Presentation on theme: "Design study of CEPC Alternating Magnetic Field Booster"— Presentation transcript:
1 Design study of CEPC Alternating Magnetic Field Booster Tianjian Bian Jie Gao Michael Koratzinos (CERN) Chuang Zhang Xiaohao Cui Sha bai Dou Wang Yiwei Wang Feng Su
2 Wiggling Bend Scheme Introduction of Wiggling Bend Scheme The inject energy is 6GeV.If all the dipoles have the same sign, may cause problem.In wiggling bend scheme, adjoining dipoles have different sign to avoid the low field problem.Shorten the Damping times greatly.The picture below shows the FODO structure.
4 Linac Parameters Linac parameters From : Li Xiaoping, Pei Guoxi, etc, "Conceptual Design of CEPC Linac and Source".ParameterSymbolUnitValueE- beam energyEe-GeV6E+ beam energyEe+Repetition ratefrepHz50E- bunch populationNe-2×1010E+ bunch populationNe+Energy spread (E+/E-)σE<1×10-3Emitance (E-)0.3 mm mradEmitance (E+)
5 Booster ParametersContrast With the Alternating Magnetic Field Scheme.Main difference in parameters caused by wiggling bend scheme.ParameterU0 [MeV/turn]0.0190.70Damping times(x/y) [s] 115.613.12Emittances(x) [pi nm]0.0150.11Strength of dipole [Gs]33-164.3/+229.9Beam offset in dipole[cm]2.3Length of dipole [m]19.6*14.9*4Length of FODO [m]47.2
6 Booster ParametersParameter List for Alternating Magnetic Field Scheme.ParameterUnitValueBeam energy [E]GeV6Circumference [C]kmRevolutionfrequency[f0]kHz5.5135SR power / beam [P]MW6.41E-04Beam off-set in bendcm2.30E+00Momentum compaction factor[α]2.70E-05Bending radius [r]mnB/beam50Lorentz factor [g]Magnetic rigidity [Br]T·m20.01Beam current / beam [I]mA0.9197Bunchpopulation[Ne]2.08E+10Bunch charge [Qb]nC3.34emittance-horizontal[ex] inequilibriumm·rad1.11E-10injected from linac3.00E-07emittance-vertical[ey] inequilibrium1.11E-12ParameterUnitValueRF voltage [Vrf]GVRF frequency [frf]GHz1.3Harmonic number [h]235800Synchrotronoscillationtune[ns]Energy acceptance RF [h]%SR loss / turn [U0]GeV6.97E-04Energyspread[sd] inequilibriuminjected from linac0.1Bunch length[sd] inequilibriummm0.05~1.5Transversedampingtime[tx]ms3124.6turns17228Longitudinaldampingtime[te]1.69
7 Booster ParametersParameter List for Alternating Magnetic Field Scheme.Angle of dipole v.s. timeField of dipole v.s. time
8 Booster ParametersParameter List for Alternating Magnetic Field Scheme.U0 v.s. timeη v.s. time
9 Booster ParametersParameter List for Alternating Magnetic Field Scheme.Vrf v.s. timePhase v.s. time
10 Nonlinear Optimization and Sextupole Scheme Challenges we faceIt is a big ring. Nonlinear optimization for big ring is much harder than small ring.SSRF booster(only 180 meters) is also made up with FODO structure. SSRF booster's dynamic is 11sigma in horizontal and 42sigma in vertical without any sextupole optimization.Without sextupole optimization, What we have is: 3.6sigma in horizontal and 1.7sigma in vertical.We have long straight section that we can correct the chromaticity locally.In FODO structure, we can not place harmonic sextupoles easily as DBA structure do.No released code for the sextupole optimization.
11 Nonlinear Optimization and Sextupole Scheme Optimization algorithmThere are so many sextupoles in the booster. So, the tune shift effect is serious,In the paper, tune shift with amplitude is derived. We can see that it is related to the sextupole strength, beta function, working point,etc.We choose the three value as our goal function, and genetic algorithm is used in the optimization process.
12 Nonlinear Optimization and Sextupole Scheme Step1:Divide sextupoles into diferent families.See three FODOs as a cell, and there are six sextupoles in a cell as the picture below.We have 320 cells in the whole ring. Every cell use the same sextupoles. So there are six sextupole famliies in total.The most important task for sextupole is to correct the linear chromaticity and this is the constraint condition.In this step,minimize the goal function is not important, the most important task is choosing the direction of tune shift.
13 Nonlinear Optimization and Sextupole Scheme Step 2:Fake harmonic sextupoleIt is difficult to add harmonic sextupole in a cell, because there is no zero dispersion point.We arrange SH1, SH2, SH3, SH4, SH5, SH6 as fake harmonic sextupole, use zero chromaticity contribution as their constraint condition. And this is why we call them fake harmonic sextupoles.Smaller goal function values do not means bigger DA, plot DA in the process of optimization and choose the best result.
14 Nonlinear Optimization and Sextupole Scheme Tune shift optimization resultsThe working opint is not good.Direction of tune shift
15 Nonlinear Optimization and Sextupole Scheme Change working pointWorking point effects the DA greatly.
16 Nonlinear Optimization and Sextupole Scheme First order tune shift optimization is suitable for CEPC?Plot tune shift as a function of Jx.CEPC FODOHEPS DBA
17 Nonlinear Optimization and Sextupole Scheme My understandingWhy second order tune shift play an important role?First order tune shift in CEPC:Second order tune shift in CEPC:Second order tune shift in HEPS:
18 ConclusionThe low field problem is solved by the wiggling bend scheme. Strength of dipole increase from 33Gs to / Gs.A ramping method of is alternating magnetic field booster proposed.Shorter damping times are obtained, which is 3.12 seconds.DA is still a problem. The "second order tune shift" idea is proposed and waiting to try and carefully thought.