Lattice design for CEPC PDR Yiwei Wang Feng

Lattice design for CEPC PDR Yiwei Wang, Feng Su, Jie Gao 1 st July 2016, CEPC AP meeting

CEPC primary parameter （wangdou 20160325） Number of IPs Energy (Ge. V) Circumference (km) SR loss/turn (Ge. V) Half crossing angle (mrad) Piwinski angle Ne/bunch (1011) Bunch number Beam current (m. A) SR power /beam (MW) Bending radius (km) Momentum compaction (10 -5) IP x/y (m) Emittance x/y (nm) Transverse IP (um) x/IP y/IP VRF (GV) f RF (MHz) Nature z (mm) Total z (mm) HOM power/cavity (kw) Energy spread (%) Energy acceptance by RF (%) n Life time due to beamstrahlung_cal (minute) F (hour glass) Lmax/IP (1034 cm-2 s-1) Pre-CDR H-high lumi. H-low power W Z 2 120 54 3. 1 0 0 3. 79 50 16. 6 51. 7 6. 1 3. 4 0. 8/0. 0012 6. 12/0. 018 69. 97/0. 15 0. 118 0. 083 6. 87 650 2. 14 2. 65 3. 6 0. 13 2 6 0. 23 47 2 120 54 2. 96 15 2. 85 67 16. 9 50 6. 2 2. 5 0. 25/0. 00136 2. 45/0. 0074 24. 8/0. 1 0. 03 0. 11 3. 62 650 3. 1 4. 1 2. 2 0. 13 2 2. 2 0. 47 36 2 120 54 2. 96 15 2. 67 44 10. 5 31. 2 6. 2 2. 2 0. 268 /0. 00124 2. 06 /0. 0062 23. 5/0. 088 0. 032 0. 11 3. 53 650 3. 0 4. 0 1. 3 0. 13 2 2. 1 0. 47 32 2 80 54 0. 59 15 5 0. 74 400 26. 2 15. 6 6. 1 2. 4 0. 1/0. 001 1. 02/0. 003 10. 1/0. 056 0. 008 0. 074 0. 81 650 3. 25 3. 35 0. 99 0. 09 2 45. 5 54 0. 062 15 7. 6 0. 46 1100 45. 4 2. 8 6. 1 3. 5 0. 1/0. 001 0. 62/0. 0028 7. 9/0. 053 0. 006 0. 073 0. 12 650 3. 9 4. 0 0. 99 0. 05 1. 7 0. 3 1. 1 0. 24 0. 68 2. 04 0. 82 2. 96 0. 81 2. 01 0. 92 3. 09 0. 95 3. 09

Considerations on ARC lattice design • FODO cell, 90 /90 – non-interleaved sextupole scheme – n=5 – All 3 rd and 4 th RDT due to sextupoles cancelled – Amplitude-dependent tune shift is very small Ncell= 120 LB= 19. 96 Lcell= 47. 92 theta=. 0032188449319567555 Lring= 54820. 47999996 Nstr 1= 18 Nstr 2= 20 Vrfc= 220625000 frf= 6. 5 e+08

this lattice NIP=2 Eng=120 Lring=54820. 48 U 0=2. 933 theta. C=theta. P=Ne=2. 67 Nb=44 Ib=. 0105 Pbeam=30. 800 rho. B=6200 alfap=bxstar=bystar=ex=2. 094 e-09 ey=0 sigx. IP=sigy. IP=ksix=ksiy=Vrf=3. 53 e+09 frf=6. 5 e+08 sigmaz=. 00264 sigmazt=Phom=sigmae=. 00130 eapt=eaptrf=ngamma=tbs=Fhg=Lmax=- H-low power wangdou 20160325 NIP=2 ! Number of IPs [1] Eng=120 ! Energy [Ge. V] Lring=54*1 E 3 ! Circumference [m] U 0=2. 96 ! SR loss/turn [Ge. V] theta. C=15 ! Half crossing angle [mrad] theta. P=2. 6 ! Piwinski angle [1] Ne=2. 67 ! Ne/bunch [10^11] Nb=44 ! bunch number [1] Ib=10. 5*1 e-3 ! Beam current[A] Pbeam=31. 2 ! SR power/beam [MW] rho. B=6. 2*1 e 3 ! Bending radius [m] alfap=2. 2 e-5 ! Momentum compaction [1] bxstar=0. 268 ! beta x at IP [m] bystar=0. 00124 ! beta y at IP [m] ex=2. 06*1 e-9 ! emittance x [m*rad] ey=0. 0062*1 e-9 ! emittance y [m*rad] sigx. IP=23. 5*1 e-6 ! beam size x at IP [m] sigy. IP=0. 088*1 e-6 ! beam size y at IP [m] ksix=0. 032 ! ksix/IP [1] ksiy=0. 11 ! ksiy/IP [1] Vrf=3. 53*1 e 9 ! Vrf [V] frf=650*1 e 6 ! frf [Hz] sigmaz=3. 0 ! Nature sigmaz [mm] sigmazt=4. 0 ! Total sigmaz [mm] Phom=1. 3 ! HOM power/cavity [kw] sigmae=0. 13/100 ! Energy spread [1] eapt=2/100 ! energy acceptance [1] eaptrf=2. 1/100 ! energy acceptance by RF [1] ngamma=0. 47 ! number of gamma tbs=32 ! life time due to beamstrahlung [min] Fhg=0. 81 ! Factor of hour glass Lmax=2. 01 ! Lmax/IP [10^34/cm^2/s] Damping time 15 ms, i. e. 82 turns; filling factor 72. 2%

FODO cell ARC lattice Dispersion Suppressor Sextupole configuration

ARC lattice (cont. ) Whole ARC (w/o FFS, PDR)

Second order chromaticity • Source of the second order chromaticity – Period=5 cells h 11002= d. Q vs. dp/p for Whole ARC Mainly second order chromaticity ARC section: 24 5 cells

High order aberration correction • GOAL: To minimize up to 4 th order chromaticity while keeping other terms (d /d , 3 rd RDT…) as small as possible • METHOD: optimization algorithm with the high-order tune shift result from LEGO or MADX – under going – first try with SAD (12 families in one arc section) ARC section: 24 5 cells

2 families of sextupoles • Lattice version: ARC_4, 90/90 non-interleaved • SF 1 =(L =. 3999999997 K 2 =. 9680546863397813 ) • SD 1 =(L =. 3999999997 K 2 =-1. 8843252788338383 )

8 families of sextupoles • Lattice version: ARC_4, 90/90 non-interleaved SF 1 SD 1 SF 13 SD 13 SF 25 SD 25 SF 37 SD 37 =(L =. 3999999997 K 2 =. 9151382947512141 ) =(L =. 3999999997 K 2 =-1. 937287205321101 ) =(L =. 3999999997 K 2 =. 9044530133648844 ) =(L =. 3999999997 K 2 =-1. 9500153567123215 ) =(L =. 3999999997 K 2 =. 931221792136596 ) =(L =. 3999999997 K 2 =-2. 1991629511275144 ) =(L =. 3999999997 K 2 =. 8819986551186294 ) =(L =. 3999999997 K 2 =-1. 7097580089253885 )

24 families of sextupoles • Lattice version: ARC_4, 90/90 non-interleaved More interative steps may make a further optimization. Current only 4*variable number SF 1 =(L =. 3999999997 K 2 =. 9253055630941627 ) SD 1 =(L =. 3999999997 K 2 =-2. 026258201583385 ) SF 5 =(L =. 3999999997 K 2 =. 8287555789334372 ) SD 5 =(L =. 3999999997 K 2 =-1. 6282924454184768 ) SF =(L =. 3999999997 K 2 =. 9621106266454174 ) SD 9 =(L =. 3999999997 K 2 =-1. 8289875852516948 ) SF 13 =( =. 3999999997 K 2 =. 9569607893315597 ) SD 13 =(L =. 3999999997 K 2 =-1. 9818840760961005 ) SF 17 =(L =. 3999999997 K 2 =. 8644461056804197 ) SD 17 =(L =. 3999999997 K 2 =-1. 9435648615047783 ) SF 21 =(L =. 3999999997 K 2 =. 8513985981676337 ) SD 21 =(L =. 3999999997 K 2 =-2. 0574327675116884 ) SD 45 =(L =. 3999999997 K 2 =-1. 902716274265495 ) SF 45 =(L =. 3999999997 K 2 =. 9749491806330957 ) SD 41 =(L =. 3999999997 K 2 =-1. 9394309092869944 ) SF 41 =(L =. 3999999997 K 2 =. 7888328836347085 ) SD 37 =(L =. 3999999997 K 2 =-1. 9716540617164433 ) SF 37 =(L =. 3999999997 K 2 =. 9703059431665878 ) SD 33 =(L =. 3999999997 K 2 =-1. 9321388309336185 ) SF 33 =(L =. 3999999997 K 2 =. 9053022199253654 ) SD 29 =(L =. 3999999997 K 2 =-1. 8325339725886889 ) SF 29 =(L =. 3999999997 K 2 =. 9181808605063326 ) SD 25 =(L =. 3999999997 K 2 =-1. 9657926466360203 ) SF 25 =(L =. 3999999997 K 2 =. 8932438017621696 )