Lattice Design for the Taiwan Photon Source (TPS) at · PDF file · 2005-08-10Lattice Design for the Taiwan Photon Source (TPS) at NSRRC ... In real machine, ... Linear Lattice of

Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005

Lattice Design for the Taiwan Photon SourceLattice Design for the Taiwan Photon Source(TPS)(TPS)

at NSRRCat NSRRC

Chin-Cheng Kuo

On behalf of the TPS Lattice Design TeamAmbient Ground Motion and Civil Engineering

for Low Emittance Electron Storage Ring WorkshopJuly 21 ~ 22, 2005

NSRRC


OutlineOutline

TPS 3 GeV linear lattice designTPS 3 GeV nonlinear sextupoleconfiguration studyTPS 3 GeV preliminary design of orbit correction scheme, aperture requirements, lifetime calculations, etc.TPS injector booster designSummary


Design Concept of the TPSDesign Concept of the TPSBrightness ~ 1021 ph/s/mm2/mrad2/0.1%∆λ/λFlux ~ 1016 ph/s/0.1%∆λ/λNominal energy: 3 GeVUltra low emittanceAs many straights as possibleBeam current > 300 mA at 3 GeVLifetime > 10 hrTop-up injection


Theoretical Minimum Theoretical Minimum EmittanceEmittance

number partitionhorizontalJle (rade bend angeach dipol

E

radsmC DBdispersiontributed for dis/

matic DBgle, achro, small ante bendingfor separa/ F

FJ

CF

x

q

x

qx

===

×=

=

=

=

−

))MeV(511.0/

1084.3 15121

DBA) ( 1541

dependent. lattice is where(min)

13

32

θγ

θγεFor DBA:

For TBA (achromatic):

x

qx

x

qx

/

JC

)(l then εs are equaole lengthBut if dip

.ter dipole is the ouwhere θJ

C/pole thenn outer dilonger tha.~dipole is If center

321

31

231

1541064.1min

,1541(min) 4413

θγ

θγε

=

=

With same cells, TME(DBA) ~ 5 TME(TBA)In real machine, 2~3 times the TME

For 24For 24--cell 3GeV, theoretical cell 3GeV, theoretical minimuminimu emittanceemittance is 1.92 nmis 1.92 nm--radrad for the achromatic DBAfor the achromatic DBA


Minimum Minimum EmittanceEmittance for DBA cellfor DBA cell

0

2

4

6

8

10

12

2.6 2.8 3 3.2 3.4

Min

imum

em

ittan

ce (n

m-r

ad)

Energy (GeV)

16 DBA18 DBA20 DBA22 DBA24 DBA


A Large A Large RRing?ing?Suggested by members of Board of trustee to have larger circumference, September 2004.Where will be this bigger ring located?Is it possible to be on the NSRRC site?How large?


TPS Site PlanTPS Site Plan


Design goals of the TPSDesign goals of the TPSDecember, 2004December, 2004

Nominal energy: 3 GeVMaximum energy: 3.3 GeVCircumference: 518.4 mTarget emittance < 2 nm-rad at 3 GeVLong straights > 10 m (quad to quad)Standard straights > 6 mEnergy acceptance larger than ± 4%Beam current > 300 mA at 3 GeVLifetime > 10 hrTop-up injection


Linear Lattice of the TPSLinear Lattice of the TPSLong Straight: 11.72 m (Q-t-Q) X 6Standard Straight: 7 m (Q-t-Q) X 18 518.4 m, 24 cells, 6-fold High βx in long straight for injectionLow βx,y in standard straightReasonable βx,y in the whole ringHorizontal tune between 26 and 27Vertical tune between 12 and 13Large betatron de-coupling in the arc for sextupole chromatic correctionLarge dispersion in the arc to reduce sextupolestrengthReasonable distributed dispersion for reducing emittanceReasonable natural chromaticities


TPS Lattice StructureTPS Lattice Structure


TPS Lattice FunctionsTPS Lattice FunctionsOPTICAL FUNCTIONS TPS 2P18L1

0 10 20 30 40 50 60 70 800

5

10

15

20

25

S (m)

Opt

ical

func

tion

(m)

βx

βy

10*ηx

OPTICAL FUNCTIONS TPS 24P18K1

0 10 20 30 40 50 60 70 800

5

10

15

20

25

S(m)

Opt

ical

func

tions

(m)

βx

βy

10*ηx


TPS parametersTPS parameters

26.24 / 12.2826.22 / 12.28Betatron tune νx /νy

11.72m*6+7m*18Straights0.98733SR loss/turn, dipole (MeV)

864Harmonic number5.0RF voltage (MV)

499.654RF frequency (MHz)12.9 / 9.79 / 0.010.59 / 9.39 / 0.11βx / βy / ηx (m) LS middle

24 / 6 / DBACell / symmetry / structure5.81.7Nat. emittance εx(nm-rad)

518.4Circumference (m)400Beam current (mA)

3.0Energy (GeV)

Achromatic24p18L1

Non-achromatic24p18K1

TPS


TPS parameters (contdTPS parameters (contd.)

-78.2 / -35.3-78.2 / -32.5Nat. chromaticity ξx / ξy

10.5 / 10.5 / 5.25Damping time (ms) ( τx / τy /τ s)0.997 / 1.0 / 2.003Damping partition (Jx /Jy / Js)

9.53×10-4Nat. energy spread σE

2.5×10-4, 1.0×10-32.0×10-4, 2.3×10-3Mom. comp. (α1, α2)168 / 6Sext No. / Max. m*l (m-2)

240 / 17Quad No. / Max. field(T/m)48Number of dipoles

1.3789 / 0.95Dipole B/L (Tesla)/(m)2.652.34Bunch length (mm)

7.6×10-36.7×10-3Synchrotron tune νs


TPS Beam size and DivergenceTPS Beam size and Divergence

1.318.266.630.3Dipole centre

3.74.517.7126.57 m Standard straights

1.312.712.7172.311.72 m Long straight

σy’ (μrad)σy (μm)σx’ (μrad)σx(μm)Source point

24P18K1, εx = 1.72 nm-rad , εy= 0.0172 nm-rad


Flux at 3.0 GeV of TPS

101 102 103 104 105

1013

1014

1015

1016

SEPU25

SU15IVXU28EPU46EPU60

EPU70

U100

SW60

Bending

Flux

(Pho

t/s/0

.1%

bw)

Photon Energy (eV)


Brilliance at 3.0 GeV of TPS

101 102 103 104 105

1012

1013

1014

1015

1016

1017

1018

1019

1020

1021

SU15

SEPU25

IVXU28EPU46

EPU60EPU70

U100

SW60

Bending

Bril

lianc

e (P

hot/s

/0.1

%bw

/mm

2 /mr2 )

Photon Energy (eV)


Nonlinear optimizationNonlinear optimizationUsing OPA, BETA, Tracy-2, Patricia, etc., the sextupoleconfigurations are optimized.8 families of sextupoles are used.Chromaticities are corrected to zero.Weighting factors such as resonance strengths, de-tuning coefficients for amplitude-dependent tune shift, second-order effects are given. And the sextupole families, positions are changed.However, still tune shifts with amplitude are large. Dynamic apertures are limited.Nonlinear momentum-dependent tune-shift are also investigated.


SextupoleSextupole schemeschemeOPTICAL FUNCTIONS TPS 24P18K1

0 5 10 15 20 25 30 35 400

5

10

15

20

25

S(m)

Opt

ical

func

tions

(m)

βx

βy

10*ηx

S1 S2 SD SF

SD S5 S6 S7 S8 SD SF

SD S8 S7

Half superpeiod


Tune shift vs. Amplitude Tune shift vs. Amplitude &Energy&Energy

0.1

0.2

0.3

0.4

0.5

-30 -20 -10 0 10 20 30

Fra

ctio

nal t

une

x [mm]

Tune shift with amplitude, TPS 24p18K1

Tune XTune Y

0.1

0.2

0.3

0.4

0.5

-30 -20 -10 0 10 20 30

Frac

tiona

l tun

e

x [mm]

Tune shift with amplitude 24p18L1

Tune XTune Y

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-4 -3 -2 -1 0 1 2 3 4

Frac

tiona

l tun

e

dp/p [%}

tune vs. dp/p, TPS 24p18k1XY

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-4 -3 -2 -1 0 1 2 3 4

Frac

tiona

l tun

e

dp/p [%}

tune shift vs. dp/p TPS 24p18L1XY


Phase Space TrackingPhase Space Tracking

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-20 -15 -10 -5 0 5 10 15 20Y

'(mra

d)Y(mm)

Vertical Phase Space Tracking TPS 24P18K1

Vertical Phase Space 24P18K1

-4

-3

-2

-1

0

1

2

3

4

-30 -20 -10 0 10 20 30

X'(m

rad)

X(mm)

Horizontal Phase Space Tracking TPS 24P18K1

Horizontal Phase Space 24P18K1


Beta beat vs. energyBeta beat vs. energy

7

9

11

13

-4 -3 -2 -1 0 1 2 3 4

beta

[m]

dp/p [%]

beta vs. dp/p at straight middle 24p18K1

beta xbeta y

9

11

13

-4 -3 -2 -1 0 1 2 3 4

beta

[m]

dp/p [%]

beta vs. dp/p at straight middle 24p18L1

beta xbeta y


Dynamic aperture Dynamic aperture w/o synchrotron oscillationw/o synchrotron oscillation

0

5

10

15

20

25

30

-40 -30 -20 -10 0 10 20 30y

(mm

)x(mm)

Dynamic aperture, 1000 turns, no synchrotron oscillations TPS 24p18L1

DE=0 %DE= 3 %

DE= -3 %

24P18K1βx=10.59 mβy= 9.39 m

24P18L1βx= 12.9 mβy= 9.79 m

0

5

10

15

20

25

30

-30 -20 -10 0 10 20 30

y [m

m]

x [mm]

Dynamic aperture, 1000 turns, TPS 24p18k1dp/p = 0%dp/p = 3%dp/p = -3%


Frequency Map AnalysisFrequency Map Analysis

4vx＝105

vx＋2vy＝51 3vx－2vy＝54


Frequency Map AnalysisFrequency Map AnalysisID Chamber +/ID Chamber +/-- 5 mm in vertical plane5 mm in vertical plane


MultipoleMultipole Errors EffectsErrors Effects

-8.6 10-1030-pole

-1.6 10-718-pole

3.3 10-5-7.5 10-714-pole

-1.5 10-6Dodecapole

2.6 10-5-8.7 10-6Decapole

-1.6 10-6Octupole

-4.4 10-5Sextupole

sextupolequadrupoledipole

0

5

10

15

20

25

-30 -20 -10 0 10 20 30

y [m

m]

x [mm]

Dynamic aperture, 1000 turns, TPS 24p18k1

dp/p= 0 %, no errors multipole errors


Insertion Devices EffectsInsertion Devices Effects

1.250.640.67 (0.45)Max. By (Bx) Field (Tesla)

487666Number of Periods

955.6Period Length λ(cm)

4.53.93.9Magnet Length (m)

U9U5EPU5.6Insertion Device

0

5

10

15

20

25

-30 -20 -10 0 10 20 30 y

[mm

] x [mm]

Dynamic aperture, 1000 turns, TPS 24p18k1

dp/p= 0 %, no errors multipole errors


Girder SupportGirder Support

Precision ~ 15 µm


RMS Amplification factorsRMS Amplification factorsQuad misalignment in x/y only A= 59/52 in x/y rmsGirder misalignment in x/y only A= 33/9 in x/y rms

Errors: rms

Quad misalign w.r.t. girder: 0.03mm Girder misalign: 0.1mmBend roll: 0.2 mradGirder roll: 0.1 mradBend relative field error : 0.001

Results: rms COD X/Y= 3.07mm / 1.71mm


Amplification Amplification w.r.tw.r.t Quad or Girder displacementQuad or Girder displacement

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80

Am

plic

atio

n fa

ctor

S(m)

Girder amplification factor XGirder amplification factor Y

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80

Am

plifi

catio

n fa

ctor

S(m)

Quad amplification factor X Quad amplification factor Y


COD Correction SchemeCOD Correction Scheme


COD correction scheme (contd.)COD correction scheme (contd.)

Correctors and BPMsBefore & After correction


COD correction scheme (contd.)COD correction scheme (contd.)

Correctors, eigenvalues in use. Corrector strengths

Correctors UsedNumber of

eigenvaluesused

Mean of<|cor. Strength|>

(mrad)

Max of<|cor. Strength|>

(mrad)

Max of

<|res. C.O. at BPM|> (mm)(1,4,7) 72 6.0560E-02 2.9052E-01 1.5938E-01

168 72 5.4973E-02 2.0067E-01 1.5317E-01

168 96 4.1681E-02 2.0975E-01 7.3665E-02

C1-C7 168 144 4.4952E-02 2.5861E-01 4.1306E-02

(2,6) 48 3.0630E-02 1.5530E-01 2.3056E-01

(2,4,6) 72 3.7528E-02 2.4142E-01 2.3525E-01

168 48 1.0162E-02 7.0080E-02 1.8168E-01

168 72 1.2795E-02 1.0255E-01 1.0429E-01

C1-C7 96 1.5304E-02 1.3772E-01 9.1260E-02

144 2.1539E-02 1.7571E-01 5.4287E-02

H

oriz

onta

l

Ver

tical


Injection schemeInjection scheme

TPS septum and kicker parameters

7.18174.5Bend Angle (mrad) 0.08980.97 Field (T) 0.80 1.8Length (m)

kickerseptum

In a long straight K-t-K: 9.2mAnother option: Thick and Thin septa scheme

20.11 mm

22.6 mm

A=13.86 mm

Septum wall

Injected beam Store beam

Bumped store beam

Bumper height

Beam stay clear

5 mm6σi 4σoi

Acceptance

Bumped beam acceptance

x

x`

K4K3 K2 K1

0.8

Septum magnet

1.8

2.8 2.8 2.8

Kicker magnet 0.8 0.8 0.8

Injected beam

Store beam


Physical Aperture RequirementPhysical Aperture RequirementInjection requirement 4% energy acceptance

At least x: +/- 32 mm, y: +/- 6 mm BSC needed


TouschekTouschek & total lifetime& total lifetime

Touschek lifetime calculation using BETA

0

5

10

15

20

25

30

35

40

45

2 2.5 3 3.5 4

Tous

chek

life

time,

bun

ch le

ngth

and

RF

acce

ptan

ce

RF gap voltage (MV)

Touschek half life (hr)Bunch length (ps)

RF acceptance (%)

For 2.5mm haf gap ID chambers, 1 nTorr N2 equivalent gas lifetime is about 44 hours.>>>Total lifetime is around 22.5 hours for 3 MV RF, 0.6mA/bunch , and 1% coupling operation.

Acceptance in one super-periodGap voltage=3.5 MV, Touschek lifetime=18.25 hrs.

Position (m)

0 20 40 60 80

Acc

epta

nce

(%)

-4

-3

-2

-1

0

1

2

3

4

-15

-10

-5

0

5

10

15

Acceptance in negative (%) Acceptance in positive (%)

0.6 mA/bunch Coupling = 1%

Second order compaction factor limited Second order compaction factor limited


InstabilitiesInstabilities

• No SRF generated coupled bunch long. & transverse instabilities

• With small gap undulators, transverse coupled bunch instabilities might occur

• No transverse single bunch MCI• With 0.6 mA/bunch, longitudinal broadband

impedance need < 0.05 ohm• Beam-ion instabilities need to be addressed


Booster RingBooster Ring

2.02*1020 (@0.8 MV)

5.99*10-4

390.8

1.68*10-3

0.993/1.0/2.01

25.8/25.6/12.7

5.30

-30.5/-22.8

27.11/13.16

1.665*10-6

0.1

3

499.2

2.29 (@1.2 MV)13.6 (@0.7 MV)Quantum lifetime [minutes]

7.11*10-45.97*10-4Energy spread

562.78390.8Radiation loss [keV/turn]

0.0250.00492Momentum compaction α

0.95/1.0/2.050.98/1.0/2.02Damping partition (Jx/Jy/Je)

6.06/5.76/2.8126.1/25.6/12.6Damping time (τx/τy/τe) [ms]

12636.6Emittance [nm-rad.]

-8.02/-5.97-14.12/-13.96Nature chromaticity (ξx/ξy)

7.11/4.1716.13/7.18Tune νx/νy

0.5404*10-61.665*10-6Revolution time [s/turn]

0.10.1Injection energy [GeV]

33Extraction energy [GeV]

162499.2Circumference [m]


TPS siteTPS site


SummarySummaryDBA lattice structure with 24 cells, 6-fold symmetry could achieve natural emittance < 2nm-rad with a constrained circumference 518.4m and required straight lengths.Booster options are studied.Optimization of the linear lattice and nonlinear effects is in progress.Other issues such as orbit correction scheme, coupling control scheme, lifetime calculations, injection scheme, instabilities, ground vibration effects… are investigated.

Documents

Lattice Design for the Taiwan Photon Source (TPS) at · PDF file · 2005-08-10Lattice Design for the Taiwan Photon Source (TPS) at NSRRC ... In real machine, ... Linear Lattice of