Post on 27-Apr-2020
Beam dynamics studies for the Hybrid Multi Bend Achromat lattice of the
ESRF-EBS 6GeV upgrade and future 3GeV storage rings
S.M.Liuzzo, ESRF, Tsukuba, 06/July/2016 on behalf of the ESRF beam dynamics group and ESRF-EBS upgrade project team
OUTLINE
ESRF upgrade to ultra low horizontal natural emittance (EBS) - Beam dynamics issues - Emittance optimization - Linear and non linear optics optimization - Tolerances to alignment, field, multipole and survey errors Technical challenges - Magnets - Losses - Impedance - Bending magnets beamlines Progress of the project 3GeV HMBA - Linear and non linear optics optimization
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CURRENT ESRF, ACCELERATOR CHAIN LAYOUT AND MAIN PARAMETERS
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ERSF Storage ring
C=844 m E=6 GeV
τ= 12-60 h * VRF= 8 MV εx=4 nm rad εy= 5 pm rad
I = 40-200 mA *
(*) according to filling mode
0.2-6GeV
6GeV
ABOUT ESRF: EUROPEAN SYNCHROTRON RADIATION FACILITY
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Cell 4 Injection, Cell 5, 7, 25 RF
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RADIATION SPECTRA AND COHERENT FRACTION
ESRF upgrade
Hor. Emittance [pmrad] 4000 135
Vert. Emittance [pmrad] 5 5 Energy spread [%] 0.1 0.09 βx[m]/βz [m] 37/3 6.9/2.6
Brilliance Coherence
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E.B.S. : Extremely Bright Source
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Upgrade ESRF
Energy [GeV] 6.00 6.04
Tunes 75.21, 26.34 36.44, 13.39
Emittance x [pmrad] 135 4000
Emittance y (target) [pmrad] 5 5
Energy loss per turn [MeV] 2.6 4.9
RF voltage (acceptance) [MV] 6 (5.6%) 9 (4%)
Chromaticity 6, 4 4, 7
Circumference [m] 843.98 844.39
Energy spread [%] 0.095 0.106
Beam current [mA] 200 200
Lattice type HMBA DBA
Touschek lifetime [h] ~20 ~60
MAIN LATTICE PARAMETERS
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REDUCE EMITTANCE FOR HIGHER BRILLIANCE
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B = Photons/(s mm2 mrad2 BandWidth ) Diffraction limit, at λ=10nm is 10 pmrad (lower ε does not increase B)
✏(x,y) <�
4⇡
Combined function magnets
Small bending angles
Small beam Energy
Optics: Twiss and dispersion
Strong focusing
Strong chromaticity
Non linearity
X-ray energy Available space, €
Beam lifetime
Injection
Aperture
CURRENT ESRF STORAGE RING LATTICE: DOUBLE BEND ACHROMAT
16 superperiods (mirrored cell above, 32 cells in total). Achromatic condition broken for lower emittance (εx from 7 nmrad to 4 nmrad ).
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Already a “low emittance lattice”
sextupoles
quadrupoles
dipoles
undulators undulators BM source
PROPOSED LATTICE LAYOUT FOR THE UPGRADE IN 2020: HYBRID MULTI BEND ACHROMAT
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Strong focusing (large K1) Dx, βx~0 @ 7 dipoles
2 Local dispersion bumps at –I, large Dx @ sext. for chromaticity
correction with low sextupole fields (K2) Ex = 0.135nm
sextupoles
quadrupoles
dipoles
undulators undulators
Dipoles longitudinal gradient
Dipoles + quadrupole gradient
BM source
DIPOLE FIELDS OPTIMIZATION TO REDUCE EFFECTIVE EMITTANCE AT ID
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Cell is symmetric. Vary the dipole fields to minimize the horizontal effective emittance (σxσx’): • Fixed total angle • Fixed total length • Fixed key optics
(quadruoples)
4 6 8 10 12 140
0.5
1B
[T
]
s [m]
!
x= 0.3625 "
x=1.6361e!10 U
0=2.8921 MeV
!z= 0.8625 "
z=0.0000e+00 #
x@ID=9.7385e!03 $
x$
x’@ID=1.8389e!10
0
10
20
dis
pe
rsio
n ,
H [
cm
]
B [T]#
x [cm]
H [10!2]
4 6 8 10 12 140
0.5
1
B [
T]
s [m]
!
x= 0.3625 "
x=1.3520e!10 U
0=3.3747 MeV
!z= 0.8625 "
z=0.0000e+00 #
x@ID=1.4701e!02 $
x$
x’@ID=1.7615e!10
0
10
20
dis
pers
ion
, H
[cm
]
B [T]#
x [cm]
H [10!2]
εx = 164 pm rad
εx = 135 pm rad O
PTIM
IZER
: -18%
Stronger bending where small beta and dispersion
ADVANTAGES AND CHALLANGES OF H.M.B.A. CELL
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Challenges: - Strong gradients -> small apertures - Limited free space - Installation in preexisting infrastructure - Reduced Touschek lifetime and dynamic aperture for injection
Advantages: - Lower emittance, higher brilliance - Lower RF power (6.5 instead of 8.5 MV) - Lower consumption (permanent dipoles) - (for ESRF) independent P.S.
DYNAMIC APERTURE OF UPGRADE LATTICE CELL, WITHOUT INJECTION SECTION
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Off-axis injection requires large dynamic aperture at injection Injection in a standard straight section has an efficiency of 22% (average of 10 seeds of errors), Two solutions are
adopted: 1) An ad-hoc injection cell with high beta 2) Optimized injected beam shape and emittance
Stored beam Kicked beam
septum
Injected beam 3σh=4.5 mm
Injection bump
S3 septum
K3 K2 K1 K4
S1-S2
INJECTION CELL ESRF UPGRADE (S28A)
Identical to arc cell. Identical to arc cell.
Touschek Lifetime With errors Without errors
Without injection 24.5 h 55.6 h
With injection 21.3 h 35.1 h
With injection + sextupoles 21.3 h 43.1 h
Retuning of the sextupoles in the injection cell. Sextupoles are not re-adjusted after setting errors and correction.
βx=22m , standard ID straight section βx=6.9m
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INJECTION CELL TUNING
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OP
TIMIZE
D
The injection cell brakes the periodicity of the lattice, with a relevant impact on Touschek lifetime. It is possible to tune the sextupoles and octupoles of the injection cell to restore the periodicity of the chromatic RDT, chromatic optics and dispersion.
Courtesy N.Carmignani
DYNAMIC APERTURE OF UPGRADE LATTICE CELL, WITH INJECTION SECTION
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Off-axis injection requires large dynamic aperture at injection Injection in ad-hoc straight section has an efficiency of 62% (average of 10 seeds of errors), Two solutions are
adopted: 1) An ad-hoc injection cell with high beta 2) Optimized injected beam shape and emittance
Stored beam Kicked beam
septum
Injected beam 3σh=4.5 mm
Injection bump
INJECTOR UPGRADE: EMITTANCE REDUCTION
The injection efficiency is a critical point for the new machine, so the following improvements are foreseen: Reduction of the horizontal emittance:
• Booster linear optics optimisation: εx: 120 to 95 nm On-going tests • Work off-energy by shifting the RF frequency: εx: 95 to 60 nm Tested (EBS Inj. eff. 83%) • Couple H and V emittances via equal tunes: εx: 60 to 30 nm Tested (EBS Inj. eff. 92%)
Beam shaping using a sextupole in the TL2 transfer line (+2% injection efficiency):
Page 16 1st MAC MEETING – 14-15 April L. Farvacque
• The TL2 optics is ready and working • The sextupole is installed and
connected since March 2015. • Tests started consistent with
expected (smaller optimal horizontal beta at end of TL2)
X'
Stored beam Injected beam
X
X' Emittance shaping using a sextupole Classical injection
Septum
S.White et al. IPAC2016, and work under publication
Courtesy T.Perron, L.Farvacque, S.White
DYNAMIC APERTURE OF UPGRADE LATTICE CELL, WITH INJECTION SECTION
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Off-axis injection requires large dynamic aperture at injection Injection in ad-hoc straight section has an efficiency of 92% (average of 10 seeds of errors), Two solutions are
adopted: 1) An ad-hoc injection cell with high beta 2) Optimized injected beam shape and emittance
Stored beam Kicked beam
septum
Injected beam 3σh=4.5 -> 2.2 mm
Injection bump
LINEAR AND NON LINEAR OPTIMIZATIONS
Lattice optics and non linear elements tuning is devoted to the improvement of Injection Efficiency and Touschek lifetime. However often the two optimizations are often in contrast.
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0 10 20 30 40 50
!0.06
!0.04
!0.02
0
0.02
0.04
0.06
s (m)
Mom
entu
m a
pert
ure
3.0 MV4.0 MV5.0 MV6.0 MV
⌧t /p
"y�z
Ib�3acc
After conditioning: Vacuum lifetime ~300h, Touschek lifetime < 20h.
1
⌧=
1
⌧t+
1
⌧vac
βx , ηx
βy, αy, ηx
βy
µx, µy
M(1,2), M(3,4), -I transformation
LINEAR LATTICE OPTIMIZATIONS
The variables used for the cell optimization are linear parameters and nonlinear magnets (3 sextupole families and 1 octupole). Each parameter is linked to mainly one parameter of interest for Beam dynamics (variations of tune with amplitude and momentum, chromaticity, emittance). These parameters are tuned empirically and using NSGAII (a.k.a. MOGA).
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OTHER OPTIMIZATIONS: CHROMATICITY SCANS
High chromaticity improves lifetime probably due to overcompensation at small amplitude of path lengthening effects.
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The strong path lengthening effect implies that the use of an harmonic cavity could help to increase D.A.
Nat.Chrom.
(10,10)
(-10,-10)
OPTIMIZATIONS OF LATTICE WITH ERRORS
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Optimizations computing the objective functions on several seeds of errors, usually 10. Each point in the plot is the average on 10 error seeds! For each seed on 1 core: 3-4h errors and correction 1h Dynamic aperture 3h Touschek lifetime A very large computer power is needed.
NSGAII optimization, with free chromaticities. Optimum values have positive chromaticities: 10-5.
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Courtesy N.Carmignani
Starting point
Pareto front of optimal solutions
Initial population
TUNE WORKING POINT SCANS
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In this figures: sextupoles optimized at (.23, .34) and no injection cell
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NEEDS AND CHALLENGES FOR OPTICS CORRECTION: CORRECTORS AND BPM
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Correctors in all sextupoles plus 3 separated correctors All magnets have independent power supplies
10 BPM 9 correctors, horizontal,
vertical and skew quadrupole in all
sextupoles and 3 dedicated correctors
16 quadrupoles
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DQ DL DL DQ
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EXAMPLE OF CORRECTION OF RANDOM ERRORS
Simulation of the whole correction sequence, from transfer line to ORM* fit.
- Find a closed orbit correcting open trajectories
- Correct orbit
- Create lattice error model fitting ‘measured’ RM (partial, 14/288 cor.)
ORMerr = [Δ ORM/ΔK ] * ΔKfit
- Compute Resonance Driving Terms and correct simultaneously normal and skew quadrupole RDT and dispersion
- Fix tune and chromaticity
- Iterate a few times
*Orbit Response Matrix
Closed orbit only
After tuning
Current ESRF
X [µm] 160(675) 116 61 Y [µm] 111(250) 58 70
Dx-Dx0 [m] 0.017 0.001 0.028 Dy [m] 0.002 0.0002 0.002
β-beating x [%] 26.2 0.7 4.9 β-beating y [%] 26.5 0.8 3.3
Tune x [.21] 0.208 0.21 0.44 Tune y [.34] 0.336 0.34 0.39
Q’x [6] 6.328 6.00 3.89 Q’y [4] 3.971 4.00 6.92
εx [134.7 pmrad] 250.4 134.7 4099 εy [ 0.04 pmrad] 2.2 0.18 3.123
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DISPERSION AND BETA BEATING CORRECTION (NORMAL AND SKEW QUAD.)
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1) Create lattice error model fitting ‘measured’ Response Matrix (partial,
14/288 correctors)
ORMerr = [Δ ORM/ΔK ] * ΔKfit 2) Compute normal (K1s) and skew (K1s) quad. Resonance Driving Terms: these quantities are linear with K1 and K1s. 3) Correct simultaneously RDTs and dispersion à correct beta-beating, coupling and dispersion .
IMPACT OF ALIGNMENT ERRORS
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The above correction scheme is used for each simulated lattice. The same figure generated for D.A., emittances, optics,… and several other error sources to determine tolerable lattice errors.
See legend for error ranges
S25, no injection cell
TOLERABLE RANDOM ERRORS
Each error, on each magnet family, is studied individually looking at the dependence of DA, lifetime, emittances and all relevant parameters vs error amplitude.
Required: DX DY DS DPSI DK µm µm µm µrad 10^-4
DL >100 >100 1000 500 10
DQ, QF[68] 70 50 500 200 5
Q[DF][1-5] 100 85 500 500 5
SFD 70 50 500 1000 35
OF 100 100 500 1000
Sextupoles and high gradient quadrupoles are the most relevant limitations, nevertheless, these alignment specifications are currently achievable.
(DX=DY=60µm, 84 µm between two magnets). l KEK Accelerator Seminar l June 2016 l S.M.Liuzzo Page 27
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MULTIPOLE ERRORS
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Simulated systematic and random multipole errors to estimate tolerance
define tolerated DG/G@7mm
CURRENT ESRF SURVEY
X-ray beam direction is strongly influenced by the position of the storage ring and orbit distortion. The colleagues from the alignment group provided 50 simulation of possible lattice positioning errors for the EBS storage ring lattice.
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!0.01 0 0.01 0.02
!0.015
!0.01
!0.005
0
0.005
0.01
0.015
x [m]
y [m
]
X!ray beam position after: 60 m
S28A surv.ESRF surv.
INSTALLATION OF THE STORAGE RING ON THE PRESENT SURVEY
All ID are assumed to be at 60m from the source. The position of the beam after 60m is very similar for ESRF and S28A considering the current survey measurement. The position if the ring was aligned on the reference circumference would be about (0,0) for al ID.
Current (simulated) position of the X-ray at the beamline
position of the X-ray at the beamline for S28A on the same survey
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SUMMARY OF ERROR IMPACT
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Studied and selected error sources provide DA, injection efficiency and Touschek lifetimes within the requirements
Systematic and random multipole errors Survey errors
Alignment and main field errors
S28C
LOSS SIMULATIONS
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The simulation of Touschek losses allowed to conceive a collimation scheme that concentrates Touschek losses on two horizontal scrapers without affecting lifetime. These simulations are also used for radioprotection issues.
Courtesy R.Versteegen
IMPEDANCE BUDGET
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Total impedance budget comparable to current machine impedance: Z=0.65 Ω
Courtesy S.White
BUNCH LENGTHENING VS CURRENT
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Operating modes: 200mA / 876 bunches Lifetime: 18.9 ± 1.1 h 96mA / 16 bunches Lifetime: 1.9 ± 0.1 h 40mA / 4 bunches Lifetime: 1.1 ± 0.1 h Continuous top-up since April 2016
Courtesy N.Carmignani
MAGNETS DESIGN
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Courtesy G. Le Bec
BENDING MAGNET RADIATION SOURCES
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Courtesy P.Raimondi, J.Chavanne
PROJECT STATUS
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Courtesy P. Raimondi
3 GEV HMBA
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HMBA@3GeV, 506m D.A.@ID, no errors: 8mm Touschek Lifetime: 9.4h
b2 < 56 T/m, b3<1000 T/m2
This lattice has relaxed features compared to ESRF-EBS 6GeV HMBA: lower field magnets, more space between magnets, no octupoles.
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Lattice optimizations A slow but rewarding iterative process of optimization led to the lattice presented here. The optimization shown on the sides are: • Optics, Sextupoles: 6.5h lifetime and 8mm DA • Dipole fields (at fixed optics)
• Longitudinal gradient in DL decrease emittance of 20pmrad and increase dispersion at sextupoles by 5%
• DQ length to increase dispersion at the sextupoles
• Dispersion at ID can further decrease the emittance, stronger sextupoles
• Working Point scan with small errors over several units (6.5h to 9.4h lifetime)
Final DA is comparable to ESRF-EBS 6GeV HMBA.
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Lattice optimizations A slow but rewarding iterative process of optimization led to the lattice presented here. The optimization shown on the sides are: • Optics, Sextupoles: 6.5h lifetime and 8mm DA • Dipole fields (at fixed optics)
• Longitudinal gradient in DL decrease emittance of 20pmrad and increase dispersion at sextupoles by 5%
• DQ length to increase dispersion at the sextupoles
• Dispersion at ID can further decrease the emittance, stronger sextupoles
• Working Point scan with small errors over several units (6.5h to 9.4h lifetime)
Final DA is comparable to ESRF-EBS 6GeV HMBA.
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Lattice optimizations A slow but rewarding iterative process of optimization led to the lattice presented here. The optimization shown on the sides are: • Optics, Sextupoles: 6.5h lifetime and 8mm DA • Dipole fields (at fixed optics)
• Longitudinal gradient in DL decrease emittance of 20pmrad and increase dispersion at sextupoles by 5%
• DQ length to increase dispersion at the sextupoles
• Dispersion at ID can further decrease the emittance, stronger sextupoles
• Working Point scan with small errors over several units (6.5h to 9.4h lifetime)
Final DA is comparable to ESRF-EBS 6GeV HMBA.
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DA comparable to ESRF-EBS 6GeV HMBA at IDs without errors.
3 GEV LATTICE DESIGNS COMPARISON : PERFORMANCE FACTOR
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MAX IV [1] Sirius [3] DTBA [4] HMBA SSRF-U [5]
Circ. [m] 528 518.4 561 506 432 #cells 20 20 24 22 20
Emittance 330 280 100 140 203
Jx 1.8 1.31 1.38 1.42 2 Tune 42.24,16.27 44.60,12.40 57.20,20.30 54.59,15.43 43.22,17.31
Nat. Chrom. -50,-50 -113,-80 -105,-79 -88,-71 -74.2,-59.3
Drift [%] 17.9 27.1 34.7 25.2 25.9 performance 54 97 347 179 128
Performance = Drift [%] / emittance [nm]
More space for undulators, smaller emittance
OUTLINE FOR QUESTIONS
ESRF upgrade to ultra low horizontal natural emittance (EBS) - Beam dynamics issues - Emittance optimization - Linear and non linear optics optimization - Tolerances to alignment, field, multipole and survey errors Technical challenges - Magnets - Losses - Impedance - Bending magnets beamlines Progress of the project 3GeV HMBA - Linear and non linear optics optimization
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REFERENCES
[1] J.C. Biasci et al. , “A low emittance lattice for the ESRF”, Synchrotron Radiation News, vol. 27, Iss.6, 2014.
[2] “ESRF upgrade programme phase II”, ESRF, December 2014.
[3] N.Carmignani et al., “ Linear and Nonlinear Optimizations for the ESRF Upgrade Lattice”, TUPWA013, IPAC’15, Richmond, Virginia,USA (2015).
[4] S.M. Liuzzo et al., “ Influence of errors in the ESRF upgrade lattice”, TUPWA014, IPAC’15, Richmond, Virginia,USA (2015).
[5] J. Chavanne, "Implementation of short wigglers as photon sources for the bending magnet beamlines in the new ESRF lattice", ESRF, Grenoble, France, 01-15/IDM, Sep. 2015.
[6] S. White et al., “Horizontal phase space shaping for optimized off-axis injection efficiency ”, THPMR016, These Proceedings, IPAC’16, Busan, Korea (2016).
[7] B. Nash, et al., “New Functionality for Beam Dynamics in Accelerator Toolbox (AT)”, MOPWA014, IPAC’15, Richmond, Virginia, USA (2015).
[8] R. Versteegen et al., “Collimation scheme for the ESRF upgrade”, TUPWA016, IPAC’15, Richmond, Virginia,USA (2015).
[9] R. Versteegen et al., “Modelling of beam losses at the ESRF”, TUPWA016, IPAC’15, Richmond, Virginia,USA (2015).
[10] S.M. Liuzzo et al., “Updates on lattice modelling and tuning for the ESRF-EBS upgrade lattice”, TUPWA014, IPAC’16, Busan, Korea (2016).
[11] A. Alekou et al., “Study of a Double Triple Bend Achromat (DTBA) Lattice for a 3 GeV Light Source”, WEPOW044, Busan, Korea (2016).
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