1. CEPC optics and booster optics
Workshop on the Circular Electron-Positron Collider - EU edition
CEPC optics and booster optics
Dou Wang
on behalf CEPC AP group
May 24~26, Rome, Italy.

2. Outline Introduction Optics for collider ring Optics for booster
Summary

3. Introduction Injection energy: 10GeV
100km
Injection energy: 10GeV
10 GeV linac provides electron and positron beams for booster.
Top up injection for collider ring ~ 3% current decay
Booster is in the same tunnel as collider ring, above the collider ring.
Double ring collider with 2 IPs, crab-waist collision
Collider ring adopt twin-aperture quadrupoles and dipoles in the ARC

4. CEPC CDR Parameters Higgs W Z（3T） Z（2T） Number of IPs 2
Higgs W
Z（3T）
Z（2T）
Number of IPs 2
Beam energy (GeV)
120 80
45.5
Circumference (km)
100
Synchrotron radiation loss/turn (GeV)
1.73
0.34
0.036
Crossing angle at IP (mrad)
16.5×2
Piwinski angle
2.58
7.0
23.8
Number of particles/bunch Ne (1010)
15.0
12.0
8.0
Bunch number (bunch spacing)
242 (0.68s)
1524 (0.21s)
12000 (25ns+10%gap)
Beam current (mA)
17.4
87.9
461.0
Synchrotron radiation power /beam (MW) 30
16.5
Bending radius (km)
10.7
Momentum compact (10-5)
1.11
 function at IP x* / y* (m)
0.36/0.0015
0.2/0.0015
0.2/0.001
Emittance ex/ey (nm)
1.21/0.0031
0.54/0.0016
0.18/0.004
0.18/0.0016
Beam size at IP sx /sy (m)
20.9/0.068
13.9/0.049
6.0/0.078
6.0/0.04
Beam-beam parameters x/y
0.031/0.109
0.013/0.106
0.0041/0.056
0.0041/0.072
RF voltage VRF (GV)
2.17
0.47
0.10
RF frequency f RF (MHz) (harmonic)
650 (216816)
Natural bunch length z (mm)
2.72
2.98
2.42
Bunch length z (mm)
3.26
5.9
8.5
HOM power/cavity (2 cell) (kw)
0.54
0.75
1.94
Natural energy spread (%)
0.1
0.066
0.038
Energy acceptance requirement (%)
1.35
0.4
0.23
Energy acceptance by RF (%)
2.06
1.47
1.7
Photon number due to beamstrahlung
0.29
0.35
0.55
Lifetime _simulation (min)
Lifetime (hour)
0.67
1.4
4.0
2.1
F (hour glass)
0.89
0.94
0.99
Luminosity/IP L (1034cm-2s-1)
2.93
10.1
16.6
32.1

5. Collider ring optics-IR
Crab-waist scheme* with local chromaticity correction
L*=2.2m, C =33mrad, GQD0 =136T/m, GQF1 =111T/m, LQD0 =2.0m, LQF1 =1.48m
Asymmetric IR layout (ref to: K. Oide, ICHEP16).
IP upstream: Ec < 120 keV within 400m, last bend Ec = 45 keV
IP downstream: Ec < 300 keV within 250m, last bend Ec = 97 keV
up to 3rd order chromaticity, 3rd and 4th order RDT, 1st order tune shift corrected
Break down of -I due to energy deviation corrected with ARC sextupoles
*M. Zobov et al.， Test of “Crab-Waist” Collisions at the DAΦNE Φ Factory, Phys. Rev. Lett. 104, (2010)

6. Collider ring optics-ARC
Distance of two ring is 0.35m to adopt twin-aperture Q & B magnets (save power & cost).
FODO cell, 90/90, non-interleaved sextupole scheme

7. Collider ring optics-RF
Common cavities for Higgs mode, bunches filled in half ring for e+ and e-.
An electrostatic separator combined with a dipole magnet - bend only one beam (ref: K. Oide, ICHEP16)
Dedicated small beta function to reduce the multi-bunch instability caused by RF cavities
Independent cavities for W & Z mode, bunches filled in full ring.
The outer diameter of RF cavity is 1.5m. Distance of two ring is 1.0m.
Z mode:
Bunch spacing > 25ns
Separator
Esep=1.8 MV/m , Lsep=50m

8. Collider ring optics-injection
Independent magnets for two rings
0.3m of longitudinal distance between two quadrupoles of two rings.
Phase tuning
Injection
x=600 m at injection point for off-axis injection
Injection section 66.7 m

9. Injection scheme Off-axis injection with horizontal bump
On-axis injection in vertical plane with vertical local bump

10. DA optimization
Multi-objective optimization based on differential evolution algorithm (MODE)
SAD is used
Track for a transverse damping time
10 IR sexts + 32 arc sexts +8 phase
(Max. free various=254)
RF ON (SR oscillation)
Damping at each element
Radiation fluctuation ON (100 samples)
Sawtooth on with tapering
Crab waist=100%
Coupling=0.26%
Higgs
Coupling=0.3% W
Coupling=2.2%
DA requirement 
Higgs W Z
with on-axis injection
8x 12y1.35% -
with off-axis injection
13x12y1.35%
15x 9y0.4%
17x 9y0.23% Z

11. Collider ring error study-1
LOCO based on AT is used to correct COD, beta, dispersion and coupling.
Tracking DA by SAD.
About 1500 BPMs, 1500 horizontal correctors and 1500 vertical correctors are placed in the collider ring. (4 per betatron wave)
Correction steps:
1/5 quadrupole (~600 of 3000 quadrupoles) for optics correction
About 200 Skew-quads (1/5 sextupoles) are used in the coupling correction
Component
x (mm)
y (mm)
z (mrad)
Dipole
0.05
0.1
Quadrupole
w/o FF
0.03
Sextupole
1. correct COD w/o sextupoles
2. correct optics w/ sextupoles
3. correct coupling
Component
Field error
Dipole
0.01%
Quadrupole (w/o FF)
0.02%

12. Collider ring error study-2
Residual COD  30 um (x) after orbit correction
Residual COD  50 um (y) after orbit correction
(βxy_err/βxy)max =0.01 after optics correction except for the IR region
Coupling=0.15% after coupling correction

13. Higgs DA with errors Misalignment Nominal field errors (B/Q)
W/O errors
W errors & corrections
Misalignment
Nominal field errors (B/Q)
After corrections
Coupling=0.26%
Higgs DA
Requirement 
Realize
on-axis injection
8x 12y
1.35%
16x15y
1.5%
off-axis injection
13x12y

14. Booster parameters @ injection (10GeV)H W Z
Beam energy
GeV 10
Bunch number
242
1524
6000
Threshold of single bunch current A
25.7
Threshold of beam current
(limited by coupled bunch instability) mA
127.5
Bunch charge
 nC
0.78
0.63
0.45
Single bunch current
2.3
1.8
1.3
Beam current
0.57
2.86
7.51
Energy spread %
0.0078
Synchrotron radiation loss/turn
keV
73.5
Momentum compaction factor
10-5
2.44
Emittance nm
0.025
Natural chromaticity
H/V
-336/-333
RF voltage MV
62.7
Betatron tune x/y/s
263.2/261.2/0.1
RF energy acceptance
1.9
Damping time s
90.7
Bunch length of linac beam mm
1.0
Energy spread of linac beam
0.16
Emittance of linac beam
40~120

15. Booster parameters @ extractionH W Z
Off axis injection
On axis injection
Beam energy
GeV
120 80
45.5
Bunch number
242
235+7
1524
6000
Maximum bunch charge nC
0.72
24.0
0.58
0.41
Maximum single bunch current A
2.1 70
1.7
1.2
Threshold of single bunch current
300
Threshold of beam current
(limited by RF power) mA
1.0
4.0
10.0
Beam current
0.52
2.63
6.91
Injection duration for top-up (Both beams) s
25.8
35.4
45.8
275.2
Injection interval for top-up
73.1
153.0
438.0
Current decay during injection interval 3%
Energy spread %
0.094
0.062
0.036
Synchrotron radiation loss/turn
1.52
0.3
0.032
Momentum compaction factor
10-5
2.44
Emittance nm
3.57
1.59
0.51
Natural chromaticity
H/V
-336/-333
Betatron tune x/y
263.2/261.2
RF voltage GV
1.97
0.585
0.287
Longitudinal tune
0.13
0.10
RF energy acceptance
1.8
Damping time ms 52
177
963
Natural bunch length mm
2.8
2.4
1.3
Injection duration from empty ring h
0.17
0.25
2.2

16. Booster optics - ARC 90/ 90 FODO cell Dispersion suppressor
2 booster = 3 collider
FODO length: 101m
Noninterleave sextupole scheme
Dispersion suppressor
- two standard FODO cell
- adjust bend strength- match the geometry of collider ring
Dispersion suppressor
FODO cell

17. Booster optics - RF
Booster RF straight section at the same location as collider ring
Low average beta to reduce the multi-bunch instability by RF cavities
- 90/ 90 FODO cell
- Average beta: 30 m
- Space between quadrupoles :12m
RF section

18. Booster optics – IR bypass
In CEPC detector region, booster bypasses the collider ring from the outer side.

19. Booster geometry
Booster has almost same geometry as collider ring except for the two IRs.
ARC: booster is in between the two beams of collider ring, error=0.17m
-- precision of element length: ~10-5 m
-- precision of dipole angle: ~10-7 rad
IR: separation between detector center and booster: ~25 m

20. Booster DA 10GeV 120GeV BSC w damping DA requirement DA results H V
Parameters
Dipole
Quadrupole
Sextupole
BPM (10Hz)
Transverse shift x/y (μm) 50 70
Accuracy (m)
110-7
Longitudinal shift z (μm)
100
150
Tilt (mrad) 10
Tilt about x/y (mrad)
0.2
Gain 5%
Tilt about z (mrad)
0.1
Offset after BBA(mm)
3010-3
Nominal field
310-4
210-4
10GeV
120GeV
BSC
w damping
DA requirement
DA results H V
10GeV (x= y =120nm)
4x +5mm
4y +5mm
7.7x +5mm
14.3y +5mm
120GeV (x=3.57nm, y= x*0.003)
6x +3mm
16y +3mm
21.8x +3mm
1006y +3mm

21. Eddy current effect
During ramping, parasitic sextupole field is induced in dipoles due to eddy current.
Ramping rate is limited by eddy current effect.
Dedicated ramping curve to control the maximum K2.
Maximum K2= (m-3)
Chromaticity distortion needs to be corrected during ramping.
Dynamic chromaticity correction and dynamic DA is under studying.

22. Low field dipole magnets
Challenges:
Solutions in CDR
Field error <29Gs*0.1%=0.029Gs  how to design
Field reproducibility <29Gs*0.05%=0.015Gs  how to measure
The Earth field ~ Gs, the remnant field of silicon steel lamination ~ 4-6 Gs.
With magnetic core (better material)
Without magnetic core
(Twice excitation current)
Thinking beyond CDR
Wiggler dipole scheme
Combine the magnets with core and without core …

23. Summary
Linear optics of the CEPC collider ring fulfill requirements of the parameters, geometry, photon background and key hardware.
DA of collider ring can fulfill the requirements with limited errors. Further study with errors & corrections is going on.
The design of booster optics and geometry fulfill the requirements. Error effects in the booster are tolerable.
Eddy current effect in booster is a new issue which is under studying.
Low field problem still the bottleneck for booster design. Both technical solutions and physical solutions will be explored.