Transcript Case Study 2b

Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
CASE STUDY PRESENTATION
Case number 2 :
Design a Nb-Ti superconducting quadrupole with
a 120mm aperture for the upgrade of the LHC
interaction region operating at 1.9K
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Our quadrupole design
Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Parameters:
𝑤𝑡𝑜𝑡 = 32𝑚𝑚
Rutherford cable :
Number of cable layers : 2
𝑤𝑐𝑎𝑏𝑙𝑒 = 16𝑚𝑚
𝑡𝑎𝑣−𝑐𝑎𝑏𝑙𝑒 = 1.44𝑚𝑚
(𝐾𝑒𝑦𝑠𝑡𝑜𝑛𝑒 𝑎𝑛𝑔𝑙𝑒 = 0.8°)
𝐶𝑢
= 1.56
𝑆𝐶
∅𝑆𝑡𝑟𝑎𝑛𝑑 = 0.8𝑚𝑚
𝑛𝑢𝑚𝑏𝑒𝑟𝑆𝑡𝑟𝑎𝑛𝑑𝑠 = 2 × 20
(Rutherford-like cable)
Pitch angle 14.9°
Pitch length = 120 mm
𝑡𝑎𝑣−𝑐𝑎𝑏𝑙𝑒
𝑤𝑐𝑎𝑏𝑙𝑒
Quadrupole :
𝑤𝑡𝑜𝑡
Compaction:
𝑤𝑖𝑑𝑡ℎ = −6.67%
𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = −10.0%
Insulator : 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 0.1𝑚𝑚
Filling factor : 𝜅 = 0.295
Case study 2, group B
Our quadrupole design
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Gradient as a function of coil width
175
Nb-Ti 1.9 K
150
Gradient (T/m)
125
100
75
50
25
Aperture diameter =120(mm),
Aperture radius = 60(mm)
0
0
20
40
60
80
Coil width (mm)
r=60 mm
100
120
Our choices :
• Gradient = 140(T/m)
• Coil width = 32(mm) / divided in 2 cables of 16(mm)
Our quadrupole design
Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Typical values of pitch angle
Typical values of strand diameters
NbTi Nb3Sn
NbTi Nb3Sn
Our choice : 0.8 mm
Our choice : 14.93°
Flükiger, CAS, Erice (I) 25 April - 4 May 2013
Typical values of Cu/SC ratio
(ratio btw. area of Cu and area of SC material)
Bruzzone, CAS, Erice (I) 25 April - 4 May 2013
Typical values width/thickness compaction
NbTi Nb3Sn
NbTi Nb3Sn
Our choice : Cw = -6.67%
Cth= -10%
Our choice : 1.56
4
Flükiger, CAS, Erice (I) 25 April - 4 May 2013
Bruzzone, CAS, Erice (I) 25 April - 4 May 2013
Load Line Calculation
Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
80%
𝐽𝑠𝑐−𝑜𝑝 = 80%𝐽𝑠𝑐−𝑠𝑠 = 1340𝐴/𝑚𝑚2
𝐽0−𝑜𝑝 = 396 𝐴/𝑚𝑚2
𝐺𝑜𝑝 = 112 𝑇/𝑚
𝐵𝑝𝑒𝑎𝑘−𝑜𝑝 = 7.74 𝑇
𝐼𝑜𝑝 = 10.5 𝑘𝐴
Margin :
𝐵𝑚𝑎𝑟𝑔𝑖𝑛 = 2.56 𝑇
𝐽𝑠𝑐 = 1330 𝐴/𝑚𝑚2
Limit temperature : 4 K
Δ𝑇 = 2.1 𝐾
𝑤
= 0.53
𝑟
𝜆 = 1,15
5000
Critical current density Jc (A/mm2)
100 %
Intersection : 𝐵𝑝𝑒𝑎𝑘−𝑠𝑠 = 9.68 𝑇
𝐽𝑠𝑐_𝑠𝑠 = 1680 𝐴/𝑚𝑚2
𝐽𝑜−𝑠𝑠 = 𝜅𝐽𝑠𝑐−𝑠𝑠 = 495 𝐴/𝑚𝑚2
𝐵𝑝𝑒𝑎𝑘−𝑠𝑠
𝐺𝑠𝑠 =
= 140𝑇/𝑚
𝜆𝑟
𝐼𝑠𝑠 = 𝐽𝑜−𝑠𝑠 × 𝑆𝑐𝑎𝑏𝑙𝑒 = 13,2 𝑘𝐴
4500
4000
3500
NbTi
1.9 K
Nb3Sn
, 1.9 K
3000
2500
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8 Field
9 1011121314151617181920
(T)
Comparison with Nb3Sn
Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Same parameters of the cables with Nb3Sn
100 %
𝐵𝑝𝑒𝑎𝑘−𝑠𝑠 = 13.5 𝑇
𝐽𝑠𝑐_𝑠𝑠 = 2470 𝐴/𝑚𝑚2
𝐽𝑜−𝑠𝑠 = 730 𝐴/𝑚𝑚2
𝐺𝑠𝑠 = 207𝑇/𝑚
𝐼𝑠𝑠 = 19.4 𝑘𝐴
80% :
𝐽𝑠𝑐−𝑜𝑝 = 1980𝐴/𝑚𝑚2
𝐽0−𝑜𝑝 = 584 𝐴/𝑚𝑚2
𝐺𝑜𝑝 = 166 𝑇/𝑚
𝐵𝑝𝑒𝑎𝑘−𝑜𝑝 = 10.8𝑇
𝐼𝑜𝑝 = 15.5 𝑘𝐴
Margin :
𝐵𝑚𝑎𝑟𝑔𝑖𝑛 = 3,68 𝑇
𝐽𝑚𝑎𝑟𝑔𝑖𝑛 = 2720𝐴/𝑚𝑚2
𝑇𝑚𝑎𝑟𝑔𝑖𝑛 = 4.6𝐾
Comparison 80% :
NbTi – Vs – Nb3Sn
Δ𝐺𝑜𝑝 = 54 𝑇/𝑚
Δ𝐵𝑚𝑎𝑟𝑔𝑖𝑛 = 1.12 𝑇
Δ𝐽𝑚𝑎𝑟𝑔𝑖𝑛
= 1400 𝐴/𝑚𝑚2
Δ𝑇𝑚𝑎𝑟𝑔𝑖𝑛 = 2.5𝐾
Case study 2, group B
Possible Layout
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Cancel: 𝐵6 , 𝐵10 , 𝐵14 :
sin 𝑛𝜃1 − sin 𝑛𝜃2 + sin 𝑛𝜃3 = 0, 𝑛 = [6; 10; 14]
Possible solution:
𝜃𝑖 = [21.6°; 26.1°; 33.7°]
Source : Todesco, USPAS 2012
Case study 2, group B
EM forces and stress at operational conditions
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
Sector approximation
•
•
•
a1 = 0.06 (m)
a2 = 0.0924 (m)
Jo-op = 396 (A/mm2) = 3.96 108 (A/m2)
Fx  
Fy  
2  0 J 02

2  0 J 02

3  1 12a24  36a14  a1 1  3 
  ln  a1   726kN / m

12  72
a2
 a2 3  
 3
3  5  2 3 3 1 a14 2  3 a1 3 1  3

a1   1520kN / m
a


ln
a


2

2
1


2  36
12 a2
6
a2
9 2
 
2  0 J 02 3  1 7 a24  9a14 1  a1 4  3  1
  _ mid  plane _ av  
  ln  a1 
 614 MPa


2  36
a2
3  a2 3   a2  a1
170
Stress on mid-plane (MPa)
 173.205
175
180
|𝜎𝑎𝑣 | = 614𝑀𝑃𝑎
185
190
 midd( r) 195
200
Comparison LHC Dipoles: 150 𝑀𝑃𝑎.
205
210
 211.885
215
220
0.025
a1
0.03
0.035
r
Radius (m)
0.04
0.045
a2
Dimensioning
Case study 2, group B
FERRAND, G./JECKLIN, N. / PURUSHOTHAMAN, S. / STODEL, M.H. / YUE, W.
90 % of short-sample conditions :
Iron shield: 𝑡𝑖𝑟𝑜𝑛 ≃
𝑟2𝐺
2𝐵𝑠𝑎𝑡
≃ 280𝑚𝑚.
Maximum force applied to the collar : 𝐹𝑐𝑜𝑙𝑙𝑎𝑟 = 2 2𝐹𝑥
= 2.1 (MN/m).
Strain :
𝐹𝑐𝑜𝑙𝑙𝑎𝑟
𝜖 = 𝜎𝑐𝑜𝑙𝑙𝑎𝑟 𝐸 ∝
.
𝑡𝑐𝑜𝑙𝑙𝑎𝑟
From LHC dipole collars data (including margins):
𝑡𝑐𝑜𝑙𝑙𝑎𝑟−𝑑𝑖𝑝𝑜𝑙𝑒 =10 mm for 𝐹𝑥_𝑑𝑖𝑝𝑜𝑙𝑒 = 0.7 𝑀𝑁/𝑚.
By analogy, for our quadrupole, 15 (mm) must be
enough, including margins.