Transcript Case Study 1a

CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Goal
• Design a Nb3Sn superconducting quadrupole with an 150mm aperture for the
upgrade of the LHC interaction region operating at 1.9 K
Steps of the study
• Determination of maximum gradient & coil size
• Definition of strands & cable parameters
• Determination of load-line & « short sample » conditions
• Determination of operation conditions & margins, comparison with NbTi
• Definition of the coil lay-out
• Determination of em forces & accumulated forces on the coil mid-plane
• Determination of shell & yoke dimensions
• Additional questions
CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Maximum gradient, coil size, strands and cable parameters
Source: Magnet Design – Ezio Todesco
Inner data:
• Aperture = 150mm
• Material: Nb3Sn
Assumptions:
Rutherford cable
• Filling factor = 0.33
• Block angle = 30°
• Available for one layer
Design choices:
• Coil width = 30mm = 2 layers 15mm width each
 Maximum field gradient = 167 T/m
𝑤
 Aspect ratio = = 0.2
𝑟
 λ = 1.16
Strands & cable parameters
• Strand diameter = 0,8mm
• Strands number = 40 (~ 2x 20)
• Mid-thick after compaction = 1,44mm (Cthk = -10%)
• Width after compaction = 15mm (Cwidth = -6.3%)
•
•
•
•
Insulation thickness = 150 microns
Calculated filling factor = 0.334
Cu to SC ratio = 1.2
Pitch angle = 15.4°
CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Load-line, “short sample” conditions, “operational” conditions & margins
Nb3Sn / NbTi
“Short sample” conditions
• 𝑗𝑠𝑐−𝑠𝑠 = 2280 𝐴 𝑚𝑚² (1550)
• 𝑗𝑜−𝑠𝑠 = 700 𝐴 𝑚𝑚² (494)
• 𝐼𝑠𝑠 = 20.86 𝑘𝐴 (14.2)
• 𝐺𝑠𝑠 = 170.1 𝑇 𝑚 (115)
• 𝐵𝑝𝑒𝑎𝑘−𝑠𝑠 = 14.8 𝑇 (10)
“Operational” conditions
• 𝑗𝑠𝑐−𝑜𝑝 = 1824 𝐴 𝑚𝑚² (1240)
• 𝑗𝑜−𝑜𝑝 = 560 𝐴 𝑚𝑚² (395.2)
• 𝐼𝑜𝑝 =16.7 kA (11.3)
• 𝐺𝑜𝑝 =136.1 𝑇 𝑚 (92)
• 𝐵𝑝𝑒𝑎𝑘−𝑜𝑝 = 11.84 𝑇 (8)
Margins
• 𝑇 = 4.45 𝐾 (2)
• 𝑗𝑠𝑐 = 456 𝐴 𝑚𝑚² (310)
• 𝐵𝑝𝑒𝑎𝑘 = 2.96 𝑇 (2)
𝑗 𝐵 =
1
𝐵
𝑤 . 𝜆𝑟
𝛾𝑐0 . ln(1 + )
𝑟
 When compared with NbTi, Nb3Sn results in higher margins on 𝑻𝒄 , 𝒋𝒄 and 𝑩𝒄
CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Minimizing field errors thanks to coil lay-out
Multipole coefficients:
With one sector at 30°, 𝐵6 = 0, 𝐵10 ≠ 0
 Insertion of a wedge to set 𝐵10 = 0
According to the following equations:
Wedge
𝛼3
𝛼2
𝛼1
for setting 𝐵6 = 𝐵10 = 0, several
combinations of angle are possible:
• [0°-12°, 18°-30°]
Source: Rossi, L.,
Todesco, E., Electromagnetic design
• [0°-18°, 22°-32°]
quadrupoles, Phys. Rev. STAB, 9, 102401, (2006)
• [0°-24°, 30°-36°]
• [0°-26°, 36°-44°]
… It’s not necessary to set to 0 the other multipole coefficients.
• …
of superconducting
CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Fx  
Fy  
2  0 J 02

20 J 02

f x  f r cos   f sin 
3  1 12a24  36a14  a1 1  3 
  ln
 a1 

12  72
a2
 a2 3  
f y  f r sin   f cos 
 3  𝐹𝑥 = 1.48. 106 𝑁/m
3  5  2 3 3 1 a14 2  3 a1 3 1  3
a2 

ln a1  
 2 a1 

6
2  36
12 a2
6
a2
9 2
  𝐹𝑦 = −3.26. 10 𝑁/m
  _ mid  plane 
 /6
 f rd  
0
20 J 02

3 
a2 r 4  a14 

r  r ln 
8 
r
4r 3 
σθ𝑚𝑎𝑥 = - 124 MPa
R1
R2
RI
Collars thickness= 25mm

F

p
cos(45°)
2. 𝐹𝑥 .
2
= 𝜎𝑎𝑑𝑚 . 𝑡𝑠ℎ𝑒𝑙𝑙
2

F
J0
5,6 E+08
A/m²
µ0
ϕ
r
a1
1,26 E-6
0,524
0,075
0,075
N/A²
rad
m
m
a2
G
σmax
0,105
170
200
m
T/m
MPa
t yoke
0,215
m
t shell
0,0104
m
r 2G
~ t yoke Bsat
2
𝐵𝑠𝑎𝑡 = 2𝑇
CASE STUDY N°1: Low-beta Nb3Sn quadrupoles for the HL-LHC
Group A: Roberts,W. Muranaka,T. Porhiel,A. Maeder,J. Giannelli,S. Alberty, L.
Additional questions
SC cable technology
YBCO
BSSCO-2212
Advantages
• Much higher critical field and temperature
•
•
•
•
It is the only HTS materials available in round wires
Very good thermal stability
High Jc values can be attained
High potential for improvements
Limitations
•
Costs, limited Industrialization
•
•
Costs
Poor mechanical stability
Block vs Cosθ
•
•
•
…
Similar possibilities for field quality optimization by optimization of geometrical parameters;
Cosθ is a design of confirmed robustness;
Field quality in “Cosθ” coils with large w/r ratios is easier to optimize.