1. Optics Design of the CEPC Interaction Region
Yiwei Wang, Dou Wang, Sha Bai, Huiping Geng,
Feng Su, Tianjian Bian, Yingshun Zhu, Jie Gao, Gang XU
Accelerator Center, IHEP
CEPC2014, Shanghai 12 Sep 2014

2. Outline
Introduction
Optics Design of the Interaction Region for L*=2.5m
Primary Optics Design of the Interaction Region for L*=1.5m
Summary and Further Work

3. Introduction Functions of Interaction Region (IR) optics
Provide very small beta function to achieve very small beam size: βy*=1.2mm, σy*=0.16um, for CEPC
Correct large chromaticity due to small beta function: W~L*/ βy* IP FT
CCY
CCX MT
FT: final telescopic transformer
CCY: chromatic correction section Y
CCX: chromatic correction section X
MT: matching telescopic transformer
M=-I
M=-I
CEPC IR L*=1.5m, Sep 2014, by Yiwei Wang

4. Introduction
In the past several months we worked on a IR design for L*=2.5m
IR Optics and optimization dynamic aperture of whole ring
Dynamic aperture is small due to large chromaticity at final doublet which is difficult to well correct
Reduce chromaticity at final doublet by reducing L* from 2.5m to 1.5m
primary design for L*=1.5m due to time being

5. Optics Design of the Interaction Region (L*=2.5m)
Based on Yunhai Cai’s design
L*=2.5m
βx*=0.8m
βy*=1.2mm
entrance
βx*=75.6m
βy*=25.6m

6. Final Doublet lattice function (L*=2.5m)IP
L*=2.5m
Q1: L=0.56m, G=-516T/m
D2=1.14m
Q2: L=0.58m, G=364T/m

7. The tune dependence on the energy deviation

8. Dynamic Aperture (L*=2.5m)
Dynamic Aperture of the whole ring
Beam size at IP: 73.7m/0.16m ( 𝜎 𝑥 / 𝜎 𝑦 )
Working point: /206.22
Sextupole length in IR: 0.3m (0.4m for arc)
5x
3y
With IR
DA for 2%,-2% is 0

9. Dynamic Aperture (L*=2.5m)
transfer matrix to instead real arc In order to optimize the IR independent of the arc
Beam size at IP: 73.7m/0.16m ( 𝜎 𝑥 / 𝜎 𝑦 )
Sextupole length in FFS: 0.3m (0.4m for arc)
DA for 2%,-2% is 0
4y
By Dou Wang and
Demin Chou
5x

10. Optimization of the Bandwidth with Octupoles
Octupoles are placed beside each sextupoles
Octupole
Octupole
By Feng SU, Aug 2014

11. Optimization of the Bandwidth with Octupoles
By Feng SU, Aug 2014
K3=0
K3=15.5
DA for on momentum decreased
may due to too many octupoles
to optimize the number of octupoles and their positions

12. Optimize the bandwidth by adjusting working point
Idea from CERN people
After reaching the quadrupoles and sextupoles in the ARC, the tune changes, and the momentum bandwidth for x plane is more flat
By Sha BAI, Aug 2014

13. Optimize the bandwidth by adjusting working point
On momentum (dp=0)
Off momentum (dp=2%)
By Sha BAI, Aug 2014

14. Optimize the bandwidth by adjusting working point
After optimization the momentum bandwidth using the quadrupoles and sextupoles in the Ring, the dynamic aperture in the phase space seems no change.
strong chromatic aberrations in the IR should be the main reason
should go back to optimize the IR

15. Primary IR optics with L*=1.5m (1)
betx*=0.8m, bety*=1.2mm, L*=1.5m
Yiwei Wang, 3 Sep 2014 IP FT
CCY
CCX MT
FT: final telescopic transformer
CCY: chromatic correction section y
CCX: chromatic correction section x
MT: matching telescopic transformer

16. Final Telescopic TransformerQ1 Q2 IP
L*(D1) =1.5m
Q1: L=0.76m, G=-400T/m
D2=2.45m
Q2: L=0.42m, G=283T/m

17. Optics of whole ring
IR+ARC

18. Dynamic Aperture Dynamic Aperture of the whole ring
Designed Beam size at IP: 74m/0.16m ( 𝜎 𝑥 / 𝜎 𝑦 )
Working point: 0.08/0.22
On momentum
69 𝜎 𝑦
Off momentum:
2%,  1%
14 𝜎 𝑥

19. Primary IR design for L*=1.5m (2)
Yiwei Wang, 11 Sep 2014 IP FT
CCY
CCX MT
L*=1.5m
βx*=0.8m
βy*=1.2mm
entrance
βx*=75.6m
βy*=25.6mm
CEPC IR L*=1.5m, Sep 2014, by Yiwei Wang

20. Final Doublet lattice function (L*=1.5m)IP
L*=1.5m
Q1: L=1.25m, G=-300T/m
D2=0.5m
Q2: L=0.72m, G=300T/m

21. Chromatic Correction
with total 4 sextupoles in the chromatic correction
For the first try, zero length of sextupoles are used to neglect the finite length effect.
bandwidth of horizontal plane quite good but vertical plane need to be optimized
β* vs. 𝐸/𝐸

22. Final Doublet Beam stay-clear region Rx=5 σx_inj, Ry=5 σy_inj
x_inj=21.8nm, y_inj=2.2nm (assume 10% coupling for injection beam)
Inner radius of vacuum chamber at Q1 and Q2: 1.3cm IP Q1 Q2
[m]
L*=1.5m
Q1: L=1.25m, Rin=1.3cm, G=-300T/m, Rout=20cm, Lact=1.6m
D2=0.5m
Q2: L=0.72m, Rin=1.3cm, G=300T/m, Rout=20cm, Lact=1.05m
vacuum chamber Ry Rx
Out aperture of quadrupoles
estimated by Yingshun Zhu

23. Final Doublet Beam stay-clear region (L*=2.5m)
Rx=5 σx_inj, Ry=5 σy_inj
x_inj=21.8nm, y_inj=2.2nm (assume 10% coupling for injection beam)
Inner radius of vacuum chamber at Q1 and Q2: 1.8cm IP Q1 Q2
[m]
vacuum chamber
L*=2.5m
Q1: L=0.56m, R=1.8cm, G=-516T/m
D2=1.14m
Q2: L=0.58m, R=1.8cm, G=364T/m Ry Rx

24. Primary IR design for L*=1.5m
get a primary IR optics design for L*=1.5m due to time being
The work on dynamic aperture with IR in undergoing.

25. Summary
Several method to optimizing dynamic aperture for the IR Optics L*=2.5m have been tried
transfer matrix to instead real arc In order to optimize the IR independent of ARC
Optimization of bandwidth with Octupoles
Optimize the bandwidth by adjusting working point
Dynamic aperture is small due to large chromaticity at final doublet which is difficult to well correct
Reduce chromaticity at final doublet by reducing L* from 2.5m to 1.5m
primary design for L*=1.5m due to time being
The work on dynamic aperture with IR in undergoing.

26. Further Work
Further optimize IR bandwidth with transfer matrix for the ARC
Further optimize the aperture with IR and ARC together

27. Reserved

28. CEPC Dynamic Aperture (ARC only)
Dynamic Aperture of the ring with ARC only
IR optics is replaced by the straight section with same length
Working point: /206.22
On momentum
509.3σy
59.2σx
1%，-1%
2%,-2%的孔径是0
Without FFS

29. CEPC lattice with IR In this design: Circumference: 52.1 km
16*arcs: 2.64 km (60 FODO)
12*short straight: 352m (8 FODO)
4*long straight: ~700 m
Bending radius: 5.7 km
U0: 3.77GeV
Nature emittance: 7.67 nm
Nature energy spread: 0.19%
Nature bunch length : 2.82mm
Momentum compaction: 3.3E-5

30. Treat arcs as transfer matrix
Calculate transfer matrix for arc1 and arc2 by SAD.
Join the real lattice for IP1 and IP3 with the matrix of two arcs.
Track DA by SAD for the faked ring (240 turns).
two “point” cavities at IP2 and IP4