1. Multipole Limit Survey of FFQ and Large-beta Dipole
G.H. Wei, V.S. Morozov, Fanglei Lin
JLEIC Meeting, JLab, Dec 3, 2015
F. Lin

2. Contents
Review
Dynamic Aperture Shrinking is mainly caused by Multipoles of large-beta magnets, especially FFQ and top two large-beta dipoles
Study Plan
Multipole limit survey of large-beta dipoles
Multipole limit survey of 6 FFQ
Summary & Questions

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

4. Beam Size
σx:10-6
σy:10-6

5. One Lattice for JLEIC Ion Collider Ring
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%
>70 σ of H & V

6. Error types Magnets: Super-Ferric dipole, Quads, Sextupole, corrector
static errors : independent on time
Misalignment, strength error of magnets; offset of BPM
Multipole error of magnets
(systematic error & random error)
dynamic errors: dependent on time
Noise signal of BPM
Field jitter of magnets

7. Misalignment, strength error &correction
Suggested by Uli Wienends: 3 times larger
Dipole
Quadrupole
Sextupole
BPM(noise)
Corrector
x misalignment(mm)
0.3
0.3, FFQ0.03
0.02 -
y misalignment(mm)
x-y rotation(mrad)
0.3, FFQ0.05
s misalignment(mm)
Strength error(%)
0.1
0.2, FFQ0.03
0.2
0.01

8. Misalignment, strength error &correction
Closed orbit correction
Beta-beat correction
Tune correction
Chromaticity correction
Decoupling

9. Dynamic Aperture after Correction
Without error
After Correction
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%
All seeds: Δp/p=0
>70 σ of H & V
~50 σ of H & V

10. Multipoles of Super-Ferric dipole
Peter McIntyre
MEIC Fall 2015

11. Multipoles of Super-Ferric dipole 100 GeV
ΔBn is the field due to order of n
B0 is the main dipole field
Multipole errors of super-ferric dipole at radius 20 mm (unit: 10^-4)
multipole type
∆ 𝐵 1 𝐵 0
∆ 𝐵 2 𝐵 0
∆ 𝐵 3 𝐵 0
∆ 𝐵 4 𝐵 0
∆ 𝐵 5 𝐵 0
∆ 𝐵 6 𝐵 0
∆ 𝐵 7 𝐵 0
∆ 𝐵 8 𝐵 0
∆ 𝐵 9 𝐵 0
∆ 𝐵 10 𝐵 0
systematic
-0.151
-0.537
0.126
0.850
0.714
0.366
-0.464
-0.410
0.009
0.027
Random

12. Multipoles of Super-Ferric dipole 100 GeV
Without error
Multipole all
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%
Multipole 1
Multipole 2
Multipole 3

13. Multipoles of Super-Ferric dipole 100 GeV
10 sigma H & V (1.8, 0.36) e-4
Multipole 7
Multipole 3-8
Multipole 8

14. Multipoles except 2 β>1km dipole
> 20 σ of H & V: 2*(1.8, 0.36) e-4

15. Multipoles except dipoles of β > 200m
~50 σ of H & V: 5*(1.8, 0.36) e-4

16. multipoles of Super-Ferric dipole
SC + dp/p
SC + FFQ + Q
SC + Q
SC + FFQ

17. A limit comes from injection
For Proton: σ > 5.5 times
For ion: Even Larger

18. Study Plan
The main short-term goal is to provide specifications for SF magnets.
Updated suggested plan of work:
Apply systematic multipoles only (ignore quadrupole multipole, no random multipoles and misalignments), provided by TAMU to all arc dipoles – Done
Since there are no quadrupole data, set limits on systematic multipoles for quadrupoles (no random multipoles and misalignments): find range of each multipole reducing the DA to 20 for 3 groups of quads – In progress
x,y > 1 km (mostly FFQs)
200 m < x,y < 1 km (mostly in chromaticity correction sections)
x,y < 200 m (arc quads)
Similarly set multipole limits for dipoles with x,y > 200 m (except quadrupole multipole) – In progress
Compare to existing data from RHIC, LHC, etc.
Develop injection lattice and repeat steps 1-3
Include all systematic multipoles (except quadrupole) and check DA
Study effect of each random multipole (including quadrupole) for the above groups of magnets (including all systematic multipoles except quadrupole), e.g. find each multipole rms value that on average reduces DA to 15 
Include systematic (except quadrupole) and random multipoles for all magnets using the limits obtained above and check the DA
Include misalignments and strengths errors and apply orbit, beta-beat, betatron tune, chromaticity, and coupling corrections

19. Multipole limit survey of large-beta dipoles
Multipoles
Normal: Systematic + Random
Skew: Systematic + Random

20. Multipole limit survey of large-beta dipoles3 4 5
20 σ of H & V: 2*(2.32, 0.46) 60 GeV 6 7 8

21. Multipole limit survey of large-beta dipoles
< 20 σ of H & V: 2*(2.32, 0.46) 60 GeV

22. Multipole limit survey of large-beta dipoles3 4 5
~35 σ of H & V: 3.5*(2.32, 0.46) 60 GeV 6 7 8

23. Multipole limit survey of large-beta dipoles
For all dipole
20 σ of H & V: 2*(2.32, 0.46) 60 GeV

24. Multipole limit survey of large-beta dipoles
Multipole errors of super-ferric dipole at radius 20 mm (unit: 10^-4)
multipole type
∆ 𝐵 1 𝐵 0
∆ 𝐵 2 𝐵 0
∆ 𝐵 3 𝐵 0
∆ 𝐵 4 𝐵 0
∆ 𝐵 5 𝐵 0
∆ 𝐵 6 𝐵 0
∆ 𝐵 7 𝐵 0
∆ 𝐵 8 𝐵 0
∆ 𝐵 9 𝐵 0
∆ 𝐵 10 𝐵 0
systematic
-0.151
-0.537
0.126
0.850
0.714
0.366
-0.464
-0.410
0.009
0.027
35sigma-plus
1.671E-01
3.193E-02
1.116E-02
1.750E-03
8.294E-04
1.054E-04
35sigma-minus
2.156E-01
2.810E-02
1.891E-02
1.494E-03
9.177E-05

25. Multipole limit survey of FFQ2 3 4
~35 σ of H & V: 3.5*(2.32, 0.46) 60 GeV 5 6 7

26. Multipole limit survey of FFQ8 9 10
~35 σ of H & V: 3.5*(2.32, 0.46) 60 GeV 11 12 13

27. Multipole limit survey of large-beta dipoles
20 σ of H & V: 2*(2.32, 0.46) 60 GeV

28. Multipole limit survey of FFQ
Multipole errors of super-ferric dipole at radius mm (unit: 1)
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
-5.14
E-06
-1.51
E-05
3.44
-2.72
-1.96
1.31
-1.24
6.79
-1.26
35sigma-plus
6.70
E-04
6.56
1.98
7.12
1.45
8.33
E-07
1.28
8.69
E-08
1.22
35sigma-minus
-3.80
-8.60
-1.75
-1.03
-1.28
-8.43
-1.11
-8.06
-1.09
Multipole errors of super-ferric dipole 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-07
-1.22
E-06
-1.42
35sigma-plus
9.97
E-09
1.26
8.65
E-10
35sigma-minus
-8.40
-1.13
-3.94

29. Summary
Multipole Limit Survey is studied for systematic multipole of FFQ and large beta dipole. Some of them seems too small, even 2~3 order smaller than Super-Ferric Data and PEP-II FFQ Data.
Multipole Limit Survey is based on emittance requirement, survey method, Lattice, and tune etc, which are also need to be modified.

30. Summary
Work next:
Survey whether a sextupole in the middle of a dipole is needed or not
Survey for magnet multipole data of LHC, RHIC, and Tevatron.
Finish the study plan of Multipole study

31. Thank you
F. Lin

32. LHC

33. LHC

34. Tune correction Tune correction (Tune measurement error < 0.001)
Tune error : < 0.1 % PC
data
Beam
Time
Gene-rator
Kicker
Pulse Mode
Pulse

35. Beta-beat correction Beta-beat correction: beta measurement
Fermilab Recycler Ring, Mar.2000
LHC: 2008; J-PARC: 2008

36. Beta-beat correction Beta-beat correction: beta measurement
Beta error at IP & Beta > 500 : < 1 %
Beta error at Beta < 500 : < 5 %

37. Beta-beat correction Beta-beat correction:
Matrix corrction (-I or SVD method)
This moment, I just use simple matching.

38. Chromaticity correction
Linear Chromaticity (+1, +1)
W function at IP = (0, 0)

39. Decoupling We can calculate the off-diagonal terms of
The optimum positions for four coupling correctors are at .