CERN Accelerator School Superconductivity for Accelerators Case study 3

CERN Accelerator School

Superconductivity for Accelerators

Case study 3

Paolo Ferracin([email protected])

European Organization for Nuclear Research (CERN)

Case study 3

High field - large aperture magnet for a cable test facilityIntroduction

High field (Bbore>10 T) magnets are needed to upgrade existing accelerators in Europe and to prepare for new projects on a longer timescale.Nb3Sn is today the right candidate to meet those objectives, because of its superconducting properties and its industrial availability.On the very long term, further upgrades could require dipole magnets with a field of around 20 Tesla (T): a possible solution is to combine an outer Nb3Sn coil with an inner coil of High Critical Temperature (HTS) conductor, both contributing to the field.In addition, an high-field dipole magnet with a large aperture could be used to upgrade the Fresca test facility at CERN, in the aim of meeting the strong need to qualify conductor at higher fields.

GoalDesign a superconducting dipole with an 100 mm aperture and capable of reaching 15 T at 1.9 K (~90% of Iss).

Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013

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Case study 3

High field - large aperture magnet for a cable test facilityQuestions

1. Determine maximum gradient and coil size (using sector coil scaling laws)

2. Define strands and cable parameters1. Strand diameter and number of strands2. Cu to SC ratio and pitch angle3. Cable width, cable mid-thickness and insulation thickness4. Filling factor κ

3. Determine load-line (no iron) and “short sample” conditions 1. Compute jsc_ss , jo_ss , Iss , Bss , Bpeak_ss

4. Determine “operational” conditions (80% of Iss ) and margins1. Compute jsc_op, jo_op , Iop , Bop , Bpeak_op

2. Compute T, jsc , Bpeak margins5. Compare “short sample”, “operational” conditions and margins if

the same design uses Nb-Ti superconducting technology6. Define a possible coil lay-out to minimize field errors7. Determine e.m forces Fx and Fy and the accumulated stress on the

coil mid-plane in the operational conditions (80% of Iss ) 8. Evaluate dimension iron yoke, collars and shrinking cylinder,

assuming that the support structure is designed to reach 90% of Iss Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013

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Case study 3

Additional questionsEvaluate, compare, discuss, take a stand (… and justify it …) regarding the following issues

High temperature superconductor: YBCO vs. Bi2212

Superconducting coil design: block vs. cos

Support structures: collar-based vs. shell-based

Assembly procedure: high pre-stress vs. low pre-stress


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Case study 3 solutionMaximum field and coil size

The max. field that one could reach with 60 mm wide coil is about 16.5 T


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Case study 3 solutionMaximum gradient and coil size

With a w/r of 60/50 = 1.2 λ of 1.04


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Case study 3 solutionMaximum gradient and coil size


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Case study 3 solutionCable and strand size

We assume a strand diameter of 0.80 mm

We assume a pitch angle of 17


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We assume Thick. Comp. = -12 %Width. Comp. = -1.5 %35 strandsIns. Thick. = 150 μm

We obtainCable width: 15 mmCable mid-thick.: 1.4 mm


SummaryStrand diameter = 0.80 mmCu to SC ratio = 1.1Pitch angle = 17N strands = 35Cable width: 15 mmCable mid-thickness: 1.4 mmInsulation thickness = 150 μmArea insulated conductor = 26.0 mm2

We obtain a filling factor k = area superconductor/area insulated cable = 0.31


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2. Compute T, jsc , Bpeak margins5. Compare “short sample”, “operational” conditions and

margins if the same design uses Nb-Ti superconducting technology

6. Define a possible coil lay-out to minimize field errors7. Determine e.m forces Fx and Fy and the accumulated stress on the coil

mid-plane in the operational conditions (80% of Iss ) 8. Evaluate dimension iron yoke, collars and shrinking cylinder,


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Case study 3 solutionMargins

Let’s work now on the load-lineThe bore field is given bySo, for a Jsc= 1000 A/mm2

jo = jsc * k = 465 A/mm2

Bbore = 12.8 T

Bpeak = Bbore * λ = 12.8 * 1.04 = 13.3 T


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Nb3Sn parameterization

Temperature, field, and strain dependence of Jc is given by Summers’ formula

where Nb3Sn is 900 for = -0.003, TCmo is 18 K, BCmo is 24 T, and

CNb3Sn,0 is a fitting parameter equal to 60800 AT1/2mm-2 for a Jc=3000 A/mm2 at 4.2 K and 12 T.

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Nb-Ti parameterizationTemperature and field dependence of BC2 and TC are provided by Lubell’s formulae:

where BC20 is the upper critical flux density at zero temperature (~14.5 T), and TC0 is critical temperature at zero field (~9.2 K)Temperature and field dependence of Jc is given by Bottura’s formula

where JC,Ref is critical current density at 4.2 K and 5 T (~3000 A/mm2) and CNb-Ti (27 T), Nb-Ti (0.63), Nb-Ti (1.0), and Nb-Ti (2.3) are fitting parameters.

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Case study 3 solutionMargins Nb3Sn

Let’s assume = 0.000The load-line intercept the critical (“short-sample” conditions) curve at

jsc_ss = 1230 mm2

jo_ss = jsc_ss * k = 381 mm2

Iss = jo_ss * Ains_cable= 9900 A

Bbore_ss = 15.8 T

Bpeak_ss = 16.4 T


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The operational conditions (80% of Iss)

jsc_op = 984 mm2

jo_op = jsc_op * k = 305 mm2

Iop = jo_op * Ains_cable= 7930 A

Bbore_op = 12.7 T

Bpeak_op = 13.2 T


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In the operational conditions (80% of Iss)

4.6 K of T margin(3000-984) A/mm2 of jsc

margin(17.2-13.2) T of field margin


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Case study 3 solutionMargins Nb-Ti

“Short-sample” conditionsjsc_ss = 850 mm2

jo_ss = jsc_ss * k = 264 mm2

Iss = jo_ss * Ains_cable= 6900 A

Bbore_ss = 11.0 T

Bpeak_ss = 11.4 T

The operational conditions (80% of Iss)

jsc_op = 680 mm2


Iop = jo_op * Ains_cable= 6350 A

Bbore_op = 8.8 T

Bpeak_op = 9.1 T2.1 K of T margin(1850-680) A/mm2 of jsc

margin(11.5-9.1) T of field marginSuperconductivity for Accelerators, Erice, Italy, 25 April - 4 May,

2013Case study 3 20

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Case study 3 solutionCoil layout

One wedge coil sets to zero b3 and b5 in quadrupoles~[0°-48°, 60°-72°] ~[0°-36°, 44°-64°]

Some examples


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2. Compute T, jsc , Bpeak margins5. Compare “short sample”, “operational” conditions and margins if the

same design uses Nb-Ti superconducting technology6. Define a possible coil lay-out to minimize field errors7. Determine e.m forces Fx and Fy and the accumulated stress

on the coil mid-plane in the operational conditions (80% of Iss )

8. Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May,

2013Case study 3 23

Case study 3 solutionE.m. forces and stresses

For a dipole sector coil, with an inner radius a1, an outer radius a2 and an overall current density jo , each block (quadrant) see

Horizontal force outwards

Vertical force towards the mid-plan

In case of frictionless and “free-motion” conditions, no shear, and infinitely rigid radial support, the forces accumulated on the mid-plane produce a stress of


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Case study 3 solutionE.m. forces and stresses

In the operational conditions (Bbore_op = 12.7 T)Fx (quadrant) = +5.68 MN/mFy (quadrant) = -4.89 MN/m

The accumulates stress on the coil mid-plane is


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Case study 3






2. Compute T, jsc , Bpeak margins5. Compare “short sample”, “operational” conditions and margins if the

same design uses Nb-Ti superconducting technology6. Define a possible coil lay-out to minimize field errors7. Determine e.m forces Fx and Fy and the accumulated stress on the


assuming that the support structure is designed to reach 90% of Iss


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Case study 3 solutionDimension of the yoke

The iron yoke thickness can be estimated with

Therefore, beingBbore = 14.2 T (at 90% of Iss )

r = 50 mm and Bsat = 2 T

we obtain tiron = ~360 mm


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satironBtrB ~

Case study 3 solutionDimension of the support structure

We assume a 25 mm thick collarImages not in scale


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Case study 3 solutionDimension of the support structure


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We assume that the shell will close the yoke halves with the same force as the total horizontal e.m. force at 90% of Iss

Fx_total = Fx_octant * 2 = +14.4 MN/m

Assuming an azimuthal shell stress after cool-down of

shell = 200 MPa

The thickness of the shell istshell = Fx_total /2/1000/ shell ~ 36 mm

Case study 3 solutionMagnet cross-section

Coil inner radius: 50 mm

Coil outer radius: 110 mm

The operational conditions (80% of Iss) jsc_op = 984 mm2


Iop = jo_op * Ains_cable= 7930 ABbore_op = 12.7 TBpeak_op = 13.2 T

Collar thickness: 25 mm

Yoke thickness: 330 mm

Shell thickness: 36 mm

OD: 1 mSuperconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013

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Comparison


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CERN Accelerator School Superconductivity for Accelerators Case study 3

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