Design Study of CEPC Booster and Mainring Lattice

Design Study of CEPC Booster and Mainring Lattice Tianjian Bian 1, Jie Gao 1, Yunhai Cai 2, Michael Koratzinos 3, Chuang Zhang 1, Xiaohao Cui 1, Yiwei Wang 1, Sha bai 1, Dou Wang 1, Feng Su 1, Ming Xiao 1 1 Institute of High Energy Physics, Beijing, China, 2 SLAC National Accelerator Laboratory, CA, USA, 3 University of Geneva, Switzerland Mail to: biantj@ihep. ac. cn

Outline n Design Goal of CEPC booster. n Possible Options: l Normal Bend Scheme. l Wiggling Bend Scheme. n Summary

Design Goal n Consideration of injection Ø Inject in X direction. Injected Beam Circulating Beam Closed orbit kickers p/2

Design Goal n Consideration of injection Ø Emit in mainring is 2 E-9 m*rad, asuming beta_x=590 meter in the injection point. Ø Asuming DA_x=20 sigma@dp=0. 5% in the mainring. Ø Asuming beta_x=590 meter in the injection point. Ø The total space for injection: Ø 8 sigma is retained for revolution beam to get enough quantum life time: Ø 6 sigma is retained for injection beam to loss less particles: Ø 3. 2 mm is lefted for septum and emit of booster@120 Gev is 3. 5 E-9 m*rad.

Design Goal n Design Goal Ø For injection, emit of booster@120 Gev should be about 3. 5 E-9 m*rad. Ø 1 percent energy acceptance for enough quantum lifetime. Ø DA_x and DA_y should bigger than 5~6 sigma for injection with all kinks of error. n Linac parameters Ø From : Li Xiaoping, Pei Guoxi, etc, "Conceptual Design of CEPC Linac and Source". Parameter Symbol Unit Value beam energy Ee- Ge. V 6 E+ beam energy Ee+ Ge. V 6 Repetition rate frep Hz 50 E- bunch population Ne- 2× 1010 E+ bunch population Ne+ 2× 1010 Energy spread (E+/E-) σE <1× 10 -3 E- Emitance (E-) 0. 3 mm mrad Emitance (E+) 0. 3 mm mrad

Normal Bend Scheme n Introduction of Normal Bend Scheme Ø The inject energy is 6 Ge. V. Ø The earth field is about 0. 5 Gs, so in the normal bend scheme start at 30 Gs@6 Ge. V may be difficult. Ø Shielding and correcting are needed. Ø With earth field, booster is a broken ring. So the first turn orbit correction is important. After the first turn orbit correction, the circular beam is existed and the closed orbit correction can be done.

Earth field Orbit Correction n First turn orbit correction Ø As we have said, the first turn orbit correction is important. It is similar to the closed orbit correction. This code is finished using Matlab.

Earth field Orbit Correction n Closed orbit correction Ø After the first turn orbit correction, the closed orbit is existed. Closed orbit after first turn orbit correction and closed orbit correction

Linear Optics Ø 90 degree FODO Ø FODO length: 70 meter

Chromaticity Optimization n Sextupole scheme Ø Non-interleaved sextupoles are used. Ø Another pair of sextupole with the same strength apart by 90°phase advance for cancel the second order chromaticity automatically. Ø 8 sextupole families, optimize using both symbolic differential algebra and numeric way. Ø Only optimizing the 8 sextupole families is not enough. Ø Appropriate phase advance between arcs is necessary. SF 1 SF 2 SD 1 SD 2 SF 3 SD 2 SD 3 SF 4 SD 3 SD 4

Chromaticity Optimization n Optimization result before optimization after optimization

CEPC Booster Error Estimate

DA result n Tune: 190. 61/190. 88 and cavity on With error and orbit correction, dp=0. 01

Booster Parameters n Parameter List for Alternating Magnetic Field Scheme. Parameter Unit Value Beam energy [E] Ge. V 6 Circumference [C] km Revolutionfrequency[f 0] Unit Value RF voltage [Vrf] GV 0. 2138 63. 84 RF frequency [frf] GHz 1. 3 k. Hz 4. 69 Harmonic number [h] SR power / beam [P] MW 2. 16 Synchrotronoscillationtune[ns] Beam off-set in bend cm 0 Momentum compaction factor[α] Strength of dipole 1. 91 E-05 Gs n. B/beam 25. 8 50 Lorentz factor [g] 11741. 71 Magnetic rigidity [Br] T·m 20 Beam current / beam [I] m. A 0. 92 Bunchpopulation[Ne] Bunch charge [Qb] emittance-horizontal[ex] inequilibrium 2. 44 E 10 n. C 3. 91681 m·rad 0. 91 E-11 injected from linac m·rad emittance-vertical[ey] inequilibrium m·rad injected from linac m·rad Parameter Energy acceptance RF SR loss / turn [U 0] Energyspread[sd] inequilibrium injected from linac Bunch length[sd] inequilibrium injected from linac Transversedampingtime[tx] 276831 0. 21 % 4. 995 Ge. V 1. 47 E-5 % 7. 47 E-05 % 0. 1 mm 5. 85 E-05 mm ~1. 5 s 174 turns Longitudinaldampingtime[te] s turns 3 E-7 0. 046 E-11 3 E-7 174

Booster Parameters n Parameter List for Alternating Magnetic Field Scheme. Parameter Unit Value Beam energy [E] Ge. V 120 Circumference [C] km Revolutionfrequency[f 0] Unit Value RF voltage [Vrf] GV 6 63. 84 RF frequency [frf] GHz 1. 3 k. Hz 4. 69 Harmonic number [h] SR power / beam [P] MW 2. 16 Synchrotronoscillationtune[ns] Beam off-set in bend cm 0 Momentum compaction factor[α] Strength of dipole Gs n. B/beam 400 Beam current / beam [I] m. A 0. 92 Bunch charge [Qb] emittance-horizontal[ex] inequilibrium 2. 44 E 10 n. C 3. 91681 m·rad 3. 61 E-9 injected from linac m·rad emittance-vertical[ey] inequilibrium m·rad injected from linac m·rad Ge. V 2. 34 % 0. 12 % 0. 1 mm 1. 36 mm ~1. 5 Transversedampingtime[tx] ms 21. 76 Longitudinaldampingtime[te] ms Energyspread[sd] inequilibrium T·m 3 E-7 0. 1083 E-9 3 E-7 0. 21 4. 57 SR loss / turn [U 0] Magnetic rigidity [Br] 276831 % 516. 71 234834. 15 Bunchpopulation[Ne] Energy acceptance RF 2. 54 E-5 50 Lorentz factor [g] Parameter injected from linac Bunch length[sd] inequilibrium injected from linac

Conclusion n With error, orbit correction, cavities on and tune 0. 61/0. 88, DA_x=8. 6 sigma, DA_y=10. 1 sigma@dp=0% n With error, orbit correction, cavities on and tune 0. 61/0. 88, DA_x=6. 7, DA_y=6. 5@dp=1% n Contrast with the design goal we have proposed in previous section, this design is reasonable and meet requirements.

Wiggling Bend Scheme n Introduction of Wiggling Bend Scheme Ø The inject energy is 6 Ge. V. Ø If all the dipoles have the same sign, 33 Gs@6 Ge. V may cause problem. Ø In wiggling bend scheme, adjoining dipoles have different sign to avoid the low field problem. Ø The picture below shows the FODO structure. Ø The wiggler scheme using the same sextupole scheme and magnet error and the wiggler scheme has little or no effect on dynamics.

Linear Optics Ø 90 degree FODO Ø FODO length: 70 meter

DA result n Tune: 190. 61/190. 88 and cavity on with error, dp=0. 01

Booster Parameters n Parameter List for Alternating Magnetic Field Scheme. Parameter Unit Value Beam energy [E] Ge. V 6 Circumference [C] km Revolutionfrequency[f 0] Unit Value RF voltage [Vrf] GV 0. 2138 63. 84 RF frequency [frf] GHz 1. 3 k. Hz 4. 69 Harmonic number [h] SR power / beam [P] MW 2. 16 Synchrotronoscillationtune[ns] Beam off-set in bend cm 1. 2 Energy acceptance RF Momentum compaction factor[α] Strength of dipole 2. 33 E-5 Gs n. B/beam -129. 18/+180. 84 50 Lorentz factor [g] 11741. 71 Magnetic rigidity [Br] T·m 20 Beam current / beam [I] m. A 0. 92 Bunchpopulation[Ne] Bunch charge [Qb] emittance-horizontal[ex] inequilibrium 2. 44 E 10 n. C 3. 91681 m·rad 6. 38 E-11 injected from linac m·rad emittance-vertical[ey] inequilibrium m·rad injected from linac m·rad Parameter SR loss / turn [U 0] Energyspread[sd] inequilibrium injected from linac Bunch length[sd] inequilibrium injected from linac Transversedampingtime[tx] 276831 0. 21 % 5. 93 Ge. V 5. 42 E-4 % 0. 0147 % 0. 1 mm 0. 18 mm ~1. 5 ms 4. 71 turns Longitudinaldampingtime[te] ms turns 3 E-7 0. 191 E-11 3 E-7 4. 71

Booster Parameters n Parameter List for Alternating Magnetic Field Scheme. Parameter Unit Value Beam energy [E] Ge. V 120 Circumference [C] km Revolutionfrequency[f 0] Unit Value RF voltage [Vrf] GV 6 63. 84 RF frequency [frf] GHz 1. 3 k. Hz 4. 69 Harmonic number [h] SR power / beam [P] MW 2. 16 Synchrotronoscillationtune[ns] Beam off-set in bend cm 0 Momentum compaction factor[α] Strength of dipole Gs n. B/beam 400 Beam current / beam [I] m. A 0. 92 Bunch charge [Qb] emittance-horizontal[ex] inequilibrium 2. 44 E 10 n. C 3. 91681 m·rad 3. 61 E-9 injected from linac m·rad emittance-vertical[ey] inequilibrium m·rad injected from linac m·rad Ge. V 2. 34 % 0. 12 % 0. 1 mm 1. 36 mm ~1. 5 Transversedampingtime[tx] ms 21. 76 Longitudinaldampingtime[te] ms Energyspread[sd] inequilibrium T·m 3 E-7 0. 1083 E-9 3 E-7 0. 21 4. 57 SR loss / turn [U 0] Magnetic rigidity [Br] 276831 % 516. 71 234834. 15 Bunchpopulation[Ne] Energy acceptance RF 2. 54 E-5 50 Lorentz factor [g] Parameter injected from linac Bunch length[sd] inequilibrium injected from linac

Conclusion n The low field problem is solved by the wiggling bend scheme. Strength of dipole increase from 30 Gs to -129. 18/+180. 84 Gs. n Shorter damping times are obtained, which is 4. 7 seconds. n A ramping method of is alternating magnetic field booster proposed. n Serveal tunes has been test. Some tunes are sensitive to magnet errors, some are not. 0. 61/0. 88 seems good. n With error, cavities on and tune 0. 61/0. 88, DA_x=9. 2, DA_y=9. 6@dp=0% n With error, cavities on and tune 0. 61/0. 88, DA_x=6. 6, DA_y=6. 4@dp=1%

Summary n. There are two possibilities in CEPC booster design, normal scheme and wiggler scheme. n. In this report, we proposed a design of both normal scheme and wiggler scheme. l. Normal scheme: l. With error, orbit correction, cavities on and tune 0. 61/0. 88, DA_x=8. 6 sigma, DA_y=10. 1 sigma@dp=0% l. With error, orbit correction, cavities on and tune 0. 61/0. 88, DA_x=6. 7, DA_y=6. 5@dp=1% l. Wiggler scheme: l. With error, cavities on and tune 0. 61/0. 88, DA_x=9. 2, DA_y=9. 6@dp=0% l. With error, cavities on and tune 0. 61/0. 88, DA_x=6. 6, DA_y=6. 4@dp=1% n. Contrast with the design goal we have proposed in previous section, both of the two design are reasonable and meet requirements.

Plan n. There are 6 months left, our plan is: l. Optimization l. Lattice l. The code redesign, with injection and ejection. process of ramping. 2 month done 2 month 1 month n. Design goal of CDR l. For l 1 injection, emit of booster@120 Gev should be about 3. 5 E-9 m*rad. percent energy acceptance for enough quantum lifetime. l. DA_x and DA_y should bigger than 7~8 sigma for injection for both on-momentum and off- momentum(with all kinks of error). l. This design should also work at W and Z.

Moola：Modular&parallel Optics Optimization for LAttice n Introduction of Moola Ø In the lattice design process, especially in the challenging project like CEPC, we want to control every thing(such as the twiss, high order nonlinear parameter and so on), and using them for optimization. Ø Lattice design code like Mad and Sad can complete some thing very well, but they don't let us do what ever we want, beacuse we can't handle the code. Ø Based on this requirement, we need own code. Ø Moola is a c++ library, which is modular&parallel. Ø Moola is linked to Zlib.

Moola：Modular&parallel Optics Optimization for LAttice Element Simulator High Order Fields Error Simulator Beamline Modify Orbit correction* Dynamic Aperture Optimization Algorithm Optimization* Fringing Fields Simulator* Beamline Link. List Alignment Simulator* Radiation Parameters* Twiss* Tracker Arbitrary Order One Turn Map（ OTM） Frequency Map Analysis Zlib Arbitrary Order Nonlinear Parameters *in the developing process

Moola：Modular&parallel Optics Optimization for LAttice n Main physics base Ø Hamilton and canonical coordinates Ø Fourth-order symplectic integrator

Moola：Modular&parallel Optics Optimization for LAttice n CEPC mainring results from Moola

Moola：Modular&parallel Optics Optimization for LAttice n CEPC mainring results from Moola 2500 particles, 256 turns in 109 seconds

Moola：Modular&parallel Optics Optimization for LAttice n CEPC mainring results from Moola 2500 particles, 512 turns in 219 seconds

Moola：Modular&parallel Optics Optimization for LAttice n MOEA/D: Parallel test on DTLZ(pareto front)

Moola：Modular&parallel Optics Optimization for LAttice n CEPC mainring results from Moola Ø Arbitrary order chromaticity Ø Arbitrary order one-turn-map Ø Detuning terms Ø Linear optics

Moola：Modular&parallel Optics Optimization for LAttice n Introduction of Moola Ø Moola is still preliminary, many functions is waiting to be added. Ø With all the nonlinear parameters in my computer memory, we can call them in any optimization algorithm(like all kinds of evolution algorithm). Ø In the booster further design and the mainring design, Moola will play a more important role.

Introduction Multiobjective genetic algorithms (MOGA) were developed since 1970 s. Evolved further in the 1990 s with the addition of genetic algorithms. The first application to accelerator physics was about 2005. Allow to find globally optimal solutions when a large number of fit parameters is used.

Algorithm Optimize certain objectives while fulfilling certain constraints. 1: Initialize population (first generation, random) 2: repeat 3: select parents to generate children (crossover) 4: mutation (children) 5: evaluate (children) 6: merge (parents, children) 7: non-dominated sort (rank) 8: select half of (parents, children) 9: until reach a generation with the desired convergence to the PO set

Application to CEPC booster Linear lattice parameters are not varied. Lcell=70. 8 m , nx=128. 2, ny=128. 3, (60, 60) Fodo cell, For bypass lines 8 Families of sextupole strengths are selected as variables (4 families of SF, 4 families of SD, Non-interleaved). p • 2 objectives f(1)= -DA_nom_area_p*MA f(2)= -DA_nom_area_n*MA • 800 populations

The evolution of 155 generations

Result of 155 th generation 1 family of SF, and 1 family of SD 1% Δp/p: DA 49. 8 mm*23. 1 mm -1% Δp/p: DA 49. 8 mm*43. 3 mm 5 family of SF, and 5 family of SD (optimized using MOGA) 1% Δp/p: DA 62. 6 mm*36. 6 mm -1% Δp/p: DA 56. 2 mm*43. 3 mm

FMA @1% Δp/p FMA @-1% Δp/p

MA after using MOGA MA before using MOGA

MA after using MOGA MA before using MOGA

Summary MOGA now working for the dynamic aperture optimization of CEPC booster. MA of CEPC booster has been improved using MOGA. For (60, 60) FODO cell lattice , consider to decrease the emmitance and optimize the dynamic aperture at the same time to satisfy the injection of main ring.

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Summary n Optimization of lattice: reference lattice design, Lcell=47. 2 m vs. Lcell=70. 8 m. (ZC, CXH) l Linear optics l Chromaticity correction and dynamic aperture l Machine errors and correction n Sawtooth effect and their correction; n Low field at injection and its tolerance: test, simulation and mitigation; (BTJ) n Consideration of a pre-booster n Instability: further simulation study. (BTJ) n Injection: physical design. (ZC) n Ejection: work together with collider injection. (CXH) n Design of transfer line from linac to booster. (ZC) n Design of transfer line from booster to collider. (CXH) n Provide a full parameter list of reference design including field, aperture, RF, kicker pulse length, vacuum, diagnostics, and tolerances.