CERN Accelerator School Superconductivity for Accelerators Case study 4

CERN Accelerator School

Superconductivity for Accelerators

Case study 4

Paolo Ferracin([email protected])

European Organization for Nuclear Research (CERN)

Case study 4

11 T Nb3Sn dipole for the LHC collimation upgrade

IntroductionThe second phase of the LHC collimation upgrade will enable proton and ion beam operation at nominal and ultimate intensities.To improve the collimation efficiency by a factor 15–90, additional collimators are foreseen in the room temperature insertions and in the dispersion suppression (DS) regions around points 2, 3, and 7.To provide longitudinal space of about 3.5 m for additional collimators, a solution based on the substitution of a pair of 5.5-m-long 11 T dipoles for several 14.3-m-long 8.33 T LHC main dipoles (MB) is being considered.

GoalDesign a Nb3Sn superconducting dipole with an 60 mm aperture and a operational field (80% of Iss) at 1.9 K of 11 T.

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

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11 T Nb3Sn dipole for the LHC collimation upgradeQuestions

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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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 4 solutionMaximum field and coil size

With a 30 mm wide coil one could reach a bore field of 13-14 T.


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Case study 4 solutionMaximum gradient and coil size

With a w/r of 30/30 = 1 λ of 1.04


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Case study 4 solutionMaximum gradient and coil size


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Case study 4 solutionCable and strand size

We assume a strand diameter of 0.70 mm

We assume a pitch angle of 16


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We assume Thick. Comp. = -10.5 %Width. Comp. = -4 %40 strandsIns. Thick. = 150 μm

We obtainCable width: 14.5 mmCable mid-thick.: 1.25 mm


SummaryStrand diameter = 0.70 mmCu to SC ratio = 1.1Pitch angle = 16N strands = 40Cable width: 14.5 mmCable mid-thickness: 1.25 mmInsulation thickness = 150 μmArea insulated conductor = 22.9 mm2

We obtain a filling factor k = area superconductor/area insulated cable = 0.32


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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 4 solutionMargins

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

jo = jsc * k = 320 A/mm2

Bbore = 6.7 T

Bpeak = Bbore * λ = 6.7 * 1.04 = 7.0 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 4 solutionMargins Nb3Sn

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

jsc_ss = 2120 mm2

jo_ss = jsc_ss * k = 678 mm2

Iss = jo_ss * Ains_cable= 15500 ABbore_ss = 14.1 T

Bpeak_ss = 14.7 T


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The operational conditions (80% of Iss)

jsc_op = 1696 mm2

jo_op = jsc_op * k = 543 mm2

Iop = jo_op * Ains_cable= 12430 ABbore_op = 11.2 T

Bpeak_op = 11.8 T


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In the operational conditions (80% of Iss)

4.6 K of T margin(4100-1700) A/mm2 of jsc

margin(15.3-11.8) T of field margin


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Case study 4 solutionMargins Nb-Ti

“Short-sample” conditionsjsc_ss = 1450 mm2

jo_ss = jsc_ss * k = 464 mm2

Iss = jo_ss * Ains_cable= 10630 ABbore_ss = 9.6 TBpeak_ss = 10.0 T

The operational conditions (80% of Iss)

jsc_op = 1160 mm2


Iop = jo_op * Ains_cable= 8500 ABbore_op = 7.7 TBpeak_op = 8.0 T2.1 K of T margin(2500-1160) A/mm2 of jsc margin(10.8-8.0) T of field margin


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Case study 4 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 4 23

Case study 4 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 4 solutionE.m. forces and stresses

In the operational conditions (Bbore_op = 11.2 T)Fx (quadrant) = +2.54 MN/mFy (quadrant) = -2.26 MN/m

The accumulates stress on the coil mid-plane is


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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


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

2013Case study 4 26

Case study 4 solutionDimension of the yoke

The iron yoke thickness can be estimated with

Therefore, beingBbore = 12.7 T (at 90% of Iss )

r = 30 mm and Bsat = 2 T

we obtain tiron = ~190 mm


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satironBtrB ~

Case study 4 solutionDimension of the support structure

We assume a 25 mm thick collarImages not in scale


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Case study 4 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 = +6.4 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 ~ 16 mm

Case study 4 solutionMagnet cross-section

Coil inner radius: 30 mm

Coil outer radius: 60 mm

The operational conditions (80% of Iss) jsc_op = 1696 mm2


Iop = jo_op * Ains_cable= 12430 ABbore_op = 11.2 TBpeak_op = 11.8 T

Collar thickness: 25 mm

Yoke thickness: 190 mm

Shell thickness: 16 mm

OD: 582 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 4

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