design study of cepc booster - stfc ems · design study of cepc booster tianjian bian1, jie gao1,...

Design Study of CEPC Booster

Tianjian Bian1, Jie Gao1, Yunhai Cai2, Michael Koratzinos3, Chuang Zhang1, Xiaohao Cui1, Yiwei Wang1, Sha bai1, Dou Wang1, Feng Su1, Ming Xiao1

1Institute of High Energy Physics, Beijing, China, 2SLAC National Accelerator Laboratory, CA, USA,

3University of Geneva, Geneva, SwitzerlandMail to: [email protected]

eeFACT2016, 58th ICFA Advanced Beam Dynamics Workshop on High Luminosity.

Circular e+e-Colliders 24-27 October 2016, Cockcroft Institute at Daresbury Laboratory, UK.

Outlinen Design Goal of CEPC Booster.

n Possible Options:

l Normal Bend Scheme.

l Wiggling Bend Scheme.

n Optimization Code Development

l Moola：Modular&parallel Optics Optimization for LAttice

n Summary

Closed orbit kickers

Injected Beam

Circulating Beam

p/2

n Consideration of injection for mainring

Design Goal

Ø Inject in X direction.

Ø Emit in mainring is 2E-9 m*rad, asuming beta_x=200 meter in the injection point.

Ø Asuming DA_x=15 sigma@dp=0.5% in the mainring.

Ø The total space for injection:

Ø 5 sigma is retained for revolution beam to get enough quantum life time:

Ø 3 sigma is retained for injection beam to loss less particles:

Ø 3.8mm is lefted for septum and emit of booster@120Gev is 3.5E-9 m*rad.

n Consideration of injection

Design Goal

(mm)49.915200100.2 9

3.16(mm) 5200100.2 9

2.51(mm) 3200105.3 9

Ø For mainrg injection, emit of booster@120Gev should be about 3.5E-9 m*rad.

Ø 1 percent energy acceptance for enough quantum lifetime.

Ø For booster injection, DA_x and DA_y should bigger than 5 sigma.

n Design GoalDesign Goal

n Linac parametersØ From : Li Xiaoping, Pei Guoxi, etc, "Conceptual Design of CEPC Linac

and Source".Parameter Symbol Unit Value

E- beam energy Ee- GeV 6

E+ beam energy Ee+ GeV 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

Emitance (E-) 0.3 mm mrad

Emitance (E+) 0.3 mm mrad

Normal Bend Scheme

Ø The inject energy is 6GeV.

Ø The earth field is about 0.5Gs, so in the normal bend scheme ramp from 30Gs@6GeV 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.

Ø After the first turn orbit correction, the circular beam is existed and the closed orbit correction can be done.

n Introduction of Normal Bend Scheme

Linear Optics Ø 90 degree FODO

Ø FODO length:70 meter

Chromaticity Optimizationn Sextupole scheme

SF1 SF1 SF2 SF2 SF3 SF3 SF4 SF4

SD1 SD1 SD2 SD2 SD3 SD3 SD4 SD4

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 them using both symbolic differential algebra and numeric way.

Ø Only optimizing the 8 sextupole families are not enough.

Ø Appropriate phase advance between arcs is necessary.

Chromaticity Optimizationn Optimization result

before optimization after optimization

Earth field Orbit Correctionn 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 Correctionn Closed orbit correction

Ø After the first turn orbit correction, the closed orbit is existed.

Closed orbit after first turn orbit

correction

Closed orbit after first turn orbit

correction and closed orbit correction

CEPC Booster Error Estimate

DA resultn Tune:190.61/190.88 and cavity on

With error and orbit correction,

dp=0.0

With error and orbit correction,

dp=0.01

Booster Parametersn Parameter List for Normal Bend Scheme.

Parameter Unit Value

Beam energy [E] GeV 6

Circumference [C] km 63.84

Revolutionfrequency[f0] kHz 4.69

SR power / beam [P] MW 2.16

Beam off-set in bend cm 0

Momentum compaction factor[α] 1.91E-05Strength of dipole Gs 25.8

nB/beam 50

Lorentz factor [g] 11741.71

Magnetic rigidity [Br] T·m 20

Beam current / beam [I] mA 0.75

Bunchpopulation[Ne] 2.0E10

Bunch charge [Qb] nC 3.20emittance-horizontal[ex] inequilibrium m·rad 0.91E-11

injected from linac m·rad 3E-7

emittance-vertical[ey] inequilibrium m·rad 0.046E-11



RF voltage [Vrf] GV 0.2138

RF frequency [frf] GHz 1.3

Harmonic number [h] 276831

Synchrotronoscillationtune[ns] 0.21

Energy acceptance RF % 4.995

SR loss / turn [U0] GeV 1.47E-5Energyspread[sd] inequilibrium % 7.47E-05

injected from linac % 0.1

Bunch length[sd] inequilibrium mm 5.85E-05

injected from linac mm ~1.5

Transversedampingtime[tx] s 174

turns

Longitudinaldampingtime[te] s 174

turns

Conclusionn With error, orbit correction, cavities on and tune 0.61/0.88,

l DA_x=8.6sigma,DA_y=10.1sigma@dp=0% for injected beam.

l DA_x=79.6sigma,DA_y=418.2sigma@dp=0% for damped beam.

n With error, orbit correction, cavities on and tune 0.61/0.88,

l DA_x=6.7,DA_y=6.5@dp=1% for injected beam.

l DA_x=62.0,DA_y=277.4@dp=1% for damped beam.

n Contrast with the design goal we have proposed in previous section, this design is

reasonable and meet requirements.

Wiggling Bend Scheme

Ø The inject energy is 6GeV.

Ø If all the dipoles have the same sign, 33Gs@6GeV 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.

n Introduction of Wiggling Bend Scheme

Linear Optics Ø 90 degree FODO

Ø FODO length:70 meter

DA resultn Tune:190.61/190.88 and cavity on

with error, dp=0 with error, dp=0.0

with error, dp=0.01 with error, dp=0.01

Booster Parametersn Parameter List for Alternating Magnetic Field Scheme.






Beam off-set in bend cm 1.2

Momentum compaction factor[α] 2.33E-5Strength of dipole Gs -129.18/+180.84

nB/beam 50















SR loss / turn [U0] GeV 5.42E-4Energyspread[sd] inequilibrium % 0.0147


Bunch length[sd] inequilibrium mm 0.18


Transversedampingtime[tx] ms 4.71

turns

Longitudinaldampingtime[te] ms 4.71

turns



Beam energy [E] GeV 45.5






nB/beam 50


Magnetic rigidity [Br] T·m 151.67













SR loss / turn [U0] GeV 4.85E-2Energyspread[sd] inequilibrium % 0.044




Transversedampingtime[tx] ms 400

Longitudinaldampingtime[te] ms









nB/beam 50










RF voltage [Vrf] GV 1





SR loss / turn [U0] GeV 0.46Energyspread[sd] inequilibrium % 0.078














nB/beam 50















SR loss / turn [U0] GeV 2.35Energyspread[sd] inequilibrium % 0.12






Conclusionn In the wiggling bend scheme, strength of dipole increase from 30Gs to -

129.18/+180.84 Gs.

n Shorter damping times are obtained, which is 4.7 seconds.

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,



n With error, cavities on and tune 0.61/0.88,



Moola：Modular&parallel Optics Optimization for LAttice

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 Existing lattice design codes 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.

n Introduction of Moola


Element Simulator

High Order Fields Error Simulator

Fringing Fields Simulator*

AlignmentSimulator*

BeamlineLinkList

BeamlineModify

Tracker

Radiation Parameters*

Orbit correction* Twiss*

Arbitrary Order One Turn Map

（OTM）

DynamicAperture

Frequency Map Analysis

Arbitrary Order Nonlinear

Parameters

Zlib

Optimization

Optimization Algorithm

*in the developing process


Ø Hamilton and canonical coordinates

Ø Fourth-order symplectic integrator

n Main physics base

0

0

s0

222

y2

x2

pp-p

Ape-

2xhxhp-p-1xh1-H

）（）（

t

pyypx

x

v

3

5

21

)(O))2(2

()2

())2(2)1(()

2()

)2(2)1(()

2()

)2(2()(M

ssAsBsAsBsAsBsAs


n CEPC mainring results from Moola


n CEPC mainring FMA results from Moola

2500 particles, 256 turns in 109 seconds


n CEPC mainring FMA results from Moola

2500 particles, 512 turns in 219 seconds


n CEPC mainring results from MoolaØ Arbitrary order chromaticity

Ø Detuning terms

Ø Arbitrary order one-turn-map

Ø Linear optics


Ø The reason of using HEPS lattice is that HEPS is much more smaller than CEPC and don't need much computing resources.

Ø This optimization work can be done by laptop in 30 min.

Ø Optimization algorithm: MOEA/D.

Ø Improved MOEA/D to parallel version(pMOEA/D) and the searching ability of the algorithm remain the same.

n Test the capability of Moola using HEPS lattice


n Test the capability of Moola using HEPS latticeEnergy spread 0% 1% -1%

Before Optimization

AfterOptimization

Gain factorfor x/y direction 2.7/2.2 3.0/2.3 3.3/2.1


Ø It is not a carefully work, only to test the code. The whole optimization is done by laptop in 30 min.

Ø Three detuning terms are optimized. The linear optics, tune and some other important terms are omitted for convenience.

Ø For CEPC booster or mainring, more nonlinear terms will be included in optimization.

Ø Plots show the pareto frontier

for HEPS optimization.

n Test the capability of Moola using HEPS lattice


n Optimization method for CEPC booster and mainring

Ø For preliminary consideration, optimization for CEPC booster or mainring can be finished in 3 days using 40 threads server.


Ø Moola is still preliminary, many functions are waiting to be added.

Ø With all the nonlinear parameters in computer memory, we can call them in any optimization algorithm(like all kinds of evolution algorithm).

Ø Capability test for Moola using HEPS lattice shows it is powerfull in dynamic aperture optimization.

Ø For the booster and mainring, an optimization method is proposed.

n Summary for Moola

Summary

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=8.6sigma,DA_y=10.1sigma@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.

n Moola, an optimization code, is in the developing process for further study.

Thanks for your attention！

Back up

Ø For injection, emit of booster@120Gev should be about 3.5E-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.

n Design GoalDesign Goal

Parameter Symbol Unit Value Now

Emittance @120Gev x/y nmrad 3.5 / 0.17 3.5 / 0.17Energy acceptance

for enough quantum lifetime

AE % 1.0 1.0

DA requirement(inclu. errors effect) DAx/DAy

7~8 (dp/p=0 and dp/p=1%) 6

n Design Goal for CDR

Summaryn Optimization of lattice: reference lattice design, Lcell=47.2m 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.

CEPC Mainring Design

Ø Sextupole pair for the 3rd order, but it can't be used in the mainring. So 2nd and 3rd order chromaticity can only cancelled by appropriate sextupole families.

Ø Octupole pair for the 4rd order

n Achromatic module

Plann There are 6 months left, our plan is:

l Optimization code 2 month

l Lattice redesign, with injection and ejection. 2 month

l The process of ramping. 1 month

n Design goal of CDR

l For injection, emit of booster@120Gev should be about 3.5E-9 m*rad.

l 1 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.



Beam energy [E] GeV 45.5






nB/beam 50















SR loss / turn [U0] GeV 4.85E-2Energyspread inequilibrium % 0.044


Bunch length inequilibrium mm 1.15


Transversedampingtime[tx] ms 400










nB/beam 50










RF voltage [Vrf] GV 1





SR loss / turn [U0] GeV 0.46Energyspread inequilibrium % 0.078














nB/beam 50















SR loss / turn [U0] GeV 2.35Energyspread inequilibrium % 0.12






design study of cepc booster - stfc ems · design study of cepc booster tianjian bian1, jie gao1,...

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