Post on 13-Dec-2015
CERN Accelerator School
Superconductivity for Accelerators
Case study 1
Paolo Ferracin(paolo.ferracin@cern.ch)
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
Case study 1 2
Case study 1
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 3
Case study 1
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 1 4
Case study 1
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 5
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!
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 6
Case study 1 solutionMaximum gradient and coil size
Large aperture need smaller ratio w/rFor r=30-100 mm, no need of having w>r
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 7
1.0
1.1
1.2
1.3
1.4
1.5
0.0 0.5 1.0 1.5 2.0aspect ratio w eq/r (adim)
l [a
dim
]
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
Case study 1 solutionMaximum gradient and coil size
We assume a value of w/r = 0.537 mm thick coil
We should get a maximum gradient around 170 T/m
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 8
Case study 1
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 9
Case study 1 solutionCable and strand size
We assume a strand diameter of 0.85 mm
We assume a pitch angle of 18
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 10
Case study 1 solutionCable and strand size
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 11
We assume Thick. Comp. = -12 %Width. Comp. = -3 %40 strandsIns. Thick. = 150 μm
We obtainCable width: 18 mmCable mid-thick.: 1.5 mm
Case study 1 solutionCable and strand size
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 12
Case study 1
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 13
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 14
r
wjG
o
1ln60sin2 0
Case study 1 solutionMargins
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 15
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
1,
1,, 3
CC
SnNbC T
T
TB
B
B
CTBJ
0
2
0
2
020
2 ln77.1131.011,
CCCC
C
T
T
T
T
T
T
B
TB
2/17.1
0, 3331 SnNbSnNbSnNb CC
7.1
2020 31 SnNbmCC BB
3/17.1
00 31 SnNbmCC TT
Case study 1 solutionMargins
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 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
C
J
TBJ
7.1
022,
1)(
1)(
,
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 17
Case study 1 solutionMargins Nb3Sn
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 18
Case study 1 solutionMargins Nb3Sn
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 19
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
jo_op = jsc_op * k = 344 mm2
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 20
Case study 1
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 21
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 22
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
50
0 50 100 150x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
Case study 1
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 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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 24
3
12
1
2
41
42
200
3
1ln
3612
72
1
12
32a
a
a
a
aaJFx
3
131
2
1
2
413
2
200 2
2
3
9
1ln
6
32
12
1
36
325
2
32aa
a
a
a
aa
JFy
3
41
42
200
6/
0
_ 4ln
8
32
r
ar
r
arr
Jrdfplanemid
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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 25
Case study 1
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 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
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 27
satiron BtGr
~2
2
Case study 1 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
Case study 1 28
Case study 1 solutionDimension of the support structure
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 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_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
jo_op = jsc_op * k = 505 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
Case study 1 30
Comparison
Superconductivity for Accelerators, Erice, Italy, 25 April - 4 May, 2013
Case study 1 31