Lattice Design and Dynamic Aperture Optimization for CEPC Main Ring
This presentation explores lattice design and dynamic aperture optimization for the main ring of the Circular Electron Positron Collider (CEPC). It covers the optimization of dynamic aperture, increasing dispersion, beta*, managing chromaticity, and addressing various challenges in achieving optimal performance.
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Lattice design and dynamic aperture optimization for CEPC main ring Yiwei Wang, Yuan Zhang, Feng Su, Tianjian Bian, Dou Wang, Sha Bai, Huiping Geng, Jie Gao CEPC AP meeting, 18 Nov 2016
Outline Lattice of arc region, interaction region and partial double ring region Target of dynamic aperture for main ring Optimization of dynamic aperture Further optimization of dynamic aperture Increase dispersion and beta* Crab sextupole Sawtooth effect
Lattice of ARC Region FODO cell, 90 /90 , non-interleaved sextupole scheme period N=5cells all 3rd and 4th resonance driving terms (RDT) due to sextupoles cancelled, except small 4Qx, 2Qx+2Qy, 4Qy, 2Qx-2Qy tune shift dQ(Jx, Jy) is very small DA on momentum: large Chromaticity dQ( ) need to be corrected with many families DA off momentum: with many families to correct dQ( ) and I break down - -I I - -I I Sextupole configuration
Lattice of Interaction Region Local chromaticity correction with sextupoles pairs separated by I transportation all 3rd and 4th RDT due to sextupoles almost cancelled up to 3rd order chromaticity 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 L*= 1.5m x*= 0.22mm y*= 1mm GQD0= -200T/m GQF1= 200T/m LQD0=1.69m LQF1=0.90m - -I I - -I I
Lattice of Partial Double Ring Region Feng Su, Yiwei Wang Yiwei Wang CEPC-SppC Study Group Meeting 5
Lattice of the Whole Ring A lattice of the whole ring (ARC+PDR+IR) basically fulfilling the design parameters
Target of dynamic aperture for main ring Parameter Symbol Unit Value Status 1034cm-2s-1 Luminosity per IP Lmax 2.01 - x/ y Beta functions at IP m 0.275 /0.0013 0.22 /0.001 x/ y nm rad Main ring emittance 2.05 /0.0062 2.15/0.0065 x/ y nm rad Injection emittance 3.5 / 0.17 3.5/0.17 nm rad Transversacceptance* Ax/Ay 787 / 4.17 Energy acceptance AE % 2.0 1.9 16 / 45 (dp/p=0) 3 / 5 (dp/p= 2%) (no errors, mean value for two poles of axis) DA requirement from beam-beam (inclu. errors and beam-beam effect) 20 / 40 (dp/p=0) 5 / 10 (dp/p= 2%) DAx/DAy DA requirement from injection (inclu. errors and beam-beam effect) 20 / 26 (dp/p=0 and dp/p= 0.5%) DAx/DAy - Based on the parameters wangdou20160918 H-low power . *assuming coupling factor =5% for injection beam, x,r=200 m, x,i=60 m, ws = 4 mm, nr = 5, ns = 5
Optimization of dynamic aperture 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 Further optimization is possible Larger dispersion for IR sextupoles y*= 1mm -> 1.3mm (new parameters) More families in IR Study of effects such as sawtooth, quantum excitation, solenoid field, errors and misalignments are under going
Increase dispersion and beta* Dispersion increased to be ~4 times of former one Beta* increased from (0.22m, 1mm) to (0.275m, 1.3mm) which is used in the latest parameter list H low power, wangdou20160929 FFSR_1 FFSR_2
much smaller Could be further reduced with one mere additional sextupole CEPC_ARC_PDR_IR_96fam_0.25 CEPC_FFSR_opti_3_6B h11001= 7.997361925785176 h00111= -.972366733381029 h20001= (1.1336405674497374-.38979150243537286 I) h00201= (.8683153500895731-.13597336303963223 I) h10002= (-.03536835425736989+.002479685890575842 I) h21000= (-3.5699986530784864+.23005539648871576 I) h30000= (-1.1709600842855643+.2289441334267579 I) h10110= (.49977218284344715-.03256414530569174 I) h10020= (.23436980204185076-.08946446765559557 I) h10200= (.24394373091851662+.05904295382149627 I) h22000= (-259.13962817370793+2.3159778348574855e-11 I) h00220= (-562881.5948624742-1.6760376524149745e-09 I) h11110= (-2331.68678999647-3.1350630563808934e-09 I) h20020= (-525.3948102948423+353.5675628211218 I) h31000= (168.64051605455978-39.757347851171666 I) h11200= (1165.8778254410106-5.519138263809353 I) h40000= (-38.58740249469446+19.278513717900296 I) h20110= (1048.3451592717843-712.2741072844439 I) h20200= (-522.9020111037286+358.69966969043145 I) h00310= (1187.6439809519773-5.586050816302889 I) h00400= (-93811.43657520546+669.8167036627116 I) h30001= (525.2999757510321+12.059132901639712 I) h21001= (-497.8456138016568+218.48117513252248 I) h10021= (-30264.22466245458+8199.462852158655 I) h10111= (63027.3376020519-7054.736180745322 I) h10201= (-32786.683987978555-1185.03299741808 I) h11002= (55.07574515441543+5.716688960407785e-14 I) h00112= (-724.1608499947642+6.35117875929379e-12 I) h11001= 28.149064351883542 h00111= .3976260970724188 h20001= (-9.779859760016373+1.8365466770722987 I) h00201= (.12742148382285629-.3869166540226469 I) h10002= (-.03167758817237518+.00946055948653756 I) h21000= (-.00015369277249077662+8.539084261442731e-05 I) h30000= (4.0977400216024584e-05+6.049866978190266e-05 I) h10110= (.009787809724485452-.00087023889418468 I) h10020= (-.015026071103215188-.0007131032912734911 I) h10200= (.0051458491732447875+.0014050469532620943 I) h22000= (-.8235672944092407-5.967990858446459e-15 I) h00220= (-1162.4895355409612+6.421974063641755e-11 I) h11110= (-293.9283310209139-3.928848357759307e-10 I) h20020= (-69.28082863039594+30.872417463548402 I) h31000= (.46000825091343045-.5165059548894333 I) h11200= (146.87068698598296-2.10933902469786 I) h40000= (-.04383727532827475+.23531006765253526 I) h20110= (138.49928364561038-60.36205727929939 I) h20200= (-69.14535030809094+30.566329589011374 I) h00310= (87.33266255996189-.9701938059401272 I) h00400= (-193.62606630030479+17.88665801865717 I) h30001= (168.47943948902977+185.97214638993358 I) h21001= (-88.5639704919857+231.05983174998173 I) h10021= (-9255.8764697712-11174.43367113418 I) h10111= (19476.809076010686-1897.2105793657065 I) h10201= (-10172.89900846646+12712.98412347012 I) h11002= (16.110123329092108+4.059082339721252e-15 I) h00112= (-479.24263729903726-2.1878205451565785e-13 I)
Add crab section Lattice design requirement Strength* *Ref: Yuan Zhang, CW , 2008 Phase to IP: 2m /2, (2n+1) /2 for x,y plane Beta function should be easily adjusted Chromaticity contribution especially which is not on phase should be small
Whole ring lattice CEPC_ARC_4_IR_2
Dynamic aperture CEPC_ARC_4_PDR_3_IR_1 2fam CEPC_ARC_4_IR_2 2fam turn off crab sextupole y k2 VS1FFS=2000*3.3 CEPC_ARC_4_IR_2 2fam turn on crab sextupole y k2 VS1FFS=2000*3.3 SC0FFS=2000*1.4 y k2 VS1FFS=4000*7 Dynamic aperture for on-momentum particle (w/o synchrotron motion) With larger dispersion and beta*, DA on y plance increased significantly DA shape may be tuned with beta functions at main sextupole Turn on the crab sextupole, the DA decreased significantly DA may be increased by optimizing beta functions at crab sextupole
DA vs. Circumfence For Higgs factories, FODO cell is favorite for its high filling factor. Usually, phase advance of 60 /60 or 90 /90 is chosen for its property of aberration cancellation. If fix emittance bending angle ? per dipole and cell number ?????is fixed ??=????2?3 ?? 2 1 3 sin3? 4sin2? 2cos? 2 ? = ? ????? 2?????? = 2? chromaticity of ARC ? is fixed, but dispersion at sextupole ??will increase with a longer cell length ? ??(1 1 4sin2? Thus, the nonlinearity generated by sextupole ??? will decrease with a longer cell length ? 2sin? 2) ? = ????? tan? ??= ? 2 2 ?? 1 ? ?2? ? If fix emittance, L Dx K2 DA
DA vs. Circumfence (cont.) Eng=120 Lring=54820.48000000032 U0=- thetaC=15 thetaP=2.6 Ne=2.67 Nb=44 Ib=.0105 Pbeam=- rhoB=6200 alfap=- bxstar=- bystar=- ex=2.0935553797925138e-09 ey=0 sigxIP=- sigyIP=- ksix=- ksiy=- Vrf=3.53e+09 frf=6.5e+08 sigmaz=.002638957643199394 sigmazt=- Phom=- sigmae=.0013022977605895913 eapt=- eaptrf=- ngamma=- tbs=- Fhg=- Lmax=- Eng=120 Lring=74396.48000000458 U0=- thetaC=15 thetaP=2.6 Ne=2.67 Nb=44 Ib=.0105 Pbeam=- rhoB=9300 alfap=- bxstar=- bystar=- ex=1.98345500603251e-09 ey=0 sigxIP=- sigyIP=- ksix=- ksiy=- Vrf=2636910000 frf=6.5e+08 sigmaz=.0027049009699175197 sigmazt=- Phom=- sigmae=.0010632425947487473 eapt=- eaptrf=- ngamma=- tbs=- Fhg=- Lmax=- Eng=120 Lring=92707.19999999877 U0=- thetaC=15 thetaP=2.6 Ne=2.67 Nb=44 Ib=.0105 Pbeam=- rhoB=12090 alfap=- bxstar=- bystar=- ex=1.932695860302522e-09 ey=0 sigxIP=- sigyIP=- ksix=- ksiy=- Vrf=2259200000 frf=6.5e+08 sigmaz=.002734597171221037 sigmazt=- Phom=- sigmae=.0009324837783256101 eapt=- eaptrf=- ngamma=- tbs=- Fhg=- Lmax=- Real tune: 0.08, 0.22, -0.0718478 Bucket height dV/P0 = .0249642 Real tune: 0.08, 0.22, -0.0812613 Bucket height dV/P0 = .0249614 Real tune: 0.08, 0.22, -0.0892573 Bucket height dV/P0 = .0249542
DA vs. Circumfence Tracking w/o damping Q =0 with 2 families ey/ex=1 ARC length Lring=54820.48 m Lring=74396.48 m Lring=92707.20 m 83 turns 123 turns 160 turns
Reference Yuan Zhang, CW , 25 Aug 2008
Summary Further optimization of dynamic aperture with increased dispersion, beta* and crab sextupole is undergoing.
