23-27 Sep 2015 1

The IR lattice design and optimization of the dynamic aperture for the ring

Yiwei Wang, Huiping Geng, Yuan Zhang, Sha Bai, Dou Wang, Tianjian, Jie Gao

Institute of High Energy Physics (IHEP, Beijing)

CEPC workshopIHEP, 11-12 Sep 2015

Yiwei Wang

23-27 Sep 2015 2

Outline

• CEPC layout• Lattice design of the Interaction region• Optimization of the dynamic aperture• Summary

Yiwei Wang

23-27 Sep 2015 3

CEPC layout

P.S.

P.S. P.S.

IP1

IP4

IP3

IP2D = 17.3 km

½ RF

RF

RF

RF

RF

½ RF

½ RF

½ RF

RF RF

One RF station: • 650 MHz five-cell

SRF cavities;• 4 cavities/module• 12 modules, 8 m

each• RF length 120 m

C = 54 km

IP1 and IP3 for CEPC

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23-27 Sep 2015 4

CEPC parameters

Yiwei Wang

Parameter Unit Value Parameter Unit Value

Beam energy [E] GeV 120 Circumference [C] m 54752

Number of IP[NIP] 　 2 SR loss/turn [U0] GeV 3.11

Bunch number/beam[nB] 　 50 Bunch population [Ne] 　 3.79E+11

SR power/beam [P] MW 51.7 Beam current [I] mA 16.6

Bending radius [r] m 6094 momentum compaction factor [ap] 　 3.36E-05

Revolution period [T0] s 1.83E-04 Revolution frequency [f0] Hz 5475.46

emittance (x/y) nm 6.12/0.018 bIP(x/y) mm 800/1.2 (3.0)

Transverse size (x/y) mm 69.97/0.15 xx,y/IP 　 0.118/0.083

Beam length SR [ss.SR] mm 2.14 Beam length total [ss.tot] mm 2.88

Lifetime due to Beamstrahlung min lifetime due to radiative Bhabha scattering [tL]

min 52

RF voltage [Vrf] GV 6.87 RF frequency [frf] MHz 650

Harmonic number [h] 　 118800 Synchrotron oscillation tune [ns] 　 0.18

Energy acceptance RF [h] % 5.99 Damping partition number [Je] 　 2

Energy spread SR [sd.SR] % 0.132 Energy spread BS [sd.BS] % 0.119

Energy spread total [sd.tot] % 0.177 ng 　 0.23

Transverse damping time [nx] turns 78 Longitudinal damping time [ne] turns 39

Hourglass factor Fh 0.658 Luminosity /IP[L] cm-2s-1 2.04E+34

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Interaction region design

• As shown in beam-beam simulation, the luminosity are almost the same when y* increased from 1.2 mm to 3 mm.

• For the first try, we just refit the final transformer.– the parts other than FT are almost kept

L*=1.5my*=1.2mm

Yiwei Wang

L*=1.5my*=3mm

Design principle of final doublet• constraint R22=0, R44=0 at the exit of QF1

– point to parallel image on both x and y planes

– The real design just adjust the gradient a bit (less than 10%)

L* dl1 l2

QD0 QF1

L*, d, G1, G2y, x, R, B1, B2 y*, x*, ay, ax

l1, l2our main concern

Optimization of final doublet

L*=1.5m, G1=G2

• When G>200T/m– y decrease slowly with the increase of G– B increase almost linearly with G and independent of the space between

QD0 and QF1• Seems possible to reduce the gradient from 300T/m to 200T/m

– y slightly increased from -148 to -149 and B significantly decreased from 6.4 to 4.5 T with ay (7.88*10^-8 mrad) used in the pre-CDR

– With a more optimistic ay (5.33*10^-8 mrad), B could be further reduce to be 3.9 T

– need to check with a full IR lattice. At present we still work with G=300T/mL*=1.5m, G1=G2

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Local chromaticity correction• Add additional sextupoles next to the main one*

– Compensate the finite length effect (Lsext=0.3m)

Yiwei Wang

*A.Bogomyagkov et al.http://arxiv.org/abs/0909.4872

k=1, S1/S2=-0.1

• Adjust the phase advances between the final doublet and the sextupoles to minimize second order chromaticity – QD0 and VS1– QF1 and HS1

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Local chromaticity correction (cont.)

• residual functions are =6.6, =5.6 and second order dispersion is =-0.15 m

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23-27 Sep 2015 10

Lattice of the whole ring• Close the whole ring

– matching linear lattice function

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Dispersion suppressor and FODO cell in the ARC

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Tune vs. momentum deviation

• Adjust the tune to be .08/.22 (x/y)– determined by beam-

beam study• match Q’ to be ~0.5 with

the sextupoles in the ARC– Currently only 2 family

of sextupoles in the ARC

• Good region of ±1% in Dp/p

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23-27 Sep 2015 12

Dynamic aperture for the ring• without radiation damping, error of the magnets• Synchrotron motion included• Tracking with 3 times of damping time• Coupling factor =0.003 for emitty

– -2% (2x , 20y), 2% (1x , 7y)

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Result in Pre-CDR

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Optimization of the dynamic aperture

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23-27 Sep 2015 14

FFS_3.0mm_v0_Feb_2015

FFS_3.0mm_v1_Mar_2015

FFS_3.0mm_v2.2_Sep_2015

Remove 2 quads in FT

Additional sext at 1st image point

Reduce y in CCY Remove 2 quads

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Beta and tune vs. deltap

v1 v2.2v0

• Upper for FFS only and lower for the whole ring– Tune vs. deltap on vertical plane become very flat– Qx’ for FFS should be optimized in next step

Yiwei Wang 23-27 Sep 2015 15

Tune vs amplitude• Tune shift with amplitude:

– d(Qx)/d(Ex) d(Qy)/(dEy) d(Qy)/d(Ex)– v0: -2.555503E+04 4.563207E+06 -8.407153E+04– v1: -2.687453E+04 1.265348E+06 -8.279601E+04– V2.2: -2.614945E+04 1.260286E+06 -8.044155E+04

23-27 Sep 2015 17

Vertical dynamic aperture vs. deltap

• v0 -> v1: DA increased significantly for on-momentum and small off-momentum

• v1 -> v2.2: DA increased significantly for large off-momentum

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X0=0.001x

0 2-2 -1 1

Dynamic aperture for both planes

Yiwei Wang 23-27 Sep 2015 18

v1v0

• DA for off momentum increased significantly• effect from additional sextupole can be ease by further increasing

dispersionv2.2

23-27 Sep 2015 19

Summary• A preliminary designs got for the CEPC interaction region• Optimization to get a reasonable dynamic aperture for the

whole ring– Reduce the chromaticity contribution for CCS and IT;

Remove 2 quadrupoles in FT to reduce high order chromaticity; Additional sextupole at 1st image point to further reduce high order chromaticity

– DA increased significantly for both on- and off- momentum particles

– Further optimization is possible• Qx’ for FFS should be optimized

• break down of –I matrix• 2nd order dispersion• …

Yiwei Wang

23-27 Sep 2015 20

Acknowledge• Yunhai Cai, Xiaohao Cui, Yingshun Zhu, Yuanyuan Guo,

Tianjian Bian, Feng Su, Ming Xiao, Zhe Duan, Gang Xu, Jie Gao, Qing Qin, Demin Chou, Kazuhito Ohmi, Yoshihiro Funakoshi, Yukiyoshi Ohnishi, A. Bogomyagkov, Luis Eduardo Medina Medrano

• Thanks for your kind help and beneficial discussion!

Yiwei Wang

23-27 Sep 2015 21

Thank you for your attention!

Yiwei Wang

23-27 Sep 2015 22

reserved

Yiwei Wang

23-27 Sep 2015 23

Comparison of y*=1.2 mm and 3 mm

• Strengh of sextupoles in IR reduced– For y*=1.2mm: k2vs = 17.2 , k2hs = 2.92 – For y*=3mm: k2vs = 10.58 , k2hs = 2.80

• Tune vs. momentum deviation for the ring

Yiwei Wang

y*=1.2mm y*=3mm

23-27 Sep 2015 24

Comparison of y*=1.2 mm and 3 mm

• With the real ring• DA for off momentum:

– For y*=1.2mm, the DA is almost zero for off momentum 2%– For y*=3mm, the DA has been extended to 2% region:

-2% (2x , 20y), 2% (1x , 7y)

y*=1.2mm y*=3mmYiwei Wang