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

Outline Introduction Pretzel scheme design Partial double ring scheme design Summary

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

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

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

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.

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

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

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: ~40sx/600sy @0.0% dp/p, ~30sx/450sy @2.0% dp/p After adding pretzel orbit, the DA is: ~20sx/150sy @0.0% dp/p, ~16sx/120sy @2.0% dp/p

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

DA w/ pretzel and FFS Dynamic aperture has been optimized with MODE, all sextupoles has been set free DA (w/o pretzel) is,~20sx@0.0% dp/p,~16sx @1.0% dp/p,~4sx/ 6sy @2.0% dp/p DA (w/ pretzel) is,~16sx @0.0% dp/p,~6sx/ 10sy @1.0% dp/p,~0sx @2.0% dp/p

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

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 2016.9.15

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

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

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: 16sx/45sy@0.0% dp/p,~3sx/5sy @2.0% 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

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 ~3sx/5sy @2.0% momentum spread after turn damping on Optimization work are still going on……

Thank you !