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CERN Accelerator School Superconductivity for Accelerators Case study 4. Paolo Ferracin ( [email protected] ) European Organization for Nuclear Research (CERN ). Case study 4. 11 T Nb 3 Sn dipole for the LHC collimation upgrade Introduction - PowerPoint PPT Presentation
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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
Case study 4 2
Case study 4
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
Case study 4 3
Case study 4
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 4
Case study 4
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
Case study 4 5
Case study 4 solutionMaximum field and coil size
With a 30 mm wide coil one could reach a bore field of 13-14 T.
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 6
Case study 4 solutionMaximum gradient and coil size
With a w/r of 30/30 = 1 λ of 1.04
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 7
Case study 4 solutionMaximum gradient and coil size
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 8
Case study 4
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
Case study 4 9
Case study 4 solutionCable and strand size
We assume a strand diameter of 0.70 mm
We assume a pitch angle of 16
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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Case study 4 solutionCable and strand size
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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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
Case study 4 solutionCable and strand size
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 12
Case study 4
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 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,
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 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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 14
)60sin(2 0
1 wj
B
Case study 4 solutionMargins
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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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.
22
0
2
2
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00 31 SnNbmCC TT
Case study 4 solutionMargins
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 16
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.
7.1
0202 1
CCC T
TBTB
7.1/1
200
7.1/1 1C
CC B
BTBT
NbTi
NbTiNbTi
CCC
NbTi
refC
C
T
T
TB
B
TB
B
B
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J
TBJ
7.1
022,
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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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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Case study 4 solutionMargins Nb3Sn
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 18
Case study 4 solutionMargins Nb3Sn
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 19
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
jo_op = jsc_op * k = 371 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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 20
Case study 4
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
Case study 4 21
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 22
0
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Case study 4
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,
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 24
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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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 25
Case study 4
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,
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 27
satironBtrB ~
Case study 4 solutionDimension of the support structure
We assume a 25 mm thick collarImages not in scale
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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Case study 4 solutionDimension of the support structure
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 29
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
jo_op = jsc_op * k = 543 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
Case study 4 30
Comparison
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 4 31