715 A/mm²

775 A/mm²

572 A/mm²

620 A/mm²



to the 8 mm of the 2 layer design – with an outer radius of 49.5 mm. The forces per block from Roxie

are reported in Table IV. They are used as inputs in the Cast3m file. No prestress is applied to the coil.

Figure 7. Single-block design and mechanical structure

TABLE IV

Forces per block in [kN/m] calculated with Roxie and injected in Cast3m Block number Stand-alone in Fresca2

4.2 K, 13 T

in Fresca2

1.9 K, 15 T

Fx Fy Fx Fy Fx Fy

Block 1 92 -48 510 -21 542 -18

Block 2 99 -57 420 -25 443 -22

Block 3 12 -44 325 -20 342 -18

Block 4 96 -36 228 -16 238 -14

In the following 3 sub-sections are reported the results of the mechanical analysis where the magnet

is operating in stand-alone mode with a 5 T central field, inside Fresca2 at 4.2 K with a 15.52 T central

field and inside Fresca2 at 1.9 K with a 17.33 T central field. The azimuthal stress in the coil blocks as

well as the radial stress is provided. The azimuthal coil deflection is given since no pre-stress is

applied to the coil and finally the Von Mises stress in the external tube is displayed.

a) Single-layer in stand-alone: 5 T central field

In stand-alone mode there is no real mechanical issue. The level of stress is very low as shown in

figures 8-9: azimuthal peak stress of 55 MPa – radial peak stress of 15 MPa. The gap between the

upper block and the mechanical structure is around 60 µm. The Von Mises peak stress is below

120 MPa.

22 mm 12 mm 14 mm

1

2

34

x

y



Figure 8. Mechanical stress distribution in the windings of the single-layer cosine-theta magnet in [MPa] in stand-alone 5 T central field.

Left: Azimuthal stress with a peak value of 55 MPa. Right: Radial stress with a peak value of 15 MPa.

Figure 9. Left: Coil deflection in [mm] in stand-alone mode with a 5 T central field.

Right: Von Mises stress with a peak value of 120 MPa in the external tube of the mechanical structure.

b) Single-layer in Fresca2: 17.36 T central field

With Fresca2 operating at 1.9 K the background field is 15 T and the central field 17.36 T. The

azimuthal peak stress is about 235 MPa which is a very high value but still acceptable based on very

recent work carried out at the university of Twente where no degradation of impregnated Roebel

cable were observed below 250 MPa of transverse pressure (see Appendix 2, [OTT1]). The gap

between the upper block and the pole is about 160 µm and the Von Mises peak stress in the external

tube is about 550 MPa. The magnet mechanics seems to be very challenging but still possible (Figures

10-11).



Figure 10. Mechanical stress distribution in the windings of the single-layer cosine-theta magnet in [MPa] in Fresca2 17.33 T central field.


Figure 11. Left: Coil deflection in [mm] in stand-alone mode with a 17.33 T central field.

Right: Von Mises stress with a peak value of 515 MPa in the external tube of the mechanical structure.

c) Single-layer in Fresca2: 15.36 T central field

An intermediate mechanical condition with Fresca2 operating at 4.2 K is investigated in this last sub-

section (Figures 12-13). The azimuthal peak stress is of the order of 220 MPa. The coil deflection

leads to a gap of 150 µm in the polar plane and the external tube has to withstand 490 MPa.

17.33 T 17.33 T

17.33 T17.33 T



Figure 12. Mechanical stress distribution in the windings of the single-layer cosine-theta magnet in [MPa] in Fesca2 13.36 T central field.


Figure 13. Left: Coil deflection in [mm] in stand-alone mode with a 13.36 T central field. Right: Von Mises stress with a peak value of

490 MPa in the external tube of the mechanical structure.

To conclude, even if challenging, it appears to be feasible in terms of mechanics to build a single layer

cosine-theta magnet. Further data are needed to prove that any impregnated Roebel cable can

withstand transverse pressure up to 250 MPa which is one of the key issues of the HTS insert dipole

design. In addition radial stress of 70 MPa may be challenging to manage. In the next section another

important part of the design is investigated: the heads of the magnet with very severe constrains due

to the Roebel cable mechanical behavior.

15.52 T 15.52 T

15.52 T 15.52 T



3) 3D single layer model

a) 3D end design

The magnet end design is a real challenge due to the Roebel cable electromechanical properties. At

the time of this report it is believed that the easyway or softway bending radius of a Roebel cable

needs to be bigger than 10 mm to avoid degradation of its current carrying capability and the

hardway bending radius bigger than 2 m to be able to mechanically bend the cable over the dipole

head. The Roebel cable can be seen as a ribbon: very easy to curve around the binormal direction but

very fragile, and almost impossible to bend around the normal direction. After conventional

simulations of the magnet ends by block of conductors showing that 10-mm easyway or 2-m

hardway bending radii could not be achieved it was decided to have one dedicated spacer for each

turn. For comparison, in the QXF project made of Nb3Sn Rutherford cable with a 150-mm aperture

diameter [IZQ1, IZQ2], the maximal normal curvature is 136.5 m-1 and the geodesic curvature 9.1 m-1

corresponding to a minimal easyway bending radius of 7.3 mm (1/136.5 = 0.0073) and a minimal

hardway bending radius of 11 cm (1/9.1 = 0.11) ! This illustrates the necessity to have one spacer

dedicated to each turn in the magnet heads [AUC1].

Return end

As a reminder, the local curvature in [m-1] is the reciprocal of the local radius of curvature [m]. The

normal curvature is the reciprocal of the easyway bending radius and the geodesic curvature is the

reciprocal of the hardway bending radius. It comes that a normal curvature of 100 m-1 corresponds to

an easyway bending radius of 10 mm and a geodesic curvature of 0.5 m-1 corresponds to a hardway

bending radius of 2 m. An illustration of the 3D return end design is shown in figure 14.

Figure 14. 3D return end of the single layer design.

In figure 15 is shown the normal curvature for each of the cable turn in the return end. The peak

values are reported in Table V. For some of the turn the normal bending radius goes down to values

less than 10 mm, especially for the polar plane turn where the peak value is 7.6 mm (see Table V).

Fortunately, these very small normal bending radii occur over a very short length and may have no

impact on cable performance. In addition, the 10 mm limit is not yet properly defined and KIT will

carry out tests to see if the Roebel cable can undergo normal bending radius smaller than 10 mm

without any degradation [KAR1]. It can be foreseen that the results will depend on the cable

topology.



Figure 15. Normal curvature of the cable going through the magnet return end for each turn. Peak values are reported in TABLE V.

Figure 16 illustrates the geodesic curvature along the cable. None of the cable turn has a hardway

bending radius bigger than 2 m. The 2 m limit has been defined by CERN for a constant hardway bend

along the cable, in our case it can be seen that the hardway bend is most of the time way below the

2 m limit which may give us more flexibility while winding. Winding tests are foreseen to better

estimate the hardway bend limit for cos-theta magnet ends. Actually it would be interesting to

release some constraints on the hardway bend in order to have bigger normal bending radii since the

design of the ends is most of the time a trade-off between normal curvature and geodesic curvature.

This could lead to less spacers in the magnet heads where the cable could be bent by block of

conductors instead of having one dedicated spacer per cable turn. It is worth noticing that the cable

twist was not taken into consideration for this study.

Cable length in the head [mm]

No

rmal

cu

rvat

ure

in [

m-1

]

10 mm easyway bending radius

Return end



Figure 16. Geodesic curvature of the cable going through the magnet return end for each turn. Peak values are reported in TABLE V.

TABLE V

Peak values of cable curvature and bending radius for the 14 turns of the return end

turn # normal curvature [m

-1]

normal bending radius [mm]

geodesic curvature [m

-1]

geodesic bending radius [m]

length of the turn

**

[mm]

14 131.6 7.6 0.486 2.1 25 13 120.1 8.3 0.289 3.5 35 12 101.9 9.8 0.494 2.0 45 11 94.2 10.6 0.158 6.3 55 10 102.0 9.8 0.330 3.0 65

9 98.9 10.1 0.238 4.2 75 8 100.9 9.9 0.126 7.9 97 7 104.7 9.6 0.244 4.1 117 6 99.7 10.0 0.390 2.6 130 5 107.6 9.3 0.404 2.5 147 4 99.5 10.1 0.306 3.3 155 3 90.6 11.0 0.205 4.9 162 2 87.1 11.5 0.334 3.0 170 1 81.7 12.2 0.128 7.8 180

min 7.6 mm 2.0 m *turn 14 is the polar plane turn and turn 1 is the median plane turn **it is not the cable length over the turn, it is the distance along the z-axis between the straight section end and the turn apex of the turn

Return end


Geo

de

sic

curv

atu

rein

[m

-1]

2 m hardway bending radius




Lead end

The lead end design is a bit more complex due to its asymmetry as shown in figure 17. Both normal

and geodesic curvatures are of the same order of magnitude as they are in the return end (Figures

18-19). In table VI is reported for both of the half-parts of each turn the maximal normal and

geodesic bending radii (softway and hardway bending radii). If needed, it is straightforward to get

the curvature which is the reciprocal of the bending radius.

Figure 17. 3D lead end of the single layer design.

Figure 18. Normal curvature of the cable going through the magnet lead end for each half turn (asymmetric side). Peak values are reported

in TABLE VI.

Lead end


No

rmal

cu

rvat

ure

in [

m-1

]

10 mm easyway bending radius



Figure 19. Geodesic curvature of the cable going through the magnet return end for each half turn (asymmetric side). Peak values are

reported in TABLE VI.

TABLE VI

Peak values of cable bending radius for the 13 turns of the lead end

turn # normal bending radius [mm]

normal bending radius [mm]



length of the turn

*

[mm]

13 7.9 7.8 3.9 4.4 40

12 8.9 8.6 2.0 4.2 50

11 10.1 10.1 7.2 4.4 60

10 10.5 10.4 2.6 11.1 70

9 8.5 8.6 4.7 3.9 85

8 11.4 11.4 14.4 13.0 95

7 12.3 12.2 4.5 20.2 110

6 10.3 10.4 3.1 8.9 130

5 9.7 9.5 2.1 3.6 155

4 9.7 9.8 3.1 2.3 175

3 12.6 12.6 3.7 3.4 185

2 12.7 12.8 5.1 4.9 195

1 14.2 14.1 6.2 5.1 205

min 7.9 mm 7.8 mm 2.0 m 2.3 m *it is not the cable length over the turn, it is the distance along the z-axis between the straight section end and the apex of the turn

Lead end


Geo

de

sic

curv

atu

rein

[m

-1]


2 m bending radius



In a single layer design there is obviously no layer jump but the cable of the polar plane has to go out

of the magnet. The cable has to go either below or above the magnet end. Actually if the radius of

the aperture was bigger than 23 mm the cable could seat between the magnet end and the 20-mm

radius aperture. The cable would not modify the outer mechanical structure but would be located in

a slightly stronger magnetic field. In our case the cable is going on top of the head (see figure 20) and

the mechanical structure and support have to be adapted in this special region as in the Q4

quadrupole for the High Luminosity LHC upgrade [SEG1]. So far, see figures 20-23, starting from the

polar plane, the cable is double bent inwards (easyway S-shape), then twisted by 61° to be parallel to

the coil outer surface and then double bent again (easyway S-shape) to go over the head. The two S-

shape softway bendings have radii of 22 mm and angles of respectively 45° and 25° (Figure 20). In-

between the two softway bends a twist of 61° over a distance of 80 mm around the central line of

the cable has to be validated through winding tests (80 mm might not be sufficient). The two S-shape

softway bends lead to a cable centered on top of the head. At the end of the first S-shape (22 mm,

45°) one of the corner of the cable is at a radius of 36.9 mm from the magnet center. As the outer

radius of the winding or inner radius of the mechanical support will be at a radius of 22 mm + 12.4

mm = 34.4 mm which is the sum of the aperture radius and insulated cable width, the mechanical

structure will have to be changed at this point of the magnet due to the 2.5 mm penetration of the

cable into the mechanical support (36.9 – 34.4 = 2.5). This cable excursion into the mechanical part

can be reduced to 500 µm with a slight change of the path: a first S-shape (22 mm, 30°), then a 80-

mm long twist of 77° and a second S-shape (22 mm, 35°). This option will lead to a cable shift from

the magnet center as shown in figure 21. Both of the options are still under consideration.

The outwards path will probably be the weakest point of the magnet where the cable is likely to

experience high perpendicular magnetic field, it has not been checked yet. It can be worth noticing

that the cable could be maintained to a small angle (not exactly perpendicular to the field) above the

head in order to improve its carrying capability but at the expense of the thickness of the mechanical

structure in the head.

Figure 20. Cable path outwards the magnet.

45°r = 22 mm

25°

r = 22 mm

twist around central line

61° over 80 mm



Figure 21. Another option for the cable path outwards the magnet:

1st S-shape (22 mm, 30°), twist 77° instead of 61° over 80 mm, 2nd S-shape (22 mm, 35°).

Figure 22 provides an overview of the longitudinal dimensions of the magnet. The straight section is

about 225 mm in length and each of the ends is about 200 mm in length. The total magnet length is

700 mm. Figure 23 shows the whole magnet windings.

Figure 22. Longitudinal dimensions of the different parts of the magnet in [mm].

Figure 23. Whole magnet design.

65 190 3450160195350

straight section: 225 30 80 20



b) End spacers-mandrel

A first set of end spacers has been 3D printed after using the Roxie to Catia routine. Four wedges of

200 mm in length were also 3D printed. Only the first 5 turns of the magnet have been generated so

as to practice winding of Roebel cable and design the proper tooling. The mandrel, the central post

as well as another set of wedges have been machined (see figure 24). Figure 25 shows the 3D set of

return endspacers under catia software.

Figure 24. Top: 3D printed end spacers and central post on aluminium mandrel. Bottom: Catia drawing of the cable and end spacers over

the first turns of the windings [courtesy from Arnaud Acker].

Figure 25. 3D return end spacers [courtesy from William Gamache].

B. Double-shell configuration in D1

As shown in the first part of the report, it was not possible to fit a double-layer magnet in Fresca2,

therefore an investigation of what could be done using the High Luminosity LHC upgrade D1 dipole

[XU1] as outsert magnet was carried out. The D1 dipole was selected because of its large aperture of

150 mm in diameter (instead of 100 mm in Fresca2) and because it is likely to be built before the

Fresca2 magnet and available at CERN. The double-shell insert magnet is different from the double-

layer dipole described in the beginning of the report because it is made of 12-mm wide Roebel cable

(instead of a 10-mm wide Roebel cable). The main drawback of the Nb-Ti based D1 magnet is the

weak background magnetic field it creates: only 5.5-6 T.

Before going into detail in the study, it must be stated that the double-shell magnet presented

hereafter has not been designed from scratch. Since the objective was to get a rough overview of the

performance that could be reached with a double-shell magnet inserted into D1, it was decided to

use the single-layer design for the inner conductor distribution of the double-shell magnet. This leads



to a magnet design not fully optimized in terms of number of conductors and, so, in terms of

maximum field created at the center of the magnet but good enough to draw a conclusion about the

validity of such an option.

The study about this configuration is thus briefly described in this section since a new study starting

from scratch would be necessary in the event this option is selected later on.

1) 2D magnetic design

a) Stand-alone operating mode

The double-shell design is shown in figure 26 for a central field of 5 T. The magnet is surrounded by

an iron yoke with a 75-mm inner radius and a thickness of 88 mm. A current of 6 340 A is flowing

through the cable. Geometrical field harmonics are below the unit except b7 = 19 units and b9 = 2

units.

Figure 26. Double-shell magnet design based on a 12-mm wide Roebel cable of 1.2 mm in thickness.

Figure 27 shows different operating modes with the loadline of the magnet and the critical surface of

the tapes based on the same modification of the Fleiter’s fit [FLE1] as previously described in section

III.A.1. The loadline of the single-layer design in stand-alone mode is reported in grey in Figure 27 for

comparison. It can be seen that adding a layer roughly allows for doubling the central field. Operating

the double-shell configuration in stand-alone mode with 11 680 A, that is to say a 944 A/mm² tape

engineering current density, would generate 8.9 T central field with 11 % margin instead of 5 T with

30% margin for the single-layer design. If the double-shell magnet is powered with 30% margin it

could be fed with 9 220 A, that is to say a 745 A/mm² tape engineering current density, and would

create 7.2 T central field. In order to reach 5 T central field only 6 340 A are needed which

correspond to 512 A/mm² tape engineering current density and 52% margin.



Figure 27. Double-shell magnet loadline (Magnet peak field vs. Tape engineering current density) and critical surface at 4.2 K perpendicular

field of the Fleiter’s fit applied to Bruker data. Three different operating modes are depicted respectively at 11 680 A, 9 220 A and 6 430 A.

In grey is given the single layer load-line in stand-alone configuration for comparison.

b) Insert operating mode

The Double-Shell magnet (DS) can be inserted into D1 to increase its central field (Figure 28). The D1

Roxie model used in our study has been courteously provided by Michinaka Sugano and Tatsushi

Nakamoto. According to our model a current of 11 820 A injected into D1 creates a central field of

5.5 T with a peak field in the D1 conductor of 6.35 T. Based on these values the double-shell insert

can be operated at a 730 A/mm² tape engineering current density that is to say a 9 030 A current

with a 20% margin as shown in figure 29. It turned out that contrary to Fresca2 where the peak field

is decreased in the conductor blocks when the insert is turned on the D1 peak field is increased when

the DS magnet is energized raising from 6.35 T to 7.42 T due to the position of the upper block of D1

very high in the aperture. Therefore, to go back to the same magnitude of the peak field the current

in D1 is lowered. The current in D1 is set at 9 300 A to recover the 6.35 T peak field in D1 conductors.

(Another option would have been to simultaneously reduce the currents in both of the magnets).

The lowering of the current only in D1 means that D1 is now generating only 4.55 T and the insert is

operating with a slightly bigger margin of 23% (see Figure 29) adding a central field of almost 6 T.

Indeed, the whole system can now provide 10.5 T central field. All the geometrical harmonics are less

than 1 unit except b7 = 13 units and b9 = 1.2 unit.

Tap

e e

ngi

nee

rin

g cr

itic

alcu

rren

td

en

sity

J eng

[A/m

m²]

Bpeak [T]


944 A/mm²

~11% margin

1064 A/mm²

~30% margin

745 A/mm²

~52% margin

512 A/mm²



Figure 28. Double-Shell magnet design (DS) inserted in D1 (D1 current = 9 300 A and DS current = 9 030 A)

Figure 29. Double-shell magnet loadlines depending on the operation mode of D1.


The model has already been described in section II.A.2. Since the DS magnet can reach 7.2 T in stand-

alone mode the mechanical analysis is firstly done at this level of Lorentz forces with a 9 220 A

current. Then a second analysis is shown when the magnet is energized at 9 030 A inside D1

operating at 9 300 A. The external tube of the mechanical structure is 22-mm-thick (see Figure 30). In

Tap

e en

gin

eeri

ng

crit

ical

curr

ent

den

sity

[A/m

m²]

J en

g

Bpeak[T]


730 A/mm²912 A/mm²

20% margin

23% margin

950 A/mm²

4.55 T(9300 A in D1)

5.5 T(11 820 A) in D1



the insert mode which is mechanically the most demanding the azimuthal peak stress in the winding

is 200 MPa, the radial peak stress is 100 MPa and the Von Mises stress in the external tube is

350 MPa. The gap between the polar plane and the coil block is of the order of 150 µm. The results

are reported in Figures 31 and 32 for the stand-alone configuration and Figures 33 and 34 for the

insert configuration.

Figure 30. Mechanical structure dimensions of DS.

Figure 31. Mechanical stress distribution in the windings of the double-shell cosine-theta magnet in [MPa] in stand-alone 7.2 T central field.


22 mm 25 mm 22 mm5 mm

7.2 T 7.2 T



Figure 32. Left: Coil deflection in [mm] in stand-alone mode with a 7.2 T central field. Right: Von Mises stress with a peak value of 89 MPa

in the external tube of the mechanical structure.

Figure 33. Mechanical stress distribution in the windings of the double-shell cosine-theta magnet in [MPa] in D1 10.52 T central field. Left:

Azimuthal stress with a peak value of 200 MPa. Right: Radial stress with a peak value of 110 MPa.

7.2 T7.2 T

10.52 T10.52 T



Figure 34. Left: Coil deflection in [mm] in stand-alone mode with a 10.52 T central field. Right: Von Mises stress with a peak value of

313 MPa in the external tube of the mechanical structure.

3) 3D coil ends and layer jump

The inner layer cross-section of the double-shell configuration is similar to the single-layer design and

the coil ends are obviously the same, too. Here are provided the data related to the coil ends of the

outer shell (Figure 35) as well as the cable path from one shell to the other, namely the layer jump

(Figure 36). For the dipole ends since the outer shell is at a radius of 35 mm all of the turns have an

easyway bending radius bigger than 10 mm and a hardway bending radius bigger than 2 m. As for the

layer jump in the head of the magnet, a solution was found (Figure 36 Left) where softway bends of

15-mm in radius are used coupled with a twist of 58° over 100 mm. A second option (Figure 36 Right)

using the differential geometry of Roxie (usually used to design magnet ends) did not show good

results in terms of hardway and easy bends so far, but may request a deeper investigation and Roxie

development.

Figure 35. Coil ends design of the outer layer of the double-shell magnet.

Figure 36. Left: Layer jump with no hardway bend: S-bending and twist only. Right: Configuration with a combination of twist, hardway and

easyway bendings.

10.52 T 10.52 T



IV. CONCLUSION

This report intends to provide a complete overview of the study of cos-theta magnet configurations

done in the framework of the EuCARD2 WP10 Task3 project. The main objective of the project is the

realization of a magnet producing a 5 T central field and made of HTS conductor. The current

conductor baseline is Roebel cable made of REBCO. Multiple configurations with different layouts –

single or double layer designs - have been investigated. The magnet will eventually be tested in a

background field created by a bigger magnet whether Fresca2 or D1 both currently under

construction. This leads to constraints on the magnet outer dimensions and drives the whole magnet

design. Actually, due to such constraints the previous analysis demonstrates that a single-layer coil is

the only option if the magnet has to fit inside the Fresca2 test station while being mechanically self-

supported. A double-shell configuration could be designed to fit into D1 but unfortunately due to the

Nb-Ti based cable of D1 only 10.5 T could be produce by the whole system “cos-theta insert + D1”. To

date, the one option is the single-layer design that can reach the 5 T central field target in stand-

alone mode if the REBCO-Roebel cable is built from tape with the performance of the EuCARD2 tape

manufacturer partner, namely Bruker. The magnet inserted in Fresca2 operating at 13 T should

provide an additional 2.5 T magnetic field.

Several points need to be clarified such as the minimal bending radius of Roebel cable and its

windability, the impregnation of Roebel cables and their delamination, their behavior under

transverse pressure. The quench detection in Roebel cable, the magnetization of Roebel cable in cos-

theta configuration and its impact on the field quality are some of the aspects that needs likewise to

be better understood.



V. REFERENCES

[AUC1] Private discussion about coil end design, Bernhard Auchmann CERN.

(http://eucard2.web.cern.ch/science/milestones) [BOT1] L. Bottura, C. Senatore, “Cable concept design report. Milestone: MS63”, EuCARD2-Mil-MS63-Draft, May 2014.

(http://eucard2.web.cern.ch/science/milestones)

[BRU1] Bruker website: http://www.bruker.com/products/superconductors-and-metal-composite-materials/superconductors/ybco-2g-hts-

superconductors/learn-more.html [CAR1] C. Senatore et al. “Tape performance summary from worldwide producers”, 2nd Workshop on Accelerator Magnets in HTS,

Kyoto, 12-14 November 2014.

[CAS1] P. Verpaux, T. Charras, and A. Millard, “Castem 2000 une approche moderne du calcul des structures”, Calcul des structures et intelligence artificielle, pp. 261-271, 1988.

[DUR1] M. Durante, “Essais de compression sur empilements droits de conducteurs isolés et autres échantillons”, internal note CEA : 5-

2650N—2300 004 00, (oct. 2000) [DUR2] M. Durante, “Mesure du rétreint thermique d’empilements droits de conducteurs isolés et autres échantillons”, internal note CEA :

5-2650N—2300 005 00, (oct. 2000)

[FCC1] FCC website: http://cern.ch/fcc

[FER1] P. Ferracin et al. “Development of the EuCARD Nb3Sn dipole magnet FRESCA2”, IEEE Trans. on Applied Superconductivity,

vol. 23, n°3, pp4002005, (2013). [FLE1] J. Fleiter and A. Ballarino, “Parameterization of critical surface of REBCO conductors from Fujikura”,CERN internal note,

EDMS: 1426239, (September 2014).

[GOL1] W. Goldacker et al. “Roebel assembled coated conductors (RACC): Preparation, Properties and Progress”, IEEE Trans. on Applied Superconductivity, vol. 17, n°2, pp3398-3401, (2007).

[IZQ1] S. Izquierdo-Bermudez et al. “Coil end optimization of the Nb3Sn quadrupole for the high luminosity LHC”, IEEE Trans. on

Applied Superconductivity, vol. 25, n°3, 4001504, (2015). [IZQ2] S. Izquierdo-Bermudez “QXF. Mechanical endspacer design”, private communication (June 2014).

[KAR1] Private communication, WP10 meeting at Cern, January 8th 2015: Measurements at small bending radius of Roebel cables are

foreseen in a short time.

[KAR2] A. Kario et al. “Mechanical properties of Roebel coated conductor cable”, 1st Workshop on Accelerator Magnets in HTS,

Hambourg, 21-23 May 2014.

[KIR1] G. Kirby et al., “Accelerator quality HTS dipole magnet demonstrator designs for the EuCARD-2, 5T 40 mm clear aperture magnet”, IEEE Transactions on Applied Superconductivity, vol. 25, n°3, 4000805, (2015).

[LOR1] C. Lorin et al., “Cos-theta design of dipole inserts made of REBCO-Roebel of BSCCO-Rutherford cables”, IEEE Transactions on

Applied Superconductivity, vol. 25, n°3, 4000305, (2015) [MUN1] J.E. Munoz Garcia et al., “Assembly, loading, and cool-down of the Fresca2 support structure”, IEEE Transactions on Applied

Superconductivity, vol. 24, n°3, 4002905, (2014)

[NUG1] J. van Nugteren et al., “Study of a 5 T research dipole insert magnet using an anisotropic REBCO Roebel cable”, IEEE

Transactions on Applied Superconductivity, vol. 25, n°3, 4000705, (2015)

[OTT1] S. Otten, “Transverse pressure dependence of the critical current in epoxy impregnated REBCO Roebe cables”, Master thesis,

University of Twente, (October 10, 2014)

[SEG1] M. Segreti, J.M. Rifflet, E. Todesco, “A Nb-Ti 90 mm double-aperture quadrupole for the high luminosity LHC upgrade”, IEEE

Transactions on Applied Superconductivity, vol. 25, n°3, 4001905, (2015).

[TOD1] E. Todesco, F. Zimmermann, “The High-Energy Large Hadron Collider”, eds. CERN-2011-003, ISBN 978-92-9083-360-4, EuCARD-AccNet-EuroLumi Workshop, 14-16 Oct 2010, Villa Bighi, Malta.

[RAN1] T. C. Randle, “A few mathematical notes on constant perimeter layers in coil windings”, Rutherford Laboratory note, RL-74-

165,(1974). [ROS1] L. Rossi et al., “The EuCARD-2 Future Magnets project: the European collaboration for accelerator quality HTS magnets”, IEEE

Transactions on Applied Superconductivity, vol. 25, n°3, 4001007, (2015).

[ROS2] L. Rossi and E. Todesco, “Electromagnetic design of superconducting dipoles based on sector coils”, Physical review special topics – Accelerators and beams, 10, 112401, (2007).

[ROS3] L. Rossi, “Report from WAMHTS-1 in Hamburg @ EuCARD2 CM”, in WAMHTS-2, Kyoto, 12-14 Nov. 2014

(https://indico.cern.ch/event/319762) [SUP1] Superpower website: http://www.superpower-inc.com/content/wire-specification

[USO1] A. Usoshin, “Development and processing of high-field HTS coated conductors for EUCARD2 project”,WP10 meeting at Cern,

January 8th 2015 [XU1] Q. Xu et al., “Design optimization of the new D1 dipole for HL-LHC upgrade”, IEEE Transactions on Applied Superconductivity,

vol. 24, n°3, 4000104, (2014).

http://eucard2.web.cern.ch/science/milestones

http://eucard2.web.cern.ch/science/milestones

http://www.bruker.com/products/superconductors-and-metal-composite-materials/superconductors/ybco-2g-hts-superconductors/learn-more.html

http://www.bruker.com/products/superconductors-and-metal-composite-materials/superconductors/ybco-2g-hts-superconductors/learn-more.html

http://cern.ch/fcc

https://indico.cern.ch/event/319762

http://www.superpower-inc.com/content/wire-specification



VI. APPENDIXES

Appendix 1 Bruker data: Slide from Alexander Usoskin presentation during the WP10 meeting at Cern

in January 2015 [USO1]. Jc is the critical engineering current density of the tape.



Appendix 2 Transverse pressure: Figure from Simon Otten [OTT1] showing the critical current of a

impregnated Roebel cable versus the applied transverse pressure. No degradation occurs below 253

MPa. The Robel cable is made of 10 strands (SuperPower SCS12050-AP tapes). The width is 12 mm,

the transposition pitch is 126 mm and the total thickness of the cable is between 0.5 mm to 0.7 mm.

0

500

1000

1500

2000

2500

0 50 100 150 200 250 300 350

Cri

tica

l cu

rre

nt

[A]

Transverse stress [MPa]

T = 4.2 KB = 10.5 T



Appendix 3 Magnet dimensions: Magnet and cable dimensions in Roxie software

Magnet file

BLOCK 4 1 1 5 22 0.1978 2.681 9900 EUCFAKE9 2 10 0 0

2 1 4 22 21.5 33.1429 9900 EUCFAKE9 2 10 0 0

3 1 3 22 43.5 49.9241 9900 EUCFAKE9 2 10 0 0 4 1 2 22 56 61 9900 EUCFAKE9 2 10 0 0

no type nco radius phi alpha current condname n1 n2 imag turn

Cable file

INSUL 1

1 EUC_FAKE1 0.1 0.1 'EuCARD2 Clement Fake ' No Name Radial Azimut Comment

REMFIT 1

1 FIT1 1 3E+09 9.2 0.57 0.9 2.32 27.04 14.5 0 0 0 0 'MB FILAMENT

TYPE '

No Name Type C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 Comment

FILAMENT 1

1 NBTII 7 0 FIT1 FIT1 'NBTI INNER CABLES ' No Name fildiao fildiai Jc-Fit fit-| Comment

STRAND 1 1 STR01 1.065 1.6 70 1.9 10 1433.3 500.34 'MB INNER '

No Name diam. cu/sc RRR Tref Bref Jc@BrTr dJc/dB Comment

CABLE 1

1 EU_ROE_6 12 1.2 1.2 15 226 0 'Monocouche '

No Name height width_i width_o ns transp. degrd Comment

CONDUCTOR 1 1 EUCFAKE9 1 EU_ROE_6 STR01 NBTII EUC_FAKE1 NONE NONE 4.2 'Fake cable EuCARD2 Clement9 '

No Name Type CableGeom. Strand Filament Insul Trans QuenchMat. T_o Comment

cosϑ magnet design option - cern · 2015. 5. 5. · eucard-2 enhanced european coordination for...

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