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

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

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

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

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

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

The tune dependence on the energy deviation

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: 206.08/206.22 Sextupole length in IR: 0.3m (0.4m for arc) 5x 3y With IR DA for 2%,-2% is 0

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

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

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

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

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

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

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

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

Optics of whole ring IR+ARC

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

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

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

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

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

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

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.

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.

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

Reserved

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: 206.08/206.22 On momentum 509.3σy 59.2σx 1%，-1% 2%,-2%的孔径是0 Without FFS

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

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