1.  Field Quality Requirement Study of Triplet FFQ for JLEIC ion collider ring
G.H. Wei, V.S. Morozov, Fanglei Lin
Y. Nosochkov, M-H. Wang (SLAC)
JLEIC Meeting, JLab, March 3, 2016
F. Lin

2. Contents Overview at similar machines LHC RHIC Tevatron
Multipole limit survey of FFQ for JLEIC ion collider ring
Simulation method
Multipole sensitivity and limit due to 10 σ of beam
Coil Aperture and reference radius
Multipole limit with FFQ aperture which physics group suggested

3. Multipoles of FFQ in LHC
Old LHC
b* =
55/55 cm
HL-LHC b* = 15/15 cm
bmax~ 4.5km
bmax~ 21.5km

4. Multipoles of FFQ in LHC
Old LHC
b* =
55/55 cm
HL-LHC b* = 15/15 cm
bmax~ 4.5km
bmax~ 21.5km
Old LHC
HL-LHC
Gradient
~210 T/m
~140 T/m
Aperture
70 mm
150 mm
Reference
17 mm
50 mm
JLEIC-FFQ
upstream
downstream

5. Multipoles of FFQ in LHC
Aperture definition
Inner aperture
beam envelope (10 σ per beam),
beam separation (10 σ),
β-beating (20%),
peak orbit excursion (2 mm)
mechanical tolerance (1.6 mm),
spurious dispersion orbit d (1 mm)
Q1: 98 mm
Q2-Q3-D1: 118 mm
With Beam screen, Coil Aperture: 150mm
Reference radius = Coil Aperture/3 = 50mm
Beam halo: 12s

6. Multipoles of FFQ in LHC
Multipoles of FFQ in Old LHC bn: normal multipole; an: skew multipole

7. Multipoles of FFQ in LHC
Multipoles of FFQ in HL-LHC bn: normal multipole; an: skew multipole
Design data
& DA modified data

8. Multipoles of FFQ in LHC
Reference
DAmin=6.79s
DAmin=10.69s
DA with multipole data
DA with modified multipole data

9. Multipoles of FFQ in RHIC

10. Multipoles of FFQ in RHIC
Gradient
~48.1 T/m
Aperture
130 mm
Reference
40 mm

11. Multipoles of FFQ in LHC
Aperture : Coil aperture: 130 mm; reference radius : 40 mm
proton
Design: 250 GeV, 20 pi mm-mrad (IBS, nor. 95%), Beta_max= 1400
Coil aperture: ~ 16 sigma; reference radius : ~ 10 sigma
Experiment: 100 GeV, Dec 2011~ Jan 2012 Au
100 GeV, 40 pi mm-mrad (IBS, nor. 95%), Beta_max= 1400
Coil aperture: ~ 7 sigma; reference radius : ~ 5 sigma

12. Multipoles of FFQ in RHIC

13. Multipoles of FFQ in Tevatron
Layout of Tevatron

14. JLEIC Ion Collider RingQ S
ALL
133
205 75
IR area 2 6
β> 200 m 21 19 8

15. Simulation setup & method

16. Simulation setup & method
1,000 turns
ELEGANT Dynamic Aperture (line Mode,41 angles)
60 GeV / 100 GeV beam energy
Tune = 25.22, 23.16
Normalized emittance = 0.35 mm-rad / 0.07 mm-rad
σx: m
σy: m

17. Simulation setup & method
1000 turns is selected. And ~ 0.5 sigma of DA result compared with DA result by turns
Time needed
1k turns: 10 days
5k turns: 50 days
10k turns: 100 days
10 turns
100 turns
1000 turns
5000 turns
10000 turns

18. Simulation setup & method
Multipoles
Normal: Systematic + Random
Skew: Systematic + Random

19. Simulation setup & method
Single Multipole:
Normal Systematic
Combined result: Normal Systematic
Normal + Skew
Systematic
Single Multipole: Skew
Systematic
Combined result:
Skew
Systematic

20. Simulation setup & method2 3 4
~35 σ of H & V: 3.5*(2.32, 0.46) 60 GeV 5 6 7

21. Simulation setup & method8 9 10
~35 σ of H & V: 3.5*(2.32, 0.46) 60 GeV 11 12 13

22. Simulation setup & method
20 σ of H & V: 2*(2.32, 0.46) 60 GeV

23. Multipole limit survey of FFQ
Single Multipole: 20 σ of H & V
Normal Systematic
Combined result: 12 σ of H & V
Normal Systematic
10 σ of H & V
Normal + Skew
Systematic
Single Multipole: 20 σ of H & V Skew
Systematic
Combined result: 12 σ of H & V
Skew
Systematic

24. Survey of FFQ normal systematic multipole
Multipole of FFQ at radius mm (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
-5.14
E-02
-1.51
E-01
3.44
-2.72
-1.96
1.31
-1.24
6.79
-1.26
LHC mm)
0.75
0.64
0.09
-0.37
-0.02
0.02
0.04
-0.01
JLEIC-plus 11
2.46
6.92
8.55
1.45
3.08
3.83
1.125E-01
1.14
JLEIC-minus
-10.4
-2.8
-6.35
-1.09
-1.34
-2.28
-3.6
-6.93
Multipole of FFQ at radius mm (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-4.69
E-03
-1.22
E-02
-1.42
JLEIC-plus
3.67
3.63
1.06
JLEIC-minus
-2.08
-3.43
-6.42

25. Survey of FFQ skew systematic multipole
Multipole of FFQ at radius mm (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
5.28
E-01
4.02
E-02
6.21
4.32
2.53
-2.59
4.60
-1.87
4.84
E-03
LHC mm)
-0.82
-0.06
-0.47
-0.02
0.02
-0.03
-0.04
JLEIC-plus
14.8
2.4
5.5
5.67
5.59
1.5
1.3
5.09
4.03
JLEIC-minus
-14.8
-2.4
-5.5
-5.6
-5.59
-1.5
-1.29
-5.05
-3.76
Multipole of FFQ at radius mm (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-8.99
E-03
-8.22
-1.01
E-02
JLEIC-plus
1.61
1.21
4.3
JLEIC-minus
-1.51
-1.21
-4.3

26. Multipole limit survey of FFQ
Single Multipole: 16 σ of H & V
Normal Systematic
10 σ of H & V
Normal + Skew
Systematic
Single Multipole: 17 σ of H & V Skew
Systematic

27. Survey of FFQ normal systematic multipole
Multipole of FFQ at radius mm (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
-5.14
E-02
-1.51
E-01
3.44
-2.72
-1.96
1.31
-1.24
6.79
-1.26
LHC mm)
0.75
0.64
0.09
-0.37
-0.02
0.02
0.04
-0.01
JLEIC-plus 1
3.92
1.63
7.51
7.4
JLEIC-minus -1
-3.92
-1.63
-7.51
-7.4
Multipole of FFQ at radius mm (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-4.69
E-03
-1.22
E-02
-1.42
JLEIC-plus
3.83
E-01
3.87
1.77
JLEIC-minus
-3.83
-3.87
-1.77

28. Survey of FFQ skew systematic multipole
Multipole of FFQ at radius mm (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
5.28
E-01
4.02
E-02
6.21
4.32
2.53
-2.59
4.60
-1.87
4.84
E-03
LHC mm)
-0.82
-0.06
-0.47
-0.02
0.02
-0.03
-0.04
JLEIC-plus 1
1.98 5
6.67
2.22
2.69
JLEIC-minus -1
-1.98 -5
-6.67
-2.22
-2.69
Multipole of FFQ at radius mm (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-8.99
E-03
-8.22
-1.01
E-02
JLEIC-plus 1.
E-01
1.2
3.44
JLEIC-minus
-1.
-1.2
-3.44

29. Scaling method to make comparison
Scaling with reference radius r0 and coil diameter dc
coil diameter
inner diameter ?
Scaling with peak IT beta function bmax to keep contribution of the IT field non-linear resonance driving terms constant.
where n=2 is for a quadrupole, etc.
BQ is the main quadrupole field at r0

30. Different aperture of FFQ
According to different aperture in these 6 FFQ, different reference radius is setup in the simulation due to 15 sigma

31. Multipole limit survey of FFQ
Single Multipole: 18 σ of H & V
Normal Systematic
Combined result: 12 σ of H & V
Normal Systematic
10 σ of H & V
Normal + Skew
Systematic
Single Multipole: 18 σ of H & V Skew
Systematic
Combined result: 11 σ of H & V
Skew
Systematic

32. Survey of FFQ normal systematic multipole
Multipole of FFQ (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
-5.14
E-02
-1.51
E-01
3.44
-2.72
-1.96
1.31
-1.24
6.79
-1.26
LHC mm)
0.75
0.64
0.09
-0.37
-0.02
0.02
0.04
-0.01
JLEIC-plus 1
0.91
0.56
JLEIC-minus -1
-0.91
-0.56
Multipole of FFQ (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-4.69
E-03
-1.22
E-02
-1.42
JLEIC-plus
0.55
0.36
0.43
JLEIC-minus
-0.55
-0.36
-0.43

33. Survey of FFQ skew systematic multipole
Multipole of FFQ (unit: 1_10^-4)
multipole type
∆ 𝐵 1 𝐵 1
∆ 𝐵 2 𝐵 1
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
∆ 𝐵 7 𝐵 1
∆ 𝐵 8 𝐵 1
∆ 𝐵 9 𝐵 1
∆ 𝐵 10 𝐵 1
PEP-II FFQ
QD4R
5.28
E-01
4.02
E-02
6.21
4.32
2.53
-2.59
4.60
-1.87
4.84
E-03
LHC mm)
-0.82
-0.06
-0.47
-0.02
0.02
-0.03
-0.04
JLEIC-plus 1
9.33
6.68
6.55
JLEIC-minus -1
-9.33
-6.68
-6.55
Multipole of FFQ (unit: 10^-4)
multipole type
∆ 𝐵 11 𝐵 1
∆ 𝐵 12 𝐵 1
∆ 𝐵 13 𝐵 1
PEP-II FFQ
-8.99
E-03
-8.22
-1.01
E-02
JLEIC-plus
3.57
E-01
3.35
1.59
JLEIC-minus
-3.57
-3.35
-1.59

34. Summary
Multipole Limit Survey is preliminarily studied for FFQ of JLEIC ion ring. Considering LHC and RHIC case, Multipole limit looks in range of current technology level of superconduct magnets, except one thing which is the large aperture of last two downstream FFQ.
Last two FFQ have inner aperture of 157 mm and 170 mm. It is a good thing for low multipole, but looks too large considering superconduct magnet in LHC and RHIC?

35. Summary Deep study should be done considering:
Make sure of emittance after cooling
Make sure of physical aperture with physics group
Multipole limit study for heavy ion
Supercomputer is needed to get accurate result with 100,000 turns (1000 turns now)
200 GeV of JLEIC ion ring ?

36. Thank you
F. Lin

37. Multipole limit survey of FFQ
Single Multipole: 20 σ of H & V Combined result: 12 σ of H & V
12 σ of H & V: 1.2*(2.32, 0.46) 60 GeV

38. LHC FFQ measured multipoles

39. Multipoles of FFQ & large-beta dipole in LHC

40. Multipoles of FFQ & large-beta dipole in LHC

41. Multipoles of FFQ & large-beta dipole in LHC

42. Discussion: a standard of FFQ multipoles

43. Multipoles of FFQ in LHC
: Gaussian distributed random
variables cut at 1.5 sigma.
Same for all magnets of a
given class, but changes
from seed to seed
variables cut at 3 sigma.
Changes also from magnet
to magnet
G. Sabbi, E. Todesco, “Requirements for Nb3Sn Inner Triplet and Comparison With Present State of the Art”, HILUMILHC-MIL-MS-33, 2012.
WEPEA048, IPAC2013

44. Multipoles of FFQ in LHC (Yuri)
Magnets field quality specifications, Nosochkov, Yuri (SLAC) et al, 28 Nov. 2014

45. Multipoles of FFQ in LHC

46. Multipoles of FFQ in LHC

47. Scaling method to make comparison
Scaling with reference radius r0 and coil diameter dc