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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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?
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
TPS Site PlanTPS Site Plan
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
TPS Lattice StructureTPS Lattice Structure
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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)
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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)
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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.
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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%
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
Frequency Map AnalysisFrequency Map Analysis
4vx=105
vx+2vy=51 3vx-2vy=54
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
Frequency Map AnalysisFrequency Map AnalysisID Chamber +/ID Chamber +/-- 5 mm in vertical plane5 mm in vertical plane
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
Girder SupportGirder Support
Precision ~ 15 µm
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
COD Correction SchemeCOD Correction Scheme
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
COD correction scheme (contd.)COD correction scheme (contd.)
Correctors and BPMsBefore & After correction
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
Physical Aperture RequirementPhysical Aperture RequirementInjection requirement 4% energy acceptance
At least x: +/- 32 mm, y: +/- 6 mm BSC needed
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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]
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
TPS siteTPS site
Lattice Design of the TPS Chin-Cheng Kuo July 21, 2005
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.
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