1. First Look at Error Sensitivity in MEIC
G. Wei, V.S. Morozov, Fanglei Lin
MEIC Accelerator R&D Meeting, JLab, Aug 20, 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. Why do we need error study?
Error study can give information of dynamic
aperture and beam loss information
For different lattices: a judgment
For a lattice: make a vivid
integration between physics
design and hardware
suitable error for my castle
Which one has the

4. Why do we need error study?
For a lattice:
Tolerances of misalignment, strength error of magnets, multipole field error of magnets
noise level of monitors, RF system error
Corrector & BPM equipment modification
Coupling compensation
Injection acceptance shrinking
Dynamic Aperture shrinking in ramping
Luminosity reduction
...

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

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

7. 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 %

8. Lattice used for error study
Dynamic Aperture of tune scan

9. Lattice used for error study
Tune Survey

11. Lattice used for error study
Tune: (25.22, 23.16)

12. 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

13. Steps of error study 1(Dipole) 0.1(Q&S) 0.3(Dipole) 0.5(Q&S) 0.1(D&Q)
Misalignment: mm
Tilted angle: mrad
Strength Error: 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)

14. Multipole specification
Steps of error study
Multipole specification
10-4
PEP-II Y
KEKB N
SuperB
NSLS-II
RHIC
J-PARC

15. 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

16. 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

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

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

19. 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.

20. 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

21. slac-r-418a-PEPII: PEPII CDR June 1993
Multiple errors of PEPII
are used in our study.
Those data is also used
for error study by Yuri
& Ming-huey on a –I lattice

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

23. 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(%)

24. 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 %

25. Summary
CCB lattice-July has better dynamic aperture at ΔP/P=+0.3 % than CCB lattice-June. And dynamic aperture maps of tune scan has been studied. Finally CCB lattice-July with tune (25.22, 23.16) is used for error study.
Steps of error study:
Basic errors study to get a limit toleration and suggestion values for magnet error and alignment considering shrinking of dynamic apertures.
Multipole error of normal magnets & FFQ
Coupling, RF Error in ramping time
Other things: injection DA, collective effect, collision

26. Summary
Closed orbit oscillation mainly caused by X&Y misalignment of Quadrupole, K0 error of dipole, & longitudinal misalignment of dipole.
Dynamics aperture shrinking mainly caused by K1 error of Quads, Tilt error of Quads, X&Y misalignment of Sextupoles, X&Y misalignment of Quadrupoles
With basic error, Dynamics aperture shrinking: 28 %
Basic error 3 % + Multipole 10 % + FFQ 15 %
With basic error ×2 , DA shrinking: 40 %
Basic error 10 % + Multipole 10 % + FFQ 20 %

27. Summary
During to rough study, follow errors are good to our design. And two times of those errors are acceptable, but may be near the limit tolerance according to CCB lattice-July and baseline of dynamic aperture at IP
Dipole
Quad
Sext
FFQ
BPM(noise)
Corrector
x misalignment(mm)
0.1
0.01
0.02 -
y misalignment(mm)
x-y rotation(mrad)
0.05
s misalignment(mm)
Strength error(%)

28. Summary
Corrector and BPM design, matching of twiss, tune, chromaticity and decoupling should be done for error study. Suggested by Yuri Nosochkov (SLAC) 
Multipole error of PEP II magnets are used in our study. warm magnets <>super conduction magnets
Measured field or 3D simulating field of MEIC
magnets is wanted. (CODE: TOSCA/ELEKTRA?)
RF error is considered for next step. Multiple thin gaps of RF system or RF electric field map is wanted.
For deep study with more seeds, Using Pelegant CODE on a supercomputer is needed. For Personal PC, 1 seed ~ 1 hour, totally > 10,000 seeds

29. Summary
Works next:
Deep study to get limit toleration and suggestion values for magnet error and misalignment
Corrector & BPM design for COD correction
Decoupling design with skew quadrupoles
Modification of CCB lattice
RF error
Study of DA and other items in energy ramping
Electron ring, collective effect, & collision