CERN Accelerator School Superconductivity for Accelerators Case study 1 Paolo Ferracin ( [email protected] ) European Organization for Nuclear Research

CERN Accelerator School

Superconductivity for Accelerators

Case study 1

Paolo Ferracin([email protected])

European Organization for Nuclear Research (CERN)

Case study 1

Low-beta Nb3Sn quadrupoles for the HL-LHCIntroduction

LARGE HADRON COLLIDER (LHC) it will run at 6.5-7 TeV, providing 300 fb-1 of integrated luminosity within the end of the decade. After 2020, CERN is planning to have an upgrade of the LHC to obtain ten times more integrated luminosity, i.e., 3000 fb-1 . Part of the upgrade relies on reducing the beam sizes in the Interaction Points (IPs), by increasing the aperture of the present triplets. Currently, the LHC interaction regions feature NbTi quadrupole magnets with a 70 mm aperture and a gradient of 200 T/m.

GoalDesign a Nb3Sn superconducting quadrupole with an 150 mm aperture for the upgrade of the LHC interaction region operating at 1.9 K

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

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Low-beta Nb3Sn quadrupoles for the HL-LHCQuestions

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 , Gss , Bpeak_ss

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

2. Compute T, jsc , Bpeak marginsCompare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technologyDefine a possible coil lay-out to minimize field errorsDetermine e.m forces Fx and Fy and the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss ) Evaluate dimension iron yoke, collars and shrinking cylinder, assuming that the support structure is designed to reach 90% of Iss


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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 1 solutionMaximum gradient and coil size

The max. gradient that one could reach is almost 200 T/m…but with a w/r = 2

150 mm thick coil!


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Large aperture need smaller ratio w/rFor r=30-100 mm, no need of having w>r


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ISR MQ TEV MQ HERA MQSSC MQ LEP I MQC LEP II MQCRHIC MQ RHIC MQY LHC MQLHC MQM LHC MQY LHC MQXBLHC MQXA

current grading


We assume a value of w/r = 0.537 mm thick coil

We should get a maximum gradient around 170 T/m


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Case study 1 solutionCable and strand size

We assume a strand diameter of 0.85 mm

We assume a pitch angle of 18


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We assume Thick. Comp. = -12 %Width. Comp. = -3 %40 strandsIns. Thick. = 150 μm

We obtainCable width: 18 mmCable mid-thick.: 1.5 mm


SummaryStrand diameter = 0.85 mmCu to SC ratio = 1.2Pitch angle = 18N strands = 40Cable width: 18 mmCable mid-thickness: 1.5 mmInsulation thickness = 150 μmArea insulated conductor = 32.7 mm2

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


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Case study 1 solutionMargins

Let’s work now on the load-lineThe gradient is given bySo, for a Jsc= 1600 A/mm2

jo = jsc * k = 512 A/mm2

G = 142 T/mBpeak = G * r * λ = 142 * 75e-3 * 1.15 = 12.2 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 1 solutionMargins Nb3Sn

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

jsc_ss = 1970 mm2

jo_ss = jsc_ss * k = 630 mm2

Iss = jo_ss * Ains_cable= 20600 AGss = 175 T/m

Bpeak_ss = 15 T


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The operational conditions (80% of Iss)

jsc_op = 1580 mm2

jo_op = jsc_op * k = 505 mm2

Iop = 16480 A

Gop = 140 T/m

Bpeak_op = 12.1 T


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In the operational conditions (80% of Iss)

4.6 K of T margin(4000-1580) A/mm2 of jsc

margin(15.8-12.1) T of field margin


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Case study 1 solutionMargins Nb-Ti

“Short-sample” conditionsjsc_ss = 1350 mm2

jo_ss = jsc_ss * k = 430 mm2

Iss = jo_ss * Ains_cable= 14060 AGss = 119 T/mBpeak_ss = 10.3 T

The operational conditions (80% of Iss)

jsc_op = 1080mm2


Iop = 11250 AGop = 95 T/mBpeak_op = 8.2 T2.1 K of T margin(2370-1080) A/mm2 of jsc margin(11-8.2) T of field margin


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Case study 1 solutionCoil layout

One wedge coil sets to zero b6 and b10 in quadrupoles~[0°-24°, 30°-36°] ~[0°-18°, 22°-32°]

Some examples


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2. Compute T, jsc , Bpeak marginsCompare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technologyDefine a possible coil lay-out to minimize field errorsDetermine e.m forces Fx and Fy and the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss ) 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 1 23

Case study 1 solutionE.m. forces and stresses

For a quadrupole sector coil, with an inner radius a1, an outer radius a2 and an overall current density jo , each block (octant) 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 1 solutionE.m. forces and stresses

In the operational conditions (140 T/m)Fx (octant) = +1.90 MN/mFy (octant) = -4.02 MN/m

The accumulates stress on the coil mid-plane is


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2. Compute T, jsc , Bpeak marginsCompare “short sample”, “operational” conditions and margins if the same design uses Nb-Ti superconducting technologyDefine a possible coil lay-out to minimize field errorsDetermine e.m forces Fx and Fy and the accumulated stress on the coil mid-plane in the operational conditions (80% of Iss ) 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 1 26

Case study 1 solutionDimension of the yoke

The iron yoke thickness can be estimated with

Therefore, beingG = 156 T/m (at 90% of Iss )

r = 75 mm and Bsat = 2 T

we obtain tiron = ~220 mm


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satiron BtGr

~2

2

Case study 1 solutionDimension of the support structure

We assume a 25 mm thick collarImages not in scale


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Case study 1 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_quadrant * 2 * sqrt(2) = +6.8 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 ~ 17 mm

Case study 1 solutionMagnet cross-section

Coil inner radius: 75 mm

Coil outer radius: 112 mm

The operational conditions (80% of Iss) jsc_op = 1580 mm2


Iop = 16480 AGop = 140 T/mBpeak_op = 12.1 T

Collar thickness: 25 mm

Yoke thickness: 220 mm

Shell thickness: 17 mm

OD: 748 mmSuperconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013

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Comparison


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Documents

CERN Accelerator School Superconductivity for Accelerators Case study 1 Paolo Ferracin ( [email protected] ) European Organization for Nuclear Research