1. Multipole Limit Survey of Large-beta Dipoles
G.H. Wei, V.S. Morozov, Fanglei Lin
JLEIC Meeting, JLab, Nov 30, 2015
F. Lin

2. Contents Review JLEIC lattice, Error types, Purpose of error study
Misalignment, strength error and correction
Multipoles of Super-Ferric Dipole
Dynamic Aperture Study with Multipole error of Super-Ferric Dipole
Study Plan
Multipole limit survey of large-beta dipoles
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. Purpose of error study static errors : independent on time
Misalignment, strength error of magnets;
Multipoles of magnets (systematic & random error)
Give requirement on misalignment
Give requirement on multipole error of magnets
Get influence to dynamic aperture, Ext: IP
dynamic errors: dependent on time
Noise signal of BPM
Field jitter of magnets
Give requirement on BPM noise and magnet jitter

8. 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

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

10. Closed Orbit Distortion and correction
+10-4
-10-4
5*10-6
5*10-6

11. 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

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

13. 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

14. 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

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

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

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

18. The limit comes from injection
For Proton: σ > 30 times
For ion: Even Larger

19. 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

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. Thank you
F. Lin

26. LHC

27. LHC

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

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

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

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

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

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