1. Studies on orbit corrections
error analysis
Cai Meng
Institute of High Energy Physics
Joint IHEP-IMP group on C-ADS accelerator physics

2. Main topics Alignment errors and rf errors
The correction scheme of Injector-I
The correction scheme of middle β spoke cavity section
Summary

3. Alignment errors and RF dynamics errors
The maximum cold misalignment of elements is 1 mm, which is larger than warm misalignment 0.4 mm. The maximum rotation angle is 2 mrad.
For the dynamic errors, the field amplitude error is 0.5% and the field phase error is 0.5 degree (reference to SNS).
Simulation code is TraceWin.
In the correction scheme, the BPMs uncertainty are 100 micron (um).
These errors are reasonable ?
Error
Tolerance
Distribution
cold element displacement
±1 mm
Uniform
warm element displacement
±0.4 mm
element rotation
±2 mrad
BPM uncertainty
0.1 mm
RF amplitude fluctuation
±0.5%
Gaussian
RF phase fluctuation
±0.5º

4. Preliminary correction scheme of Injector-I
The phase advance per period of Injector-I is about 40~90 degree, so there are a pair of correctors and BPMs in one period.
Considering the structure of Injector-I, the correctors are attached to solenoid and BPMs are installed in the drift between Spoke cavity and solenoid.

5. Spoke012 section with anti-symmetric lattice
Spoke012 section with anti-symmetric lattice in two cryomodule.
Different percent error means that percent of the maximum error. For example, 60% error is 0.6 mm element displacement and 1.2 mrad rotation angle, the rf dynamic error is unchanged.
Centroid orbit distribution of 100 linacs with different percent error.

6. Spoke012 section with the anti-symmetric lattice
Control the centroid orbit well
Under 0.35 mm(RMS), that means the maximum centroid displacement is about 0.7mm.

7. Spoke012 section with the anti-symmetric lattice
before correction
after correction
Average emittance (normalized rms emittance ) growth percent with different percent statistics errors (100 linacs) at the lattice end
After correction scheme, the transverse emittance growth is under 14 % and longitudinal emittance is under 10%
After correction scheme, there is no beam loss.

8. Spoke012 section with the anti-symmetric lattice

9. Spoke012 section with one cryomodule scheme
Correction scheme
RMS centroid orbit 0.4 mm, the maximum centroid orbit is about 0.8 mm

10. Spoke012 section with one cryomodule scheme
before correction
after correction
Average emittance (normalized rms emittance ) growth percent with different percent statistics errors (100 linacs) at the lattice end
After correction scheme, the transverse emittance growth is under 3 % and longitudinal emittance is under 8%

11. Spoke012 section with one cryomodule scheme

12. Spoke011T section with one cryomodule scheme
Maximum centroid orbit is about 0.8 mm

13. Spoke011T section with one cryomodule scheme
After correction scheme, the transverse emittance growth is under 5.7 % and longitudinal emittance is under 8.7%

14. Spoke011T section with one cryomodule scheme

15. Comparative correction results of Injectors
Maximum rms centroid orbit after correction is controlled under 0.4 mm
The maximum centroid displacement is smaller than 0.8 mm with the maximum errors.
Maximum rms centroid orbit(horizontal/vertical) (mm)
correction
Spoke012
two CM
one CM
Spoke011T
20% error
without
1/0.98
0.76/0.7
0.65/0.62
with
0.14/0.14
0.12/0.11
0.11/0.11
40% error
1.78/1.92
1.34/1.45
1.37/1.27
0.2/0.21
0.18/0.17
0.17/0.18
60% error
2.52/3.15
2.12/2.3
1.7/2.26
0.24/0.22
0.24/0.25
0.23/0.24
80% error
4.34/3.94
2.81/2.92
2.72/2.41
0.33/0.31
0.32/0.33
100% error
5.1/4.3
3.34/3.5
3.64/3.22
0.35/0.38
0.42/0.42
0.42/0.38

16. Comparative correction results of Injectors
Average emittance growth percent
Two CM scheme has larger emittance growth, especially transverse.
Average emittance growth percent
(x / y / z) (%)
correction
Spoke012
two CM
one CM
Spoke011T
20% error
without
11.9/11.8/5.95
1.78/1.84/5.47
4.1/4/ 4.92
with
11.3/11.1/5.04
1.38/1.72/ /4.3
4.03/3.84/4.83
40% error
14.1/ 13.8/ 9.6
2.9/3.03/9.11
4.3/4.6/6.2
11.6/11.5/5.65
1.74/1.76/4.69
4.14/4.1/5.2
60% error
16.8/16.9/15.7
4.19/4.57/13.7
4.8/4.7/8.2
12/12/6.46
1.86/2.13/5.56
4.6/4.4/6.1
80% error
24.3/24.2/29.5
5.92/6.89/19.3
5.8/ 5.7/11.3
12.7/12.7/8.1
2.24/ 2.5/6.25
5/4.8/7.1
100% error
31.4/32.2/41.4
8.08/10.2/27.5
6.8/ 6.9/15.8
13.8/13.8/9.8
2.78/3.08/7.83
5.6/5.4/8.7

17. Preliminary correction scheme of middle β spoke section
Spoke021 section with two cavities and one solenoid one period
Spoke040 section with four cavities and one solenoid one period
A pair of correctors and a BPM in one period
Spoke040 section: BPM maybe put in the drift between CMs

18. Preliminary correction scheme of middle β spoke section
Maximum centroid orbit is about 0.5mm

19. Preliminary correction scheme of middle β spoke section
After correction scheme, the transverse emittance growth is under 2 % and longitudinal emittance is under 11%
After correction, there is no beam loss.

20. Preliminary correction scheme of middle β spoke section

21. Summary
According to the phase advance of lattice, a pair of correctors and a BPM are put in one period for solenoid section. The correctors are attached to solenoid.
According to the results of centroid obit and emittance growth, the performance of one cryomodule scheme is better than two cryomodule scheme.
The correction scheme can control the centroid obit in 0.8 mm even with 1 mm misalignment of elements, meanwhile it can depress the emittance growth greatly.

22. Further work
Repeat the simulation with Track code to compare the results with TraceWin
Reduce the number of BPMs to study the correction scheme
Simulate detailed and overall error analysis
and so on…

23. Thanks for your attention !