1. Error and Multipole Sensitivity Study for the Ion Collider Ring
G.H. Wei, V.S. Morozov, Fanglei Lin
Y. Nosochkov, M-H. Wang (SLAC)
JLEIC Collaboration Meeting Spring 2016
F. Lin

2. Contents JLEIC ion collider ring lattice, emittance, & Error types
Misalignment, strength error and correction
Sensitivity of magnet multipole field to dynamic aperture
Dynamic aperture with multipoles of Super-Ferric Dipoles in arc section
Dynamic aperture with multipoles of IR triplets
Summary

3. One Lattice for JLEIC Ion Collider RingQ S
ALL
133
205 75 IR 2 6
β> 200 m 21 19 8

4. One Lattice for JLEIC Ion Collider Ring
Dynamic Aperture at IP
Proton 60 GeV
ex/ey(nor. mm-mrad)
Beta(x/y, m, IP)
Alf(x/y, IP) DA
Strong Cooling
0.35/0.07
0.1/0.02
0.0/0.0
~ 70 sigma
Large emittance
1.2/1.2
~ 38 sigma

5. Error types Magnets: Dipole, Quadrupole, Sextupole, corrector
static errors : independent on time
Misalignment, strength error of magnets;
Multipole field components of magnets
dynamic errors: dependent on time
Noise signal of BPM
Field jitter of magnets

6. Misalignment, strength error &correction
With error survey at RHIC, PEP II, & other machines, and also a suggestion by Uli Wienends in JLEIC Collaboration Meeting Spring 2016, follow errors are assumed in study
Dipole
Quadrupole
Sextupole
BPM(noise)
Corrector
x displacement(mm)
0.3
0.3, FFQ0.03
0.05 -
y displacement(mm)
x-y rotation(mrad)
0.3, FFQ0.05
s displacement(mm)
Strength error(%)
0.1
0.2, FFQ0.03
0.2
0.01

7. Correction Orbit Correction
Tune correction (Tune measured accuracy < 0.001)
Tune error : < 0.1 %
Beta-beat correction: beta measurement
Beta error at IP & Beta > 500 : < 1 %
Beta error at Beta < 500 : < 5 %
Chromaticity correction
Linear Chromaticity (+1, +1)
W function at IP = (0, 0), not yet in ELEGANT
Decoupling by skew quads

8. Closed Orbit Distortion after correction
+10-4
-10-4
5*10-6
5*10-6 IP IP

9. Dynamic Aperture after Correction
Without error
With error & correction
10 seeds
ex/ey(nor. mm-mrad)
DA origin
DA with error
Case 1, strong cooling
0.35/0.07
~ 70 sigma
~ 50 sigma
Case 2, large emittance
1.2/1.2
~ 38 sigma
~ 27 sigma

10. Multipoles of Super-Ferric dipole
From Peter McIntyre’s report

11. DA with Multipoles of arc dipole
arc dipoles of beta < 200 m
All arc dipoles
ex/ey(nor. mm-mrad)
DA left figure
DA right figure
Case 1
0.35/0.07
~ 50 sigma
~ 20 sigma
Case 2
1.2/1.2
~ 27 sigma
~ 10.8 sigma
Skew Multipoles’ data isn’t given. Considering same effect of skew multipole as normal one, design is ok for arc dipole with beta < 200 m

12. Multipoles of FFQ in 3 accelerators
1. Tevatron
3. LHC
2. RHIC
Reference radius: 1/3 aperture
Multipoles have been improved one machine by one machine.

13. Multipole characters in FFQ
Scaling with reference radius r0 and coil diameter dc
(B. Bellesia, et al., Phys. Rev. ST-AB 10, (2007))
Scaling with bmax to keep contribution of non-linear resonance driving terms constant.
(S. Fartoukh, sLHC Project Report 0038)
where n=2 is for a quadrupole, etc.
BQ is the main quadrupole field at r0

14. Simulation setup & method

15. Multipole Survey due to DA of 10 sigma at IP
Single Multipole:
Normal
DA~ 20 σ at IP
Combined result: Normal
DA~ 12 σ at IP
Multipoles
Normal + Skew
to get a DA of σ at IP
Single Multipole: Skew
DA~ 20 σ at IP
Combined result:
Skew
DA~ 12 σ at IP

16. Simulation setup & method
Cases
x/y
Rref
DA_sm
DA_cm
an,bn
Non-liner drive
1.1
0.35/0.07
43 mm 20 10
not same
2.1
15 
same
1.2
1.2/1.2
20 mm
2.2
12 
3.1
LHC data
N/A
3.2
4.1
Magnet data
4.2
5.1
Reference Radius ?
5.2
5.3
survey

17. Using LHC FFQ Multipole Data
ex/ey(nor.) DA
Case 1
0.35/0.07
~ 16 sigma
Case 2
1.2/1.2
~ 8.6 sigma
Apply LHC FFQ data to IR triplets
of JLEIC ion collider ring
DA results are OK for case 1 with strong cooling, but may be an issue for case 2 with large emittances.

18. Multipole Survey due to DA of 10 sigma at IP
Considering measured data of LHC FFQ, Multipole survey shows an emit. of (ex/ey: 0.9/0.9 μm-rad, norm) is needed for 60 GeV p.
Increasing β*, FFQ aperture can enlarge the multipole limit.

19. With Multipole Data of FFQ model: QIF
Ion FFQ model (Peter McIntyre):
QIF, 90 T/m, 17 cm
Normal multipoles of b5 & b9 are very large
No skew multipole data
From Peter McIntyre’s report

20. With Multipole Data of FFQ model: QIF
100 GeV
60 GeV
ex/ey(nor.) DA
Case 1
0.35/0.07
~ 7.3 sigma
Case 2
1.2/1.2
~ 4.0 sigma
1 unit: 10^-4
FFQ-QIF: Ф17 cm, Rref 4 cm
Dynamic Aperture is mainly determined by b5 & b9.

21. With Multipole Data of FFQ model: QIF
According to Multipole survey results,
b5  b5 × 1/100
b9  b9 × 1/5

22. With Multipole Data of FFQ model: QIF
60 GeV
- Before correction
- After correction
b5 × 1/100
b9 × 1/5
ex/ey(nor.)
DA before
DA after
Case 1
0.35/0.07
7.3 sigma
16 sigma
Case 2
1.2/1.2
4.0 sigma
8.8 sigma
Case 3
0.9/0.9
4.7 sigma
10 sigma
1 unit: 10^-4
With correction on b5 & b9, DA is 10 σ of ex/ey_0.9/0.9
Skew data for deep study

23. Summary
Misalignment error suggested by Uli Wienends, has been studied. Dynamic aperture is shrinking but acceptable.
Dynamic aperture with multipoles of super-ferric dipole in arc section has been studied. And we still need to look at injection.
Multipole data of LHC FFQ was applied to JLEIC. Dynamic aperture is OK with strong cooling (ex/ey: 0.35/0.07 mm-mrad, norm.), but there may be an issue with large emittance (ex/ey: 1.2/1.2 mm-mrad, norm.)
Multipole survey has been done. Considering measured data of LHC FFQ, an emittance of (ex/ey: 0.9/0.9 mm-mrad, norm) is needed in current situation. Increasing beta-star, physical aperture of FFQ can enlarge multipole limit.
Multipole data of model FFQ (QIF) has been studied. With correction on b5 & b9, DA is 10 σ with ex/ey_0.9/0.9 mm-mrad.

24. Study Plan
Require skew multipole data of super-ferric dipole in arc section to study dynamic aperture with super-ferric dipole of beta > 200 meters
Require skew multipole data of QIF (FFQ model) to study influence on dynamic aperture
Require data of super-ferric dipole in ramping time to study whether we need a sextupole in the middle of dipole or not.
Dynamic aperture study on arc quads & 2 IR dipoles
Dynamic aperture study at injection
Put misalignment error, strength error, magnet multipoles, detector solenoid effects together to make design of multipole corrector packages.
Study influence from grab cavity and round-beam mode

25. Thank you
F. Lin

26. Error Study at Machines
Displacement
Tilted angle
Strength Error mm
mrad
10-2
PEP-II
1(Dipole)
0.1(Q&S)
0.3(Dipole)
0.5(Q&S)
0.1(D&Q)
0.2(S)
KEKB
0.1(D,Q&S)
0.2(D),
SuperB
0.2(dipole)
0.3(Q)
0.15(S)
NSLS-II
0.1(Dipole)
0.03(Q&S)
0.5(Dipole)
0.2(Q&S)
0.1(D)
RHIC
0.25(Q),0.13(S)
1(Q)
J-PARC
0.1(meas.dipole)
0.03(meas.Q&S)
0.03(meas. D,Q,&S)

27. Closed Orbit Distortion and correction
+10-4
1/3 error
1/3 error
-10-4
+2 mm
-2 mm
2/3 error
2/3 error

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

29. 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

30. Multipoles of FFQ in LHC
Multipoles of FFQ in Old LHC bn: normal multipole; an: skew multipole
1 unit = 10-4

31. 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

32. Multipoles of FFQ in RHIC

33. Multipoles of FFQ in RHIC
Gradient
~48.1 T/m
Aperture
130 mm
Ref. ratio
40 mm

34. Multipoles of FFQ in Tevatron
Layout of Tevatron

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

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

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

38. 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

39. 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

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

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

42. Beam Size
σx:10-6
σy:10-6

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

44. One Lattice for JLEIC Ion Collider Ring
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%
Proton 60 GeV
ex/ey(nor. mm-mrad)
Beta(x/y, m)
Alf(x/y)
DA of bare lattice
Case 1
0.35/0.07
0.1/0.02
0.0/0.0
~ 70 sigma
Case 2
1.2/1.2
~ 38 sigma