1. Error Sensitivity in MEIC
G. Wei, V.S. Morozov, Fanglei Lin
MEIC R&D Meeting, JLab, Sep 15, 2015
F. Lin

2. Contents Why do we need error study Lattice used for error study
Steps of error study
Error study of misalignment, strength error, BPM noise
Error study of multipole field error of magnets
Error study of FFQ (Final Focus Quadrupole)
Summary & Questions

3. Lattice used for error study
For Vasiliy, I got two CCB lattices
CCB lattice-June18
CCB lattice-July28

4. Lattice used for error study
For Vasiliy, I got two CCB lattices
CCB lattice-June18
CCB lattice-July28

5. Lattice used for error study
Dynamic Aperture of ΔP/P (-0.3%, +0.3%)
CCB lattice-July28 has better DA at ΔP/P = +0.3 %

6. Steps of error study
With a survey of error studies of PEP-II, KEKB, SuperB, NSLS-II, RHIC, and J-PARC, and comments given by Yuri and Mike, etc, an error study is started for the MEIC ion ring.
Steps:
Basic errors study on strength error of normal magnets, misalignment, BPM noise, to get a limit toleration for magnet error and alignment
Multipole error of normal magnets & FFQ
Coupling, RF Error in ramping time
4. Other things: injection DA, collective effect, collision

7. Steps of error study Basic error in step 1:
Magnet: misalignment of 3-D, x-y rotation, and strength error
FFQ: error neglected in the initial study, to keep (x=x’=0 & y=y’=0) & nonlinear IP
FFQ in KEKB study: 10 % of normal Quads
IPAC14’ MOPRO005, V.S. Morozov,etc

8. Steps of error study
BPM: only noises of X and Y direction Considering calibration and beam based alignment
Corrector: only x-y rotation error & jitter error of strength. only kicker function, no multipole error
Error: Gaussian distributions with a cut-off at 3 standard deviations.
Dipole
Quadrupole
Sextupole
BPM(noise)
Corrector
x misalignment(mm)
0.1
0.02 -
y misalignment(mm)
x-y rotation(mrad)
s misalignment(mm)
Strength error(%)
0.01

9. Before Correction, Basic error
After Correction, Basic error
Before Correction, Basic error ×2
After Correction, Basic error ×2

10. Error study of misalignment, strength error, BPM noise

11. Error study of misalignment, strength error, BPM noise
Closed orbit oscillation mainly caused by:
Q X&Y misalignment
K0 error of dipole
Longitudinal misalignment of dipole.

12. Error study of misalignment, strength error, BPM noise
Dynamic aperture shrinking mainly caused by:
K1 error of Quads
Tilt error of Quads
X&Y misalignment of Sextupoles
X&Y misalignment of Quadrupoles
1. & 3.  twiss, tune, & chromaticity matching
2.  decoupling

13. slac-r-418a-PEPII: PEPII CDR June 1993
Multiple errors of PEPII
are used in the study.

14. Error in ELEGANT
The magnet multipole tolerance is defined relative to the field component normalized at a reference radius r: ( By Min-Huey Wang)
∆ 𝐵 𝑛 𝐵 𝑁 = (𝑁−1)! 𝐵 (𝑛−1)′ (𝑛−1)! 𝐵 (𝑁−1)′ 𝑟 𝑛−𝑁 , 𝐵 (𝑛−1)′ = 𝜕 𝑛−1 𝐵 𝜕 𝑛−1 𝑥
Multipole errors of dipole at radius 30 mm
multipole type
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
systematic
1.0e−5
Random
3.2e−5
6.4e−5
8.2e−5
Multipole errors of quadrupole at radius 44.9 mm
∆ 𝐵 3 𝐵 2
∆ 𝐵 4 𝐵 2
∆ 𝐵 5 𝐵 2
∆ 𝐵 6 𝐵 2
∆ 𝐵 10 𝐵 2
∆ 𝐵 14 𝐵 2
1.03e−3
5.6e−4
4.8e−4
2.37e−3
-3.10e−3
-2.63e−3
3.2e−4
4.5e−4
1.9e−4
1.7e−4
1.8e−4
7.0e−5
Multipole errors of sextupole at radius mm
∆ 𝐵 5 𝐵 3
∆ 𝐵 7 𝐵 3
∆ 𝐵 9 𝐵 3
∆ 𝐵 15 𝐵 3
−1.45e−2
−1.3e−2
2.2e−3
1.05e−3

15. Multipole errors of quadrupole at radius 44.9 mm
Error in ELEGANT
The magnet multipole tolerance is defined relative to the field component normalized at a reference radius r: ( By Min-Huey Wang)
∆ 𝐵 𝑛 𝐵 𝑁 = (𝑁−1)! 𝐵 (𝑛−1)′ (𝑛−1)! 𝐵 (𝑁−1)′ 𝑟 𝑛−𝑁 , 𝐵 (𝑛−1)′ = 𝜕 𝑛−1 𝐵 𝜕 𝑛−1 𝑥
ELEGANT Quadrupole & Sextupole: 𝑎 𝑛 = 𝐾 𝑛 𝑟 𝑛 /(𝑛)! 𝐾 𝑚 𝑟 𝑚 /(𝑚)!
Multipole errors of quadrupole at radius 44.9 mm
multipole type
∆ 𝐵 3 𝐵 2
∆ 𝐵 4 𝐵 2
∆ 𝐵 5 𝐵 2
systematic
1.03e−3
5.6e−4
4.8e−4
Random
3.2e−4
4.5e−4
1.9e−4
∆ 𝐵 6 𝐵 2
∆ 𝐵 10 𝐵 2
∆ 𝐵 14 𝐵 2
2.37e−3
-3.10e−3
-2.63e−3
1.7e−4
1.8e−4
7.0e−5

16. Multipole errors of dipole at radius 30 mm
Error in ELEGANT
The magnet multipole tolerance is defined relative to the field component normalized at a reference radius r: ( By Min-Huey Wang)
∆ 𝐵 𝑛 𝐵 𝑁 = (𝑁−1)! 𝐵 (𝑛−1)′ (𝑛−1)! 𝐵 (𝑁−1)′ 𝑟 𝑛−𝑁 , 𝐵 (𝑛−1)′ = 𝜕 𝑛−1 𝐵 𝜕 𝑛−1 𝑥
ELEGANT Dipole:
Multipole errors of dipole at radius 30 mm
multipole type
∆ 𝐵 3 𝐵 1
∆ 𝐵 4 𝐵 1
∆ 𝐵 5 𝐵 1
∆ 𝐵 6 𝐵 1
systematic
1.0e−5
Random
3.2e−5
6.4e−5
8.2e−5
𝑏 𝑛 = (𝑛)! 𝑟 𝑛 ∆ 𝐵 𝑛+1 𝐵 1

17. Error study of multipole field error
Baseline of Dynamic Aperture at IP
10 σ of X & Y beam sizes

18. Error study of FFQ
According to error study in KEKB, follow errors of Final Focus Quadrupole (FFQ) are used in error study
Normal Quadrupole
FFQ
x misalignment(mm)
0.1
0.01
y misalignment(mm)
x-y rotation(mrad)
0.05
s misalignment(mm)
Strength error(%)

19. Error study of FFQ Dynamic aperture shrinking
Basic error ~ 3 %
Multipole error ~ 10 %
FFQ error ~ 15 %
Dynamic aperture shrinking
Basic error ~ 10 %
Multipole error ~ 10 %
FFQ error ~ 20 %

22. Lattice –I from SLAC
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%

23. Lattice –I from SLAC
Δp/p=0
Δp/p= 0.3%
Δp/p=-0.3%

24. error considered
Magnet: misalignment of 3-D, x-y rotation, strength error, BPM noise
Multipole error
FFQ error
Only orbit correction

25. Lattice –I from SLAC With error & orbit correction Δp/p=0 Δp/p= 0.3%

26. Summary error considering:
Magnet: misalignment of 3-D, x-y rotation, strength error, BPM noise
Multipole error
FFQ error
CCB lattice-July & Non-interleaved –I lattice have been studied with errors and only orbit correction

27. Summary Works next (considering Min-Huey’s ErrorCorrectionScheme):
Decoupling design with skew quadrupoles
Correct beta beat in both planes
Correct vertical dispersion ? Only in IP area?
Correct chromaticity ? W function or only ξx ξy ?
correct tune