cern accelerator school superconductivity for accelerators case study 3
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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 facility Introduction - PowerPoint PPT PresentationTRANSCRIPT
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
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 solutionMaximum field and coil size
The max. field that one could reach with 60 mm wide coil is about 16.5 T
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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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
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 solutionCable and strand size
We assume a strand diameter of 0.80 mm
We assume a pitch angle of 17
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Case study 3 solutionCable and strand size
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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
Case study 3 solutionCable and strand size
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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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 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 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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Case study 3 solutionMargins
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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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Case study 3 solutionMargins
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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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Case study 3 solutionMargins Nb3Sn
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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Case study 3 solutionMargins Nb3Sn
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
jo_op = jsc_op * k = 244 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
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 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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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,
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
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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
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
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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
jo_op = jsc_op * k = 305 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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