1. Issues in CEPC pretzel and partial double ring scheme design
H.P. Geng, F. Su, Y.W. Wang, Y. Zhang, D. Wang , J. Gao, N. Wang, Y. Peng, X. Cui, Z. Duan, S. Bai, G. Xu, Q. Qin
IHEP, CAS, China
58th ICFA Advanced Beam Dynamics Workshop on High Luminosity Circular e+e- Colliders
Cockcroft Institute at Daresbury Laboratory, UK
October 24-27, 2016

2. Outline Introduction Pretzel scheme design
Partial double ring scheme design
Summary

3. Introduction
CEPC ( a Circular Electron Positron Collider) has been proposed by IHEP to study the Higgs boson
At the end of the 2014, the Preliminary Conceptual Design Report of CEPC was published, with single ring(pretzel) scheme as the baseline design
As the design work move on, especially the demand to increase the luminosity at Z-pole, we started to study a new scheme, e.g. so called “Partial double ring scheme”
Then, the RF system raised that the RF efficiency could be too low to assure a constant voltage at the cavity for every bunch, so another scheme called “Advanced double ring scheme” was proposed to mitigate the low RF efficiency effect
Another scheme, which is relatively less complicated but more costly, the double ring scheme, is also under study
The pretzel and partial double ring scheme will be introduced in this talk

4. Parameter for CEPC single and partial double ring （wangdou20160918）
Pre-CDR
H-high lumi.
H-low power W Z
Number of IPs 2
Energy (GeV)
120 80
45.5
Circumference (km) 54 61
SR loss/turn (GeV)
3.1
2.96
0.58
0.061
Half crossing angle (mrad) 15
Piwinski angle
1.88
1.84
5.2
6.4
Ne/bunch (1011)
3.79
2.0
1.98
1.16
0.78
Bunch number 50
107 70
400
1100
Beam current (mA)
16.6
16.9
11.0
36.5
67.6
SR power /beam (MW)
51.7
32.5
21.3
4.1
Bending radius (km)
6.1
6.2
Momentum compaction (10-5)
3.4
1.48
1.44
2.9
IP x/y (m)
0.8/0.0012
0.272/0.0013
0.275 /0.0013
0.1/0.001
Emittance x/y (nm)
6.12/0.018
2.05/0.0062
2.05 /0.0062
0.93/0.0078
0.88/0.008
Transverse IP (um)
69.97/0.15
23.7/0.09
9.7/0.088
9.4/0.089
x/IP
0.118
0.041
0.042
0.013
0.01
y/IP
0.083
0.11
0.073
0.072
VRF (GV)
6.87
3.48
3.51
0.74
f RF (MHz)
650
Nature z (mm)
2.14
2.7
2.95
3.78
Total z (mm)
2.65
3.35
4.0
HOM power/cavity (kw)
3.6
0.48
0.88
0.99
Energy spread (%)
0.13
0.087
0.05
Energy acceptance (%)
Energy acceptance by RF (%) 6
2.3
2.4
1.7
1.2 n
0.23
0.35
0.34
0.49
Life time due to beamstrahlung_cal (minute) 47 37
F (hour glass)
0.68
0.82
0.92
0.93
Lmax/IP (1034cm-2s-1)
2.04
2.01
4.3
4.48

5. Pretzel orbit design
60/60 degree phase advance FODO cells, with interleaved sextupoles
Designed for 50 bunches/beam, every 4pi phase advance has one collision point
Horizontal separation is adopted to avoid big coupling
No off-center orbit in RF section to avoid beam instability and HOM in the cavity
One pair of electrostatic separators for each arc
For each arc, the first separator will be placed before the first parasitic collision point in this region to generate the orbit, and the second separator will be placed after the last collision point in this region to remove the orbit

6. Issues with pretzel orbit
Beam with off centered orbit will see extra field in quadrupoles and sextupoles.
Estimation of dipole field strength in quadrupole
Dipole field of the ring 0.066T.
Estimation of quadrupole field strength in sextupole
Quadrupole field of the ring K1=0.022.
Dipole field of the ring 0.066T.
This will break the periodicity of the beta function, especially the dispersion function, thus degrade the dynamic aperture.

7. Correction of off-center-orbit effects
A new periodic solution can be found by grouping 12 FODO cells together as one new period
The maximum adjustment of quadrupole strength is ~X%
The distortion of pretzel orbit effects on beta and dispersion functions
can be mitigated by making quadrupoles individually adjustable, which can be done by adding shunts on each quadrupoles almost without increasing the cost

8. Lattice after correction of pretzel orbit effects
After correction, the orbit and dispersion function regains periodicity, but the beta functions still have some beating
We suspect the beta beating comes from the asymmetric layout of sextupoles relative to quadrupoles

9. DA w/ pretzel (no FFS)
We use a Multi-Objective optimization by Differential Evolution(MODE, developed by Y. Zhang) code to optimize the dynamic aperture
Before adding pretzel orbit, the DA is: dp/p, dp/p
After adding pretzel orbit, the DA is: dp/p, dp/p

10. Combination with FFS
One version of FFS (which has been optimized for the ring without pretzel orbit) is inserted to the lattice with pretzel
The betatron and dispersion functions of the FFS are shown in the left plot
The whole lattice of the ring is shown in the right plot
Courtesy of Yiwei Wang, by*=3mm

11. DA w/ pretzel and FFS
Dynamic aperture has been optimized with MODE, all sextupoles has been set free
DA (w/o pretzel) dp/p,~4sx/ dp/p
DA (w/ pretzel) dp/p,~6sx/ dp/p

12. CEPC Partial Double Ring Layout
The ring is locally doubled near the two IPs, beam at other parts of the ring will be the same as the one in the pretzel scheme, but without crossing over, so no separation will be needed

13. CEPC Partial Double Ring Layout
Beams are first separated by 12 electrostatic separators were, each has a length of 4.5m, and bends the beam by 62.5urad
Further separation is achieved by 4-6 dual core superconducting quadrupoles
After enough separation, the beams are bended with normal bending magnets
The full crossing angle at the IPs is : 30urad
Version 1.0.3
sufeng

16. Lattice design of IR region
Local chromaticity correction with sextupoles pairs separated by –I transformation
all 3rd and 4th resonance driving terms due to sextupoles almost cancelled
up to 3rd order chromaticity are corrected with main sextupoles, phase tuning and additional sextupoles
tune shift dQ(Jx, Jy) due to finite length of main sextupoles corrected with additional weak sextupoles
break down of –I, high order dispersion could be optimized with odd dispersion scheme or Brinkmann sextupoles MT
CCX
CCY FT IP
by Yiwei Wang
L*= 1.5m
x*= 0.22mm
y*= 1mm
GQD0= -200T/m
GQF1= 200T/m
LQD0=1.69m
LQF1=0.90m -I -I

17. Lattice of whole PDR ring
A lattice of the whole ring (ARC+PDR+IR) basically fulfilling the design parameters
Crab sextupoles haven’t been put in the lattice
by Yiwei Wang, Feng Su

18. DA study and optimization
Dynamic aperture study
Bare lattice
Synchrotron motion included
w/o and w/ damping
Tracking with around 1 times of damping time
Coupling factor =0.003 for y
Working point (0.08, 0.22)
Downhill Simplex algorithm applied
Achieved DA:
Further optimization is possible
Larger dispersion for IR sextupoles
y*= 1mm -> 1.3mm (new parameters)
More families in IR
Study of effects such as quantum excitation, solenoid field, errors and misalignments are under going
by Yiwei Wang

19. Summary
Several schemes for CEPC are understudy at IHEP, we updated the latest design results of single ring and partial double ring scheme here
A multi-objective code MODE has been developed, and proved to be very effective in optimizing dynamic aperture
The dynamic aperture of single ring has been greatly improved, but has not reached ±2% momentum spread
The dynamic aperture for partial double ring achieved momentum spread after turn damping on
Optimization work are still going on……

20. Thank you !