review of lattice design for low emittance ring

Review of lattice design Review of lattice design for low emittance ringfor low emittance ring

R. Bartolini

Diamond Light Source Ltdand

John Adams Institute, Dept. of Physics, University of Oxford

Low Emittance Rings Workshop, Crete 3rd October 2011

MotivationsMotivations

Luminosity and brilliance scale together

yx'yy'xx24

beamIfluxbrilliance

S*

x

21revb

yx

21revb

kβ4π

NNfnS

4π

NNfnluminosity

both increase with smaller emittancesboth increase with higher current(…within limits beam-beam, collective effects, diffraction, etc)

and damping rings are required to generate small emittance beams for colliders

y,x2

t

fif e)()t(


MotivationsMotivations

Light sources

diffraction limited operation at 0.1nm requires 10’s pm

2

Colliders (B-factories)

1036 cm-2 s-1 requires 2nm (5nm for superKEKB)as present state-of-the-art light sources

Damping rings

500 pm H and 2 pm V (specs for ILC-DR)<100 pm H and 5 pm V (specs for CLIC-DR)


Accelerator physics and technology challengesAccelerator physics and technology challenges

Low emittancelattice solutionsdynamic aperture and momentum aperturelow emittance tuning

Collective effectsIBSe-cloudfast-ion, RW, CSR and others

Advanced technologyDamping wigglers - In-vacuum IDs high resolution BPMsoptical diagnostics (laser wire, pinholes, etc)high vacuum (NEG coating and low SEY material)Injection schemes (time structure for DR and DA for light

sources)


This workshop’s programme !

see R. Nagaoka’s talk

see E. Wallen’s talk

this talk

Emittance in 3Emittance in 3rdrd GLS, DR and colliders GLS, DR and colliders


Design challengesDesign challenges


• Low emittance lattices for light sources

• Low emittance lattices for damping rings

motivationsdesign approachestoolspredicted performance

1992 ESRF, France (EU) 6 GeVALS, US 1.5-1.9 GeV

1993 TLS, Taiwan 1.5 GeV1994 ELETTRA, Italy 2.4 GeV

PLS, Korea 2 GeVMAX II, Sweden 1.5 GeV

1996 APS, US 7 GeVLNLS, Brazil 1.35 GeV

1997 Spring-8, Japan 8 GeV1998 BESSY II, Germany 1.9 GeV2000 ANKA, Germany 2.5 GeV

SLS, Switzerland 2.4 GeV2004 SPEAR3, US 3 GeV

CLS, Canada 2.9 GeV2006: SOLEIL, France 2.8 GeV

DIAMOND, UK 3 GeV ASP, Australia 3 GeVMAX III, Sweden 700 MeVIndus-II, India 2.5 GeV

2008 SSRF, China 3.4 GeV2009 PETRA-III, Germany 6 GeV 2011 ALBA, Spain 3 GeV

33rdrd generation storage ring light sources generation storage ring light sources

ESRF

Diamond

> 2011 NSLS-II, US 3 GeV

MAX-IV, Sweden 1.5-3 GeVSOLARIS, Poland 3 GeVSESAME, Jordan 2.5 GeV

TPS, Taiwan 3 GeV CANDLE, Armenia 3 GeV

PEP-X, USA 4.5 GeVSpring8-II, Japan 6 GeV


under construction or planned NLSL-II

Max-IV


Photon energy

Flux

Brilliance

Stability

Polarisation

Time structure

Ring energy

Small Emittance

Insertion Devices

High Current; Feedbacks

Vibrations; Orbit Feedbacks; Top-Up

Short bunches; Short pulses

Users’ requirements Users’ requirements and Acc. Phys. and technology challengesand Acc. Phys. and technology challenges


Brilliance with IDs (medium energy light sources)Brilliance with IDs (medium energy light sources)

Medium energy storage rings with in-vacuum undulators operated at low gaps (e.g. 5-7 mm) can reach 10 keV with a brilliance of 1020 ph/s/0.1%BW/mm2/mrad2


Brilliance with IDs (ESRF upgrade)Brilliance with IDs (ESRF upgrade)

Brilliance gain on the ESRF upgrade driven by higher stored current

and smaller vertical emittance


Low emittance latticesLow emittance lattices

Lattice design has to provide low emittance and adequate space in many straight sections to accommodate long Insertion Devices

dipolex

2

x HJ

22 'D'DD2D)s(H

Zero dispersion in the straight section was used especially in early machines

avoid increasing the beam size due to energy spreadhide energy fluctuation to the usersallow straight section with zero dispersion to place RF and injectiondecouple chromatic and harmonic sextupoles

DBA and TBA lattices provide low emittance with large ratio between

Minimise and D and be close to a waist in the dipole

nceCircumfere

sections straight of Length

Flexibility for optic control for apertures (injection and lifetime)

33rdrd generation storage ring LS and damping rings generation storage ring LS and damping rings

Lattice Design:

DBA, TBA, Multi-Bend Lattice, TME-Structure

controlled dispersion in straight sections

Radiation Excitation and Damping Manipulations:

Damping Wiggler : PETRA-III, NSLS-II, MAX IV, PEP-X, Damping Rings

Combined B (Partition Control)

Robinson Wiggler (Partition Control)

see L. Nadolski’s talk

Longitudinally Variable B (Optimized Radiation Integral)

see C. Wang’s talk


DBA used at: ESRF, ELETTRA, APS, SPring8, Bessy-II, Diamond, SOLEIL,SPEAR3...

TBA used at ALS, SLS, PLS,TLS …

DBA and TBADBA and TBA

APS

ALS

Double Bend Achromat (DBA)

Triple Bend Achromat (TBA)

3

321

bx

bqx NJ

CF

154

1MEDBAF

MEDBAMETBA F9

7F

ASP

APS

Leaking dispersion in straight sections reduces the emittance

ESRF 7 nm 3.8 nmAPS 7.5 nm 2.5 nmSPring8 4.8 nm 3.0 nmSPEAR3 18.0 nm 9.8 nmALS (SB) 10.5 nm 6.7 nm

The emittance is reduced but the dispersion in the straight section

increases the beam size

Breaking the achromatic conditionBreaking the achromatic condition

154

1MEDBAF

1512

1 dispMEDBAF

2xExxx )D(

Need to make sure the effective emittance and ID effects are not made worse

New designs envisaged to achieve sub-nm emittance involve

Damping Wigglers Petra-III: 1 nmNSLS-II: 0.5 nm

MBA MAX-IV (7-BA): 0.5 nmSpring-8 (10-BA): 83 pm (2006)

10-BA had a DA –6.5 mm +9 mm reverted to a QBA (160 pm)now 6BA with 70 pm

see K. Soutome’s talk

Low emittance latticesLow emittance lattices

MAX-IV

Spring-8 upgrade

Max-IV 20-fold 7-BA achromatMax-IV 20-fold 7-BA achromat

Courtesy S. Leemans

Max-IV studies proved that a 7-BA (330 pm, and 260 pm with DW)

can deliver suffcient DA and MA to operate with standard injection

schemes

Tools used FM – driving terms

Additional octupoles were found to be effective

PEP-X 7 bend achromat cellPEP-X 7 bend achromat cell

Cell phase advances: x=(2+1/8) x 3600, y=(1+1/8) x 3600.

Natural emittance = 29 pm-rad at 4.5 GeV

5 TME units

Courtesy B. Hettel


Reduced emittance with damping wigglersReduced emittance with damping wigglers

Emittance = 11 pm-rad at 4.5 GeVwith parameters lw=5 cm, Bw=1.5 T

Courtesy Min-Huey Wang, B. Hettel, Y. Cai

Average beta function at the wiggler section is 12.4 meter.

Wiggler Field Optimization Wiggler Length Optimization


Cancellation of resonancesCancellation of resonances


All Geometrical 3rd and 4th Resonances Driven by Strong Sextupoles except 2x-2y

Third Order Fourth Order


Additional sextupoles for tuneshift and Additional sextupoles for tuneshift and 2x-2y

Without Harmonic Sextupoles With Harmonic Sextupoles

Optimized with OPA (Accelerator Design Program from SLS PSI).



Optimisation with parallel computing and ELEGANTOptimisation with parallel computing and ELEGANT


Dynamic Aperture at Injection

Excellent design of an ultimate storage ring for PEP-X

Approaching diffraction limit at one angstromReasonable beam current 200 mAGood beam lifetime 3 hoursGood injection with 10 mm acceptanceAchievable machine tolerances


New ILC Damping Ring Baseline LatticeNew ILC Damping Ring Baseline Lattice

Usually damping rings lattices have a racetrack layout with long straight sections including RF cavities, injection, extraction

and long wiggler sections


Courtesy S. Guiducci

DR for linear collider latticesDR for linear collider lattices

DR lattices are wiggler dominated:

Wigglers are needed to achieve the required damping time

Emittance with wigglers

U0 = Uarc + Uwig = Uarc (1 + Fw)

x = a/(1+Fw) + w Fw/(1+Fw)

For linear collider damping rings:

w << a ; Fw>>1

x ~ a/Fw



3.2 km Damping Ring - Lattice Comparison3.2 km Damping Ring - Lattice Comparison

26

DSB3,SuperB-style

DTC01, TME-style

DMC3, FODO

All the arc cell styles satisfy emittance and damping time requirements.

S. Guiducci, M. E. Biagini, “A Low Emittance Lattice for The ILC 3 Km Damping Ring”, IPAC’10 D. Wang, J. Gao, Y. Wang, “A New Design for ILC 3.2 km Damping Ring Based on FODO Cell”, IPAC’10 D. Rubin, DR TBR, LNF July 2011, http://ilcagenda.linearcollider.org/conferenceDisplay.py?confId=5183S. Guiducci et al., , “Updates to the International Linear Collider Damping Rings Baseline Design”, IPAC’11

S. Guiducci, M. E. Biagini, “A Low Emittance Lattice for The ILC 3 Km Damping Ring”, IPAC’10 D. Wang, J. Gao, Y. Wang, “A New Design for ILC 3.2 km Damping Ring Based on FODO Cell”, IPAC’10 D. Rubin, DR TBR, LNF July 2011, http://ilcagenda.linearcollider.org/conferenceDisplay.py?confId=5183S. Guiducci et al., , “Updates to the International Linear Collider Damping Rings Baseline Design”, IPAC’11

http://ilcagenda.linearcollider.org/conferenceDisplay.py?confId=5183

http://ilcagenda.linearcollider.org/conferenceDisplay.py?confId=5183

3.2 km ILC damping ring3.2 km ILC damping ringmain parameters comparisonmain parameters comparison

DSB3 DMC3 DTC01

Arc lattice SuberB-style FODO TME-style

Energy (GeV) 5 5 5

Circumference (m) 3238 3220 3239

Horizontal Emittance (nm) 0.66 0.36 0.45

Damping time x,y (ms) 24 23 24

Energy spread % 0.12 0.13 0.11

Energy loss/turn U0 4.5 4.7 4.5

Fw = U0wiggler/U0arc 3.5 10.8 4.6

Wiggler field (T) 1.6 1.6 1.5

Total wiggler length (m) 78 95 104



ILC-CLIC Damping Ring comparisonsILC-CLIC Damping Ring comparisons

ILC-DCO4 ILC-DTC01 CLIC

Arc lattice Modified FODO

TME-style Modified TME

Energy 5 5 2.86

Circumference (m) 6476 3239 493

Horizontal Emittance (nm) 0.45 0.45 0.079

Damping time tx (ms) 21 24 2.4

Energy spread 0.13 0.11 0.1

Energy loss/turn U0 (MeV) 10.2 4.5 3.9

Fw = Uarc/Uwiggler 10.7 4.6 6.9

Wiggler field (T) 1.6 1.5 2.5

Total wiggler length (m) 216 104 152

M.Korostelev, A.Wolski, “DCO4 Lattice Design For 6.4 Km ILC Damping Rings”, IPAC’10 Y. Papaphilippou et al., , “Lattice Options for the CLIC Damping Rings”, IPAC’09


ILC Damping Ring Dynamic ApertureILC Damping Ring Dynamic Aperture

DTC01

For ILC damping ring the DA has to be 3sx of the “large” positron beam, which is 130sx of the stored beam



Non-linear optics optimisation and control Non-linear optics optimisation and control with low emittance latticeswith low emittance lattices

Low emittance Large Nat. Chromaticity with Strong quads and Small Dispersion Strong SX Small Apertures (Dynamic and Momentum apertures)

Usually the phase advance per cell is such that low resonance driving terms are automatically compensated (to first order)

Numerical optimisation is however unavoidable

need 6D tracking (watch out alpha_2)use DA and FM plotsuse MOGA !

MOGA in elegant to optimise 8 sextupole families at Diamond improved the Touschek lifetime by 20 %


MOGA DA studies for NSLS-IIMOGA DA studies for NSLS-II


NLSL-II lattice = 0.55 nm with damping wigglers

with 3 damping wigglersTracked DA directly used as objectiveas area of ellipses for different dp/p

and-or

detuning with amplitude

Operational challengesOperational challenges


• Implementation of the linear optics of low emittance lattices

beta beatinglinear couplingLow emittance tuning

• Implementation of the non-linear optics

Frequency Map AnalysisDriving terms

Light sources optics controlsLight sources optics controls

Diamond is a third generation light source open for users since January 2007

2.7 nm emittance – 18 beamlines in operation (10 in-vacuum small gap IDs)

Most state-of-the-art light sources share the same structure

Oxford 15 miles

Diamond storage ring main parametersDiamond storage ring main parametersnon-zero dispersion latticenon-zero dispersion lattice

Energy 3 GeV

Circumference 561.6 m

No. cells 24

Symmetry 6

Straight sections 6 x 8m, 18 x 5m

Insertion devices 4 x 8m, 18 x 5m

Beam current 300 mA (500 mA)

Emittance (h, v) 2.7, 0.03 nm rad

Lifetime > 10 h

Min. ID gap 7 mm (5 mm)

Beam size (h, v) 123, 6.4 m

Beam divergence (h, v) 24, 4.2 rad

(at centre of 5 m ID)

Beam size (h, v) 178, 12.6 m

Beam divergence (h, v) 16, 2.2 rad

(at centre of 8 m ID)

48 Dipoles; 240 Quadrupoles; 168 Sextupoles (+ H and V orbit correctors + 96 Skew Quadrupoles)

3 SC RF cavities; 168 BPMs

Quads + Sexts have independent power supplies

Linear optics modelling with LOCOLinear optics modelling with LOCOLLinear inear OOptics from ptics from CClosed losed OOrbit response matrix – J. Safranek et al.rbit response matrix – J. Safranek et al.

Modified version of LOCO with constraints on gradient variations (see ICFA Newsl, Dec’07)

- beating reduced to 0.4% rms

Quadrupole variation reduced to 2%Results compatible with mag. meas. and calibrations

0 100 200 300 400 500 600-1

-0.5

0

0.5

1

S (m)

Hor

. Bet

a Bea

t (%

)

0 100 200 300 400 500 600-2

-1

0

1

2

S (m)

Ver

. Bet

a Bea

t (%

)

Hor. - beating

Ver. - beating

LOCO allowed remarkable progress with the correct implementation of the linear optics

0 50 100 150 200-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

Quad number

Str

ength

variation f

rom

model (%

)

LOCO comparison

17th April 2008

7th May 2008

Quadrupole gradient variation

Measured emittancesMeasured emittances

Coupling without skew quadrupoles off K = 0.9%

(at the pinhole location; numerical simulation gave an average emittance coupling 1.5% ± 1.0 %)

Emittance [2.78 - 2.74] (2.75) nm

Energy spread [1.1e-3 - 1.0-e3] (1.0e-3)

After coupling correction with LOCO (2*3 iterations)

1st correction K = 0.15%

2nd correction K = 0.08%

V beam size at source point 6 μm

Emittance coupling 0.08% → V emittance 2.2 pm

Variation of less than 20% over different measurements

Comparison machine/model andComparison machine/model andLowest vertical emittanceLowest vertical emittance

Model emittance

Measured emittance

-beating (rms) Coupling*

(y/ x)

Vertical emittance

ALS 6.7 nm 6.7 nm 0.5 % 0.1% 4-7 pm

APS 2.5 nm 2.5 nm 1 % 0.8% 20 pm

ASP 10 nm 10 nm 1 % 0.01% 1-2 pm

CLS 18 nm 17-19 nm 4.2% 0.2% 36 pm

Diamond 2.74 nm 2.7-2.8 nm 0.4 % 0.08% 2.0 pm

ESRF 4 nm 4 nm 1% 0.1% 3.7 pm

SLS 5.6 nm 5.4-7 nm 4.5% H; 1.3% V 0.04% 2.0 pm

SOLEIL 3.73 nm 3.70-3.75 nm 0.3 % 0.1% 4 pm

SPEAR3 9.8 nm 9.8 nm < 1% 0.05% 5 pm

SPring8 3.4 nm 3.2-3.6 nm 1.9% H; 1.5% V 0.2% 6.4 pm

SSRF 3.9 nm 3.8-4.0 nm <1% 0.13% 5 pm

* best achieved

Low emittance tuning at Low emittance tuning at Diamond and SLSDiamond and SLS for SuperBfor SuperB

Last year results on low emittance tuning and the achievement of a vertical emittance of 2.0 pm at Diamond and SLS have sparked quite some interest from the Damping ring community (CLIC and ILC) and from the Super B

In collaboration with the SuperB team (P. Raimondi,. M. Biagini, S: Liuzzo) Diamond and SLS have been used as a test-bed for new techniques for low emittance tuning based on dispersion free steering and coupling free steering.

4 MD shifts at DLSNovember 10 - February 11

See S. Liuzzo’s talk

State-of-the-art light sourceshave BPMs with turn-by-turn capabilities

e.g. Diamond

• excite the beam diagonally

• measure tbt data at all BPMs

• colour plots of the FFT

frequency / revolution frequency

BP

M n

umbe

r H

V

BP

M n

umbe

r

QX = 0.22 H tune in H

Qy = 0.36 V tune in V

All the other important lines are linear combination of

the tunes Qx and Qy

m Qx + n Qy


ESRF coupling correction with spectral lines (I)ESRF coupling correction with spectral lines (I)


See A. Franchi’s talk

Courtesy A. Franchi

ESRF coupling correction with spectral lines (II)ESRF coupling correction with spectral lines (II)

Courtesy A. Franchi


ESRF record low emittance June 2010 – At ID gaps open 4.4 0.7 pm

Reduced to 3.7 pm with additioanl skew quadrupolesCompensation of coupling during ID gaps movement• feedforward tables: gaps to skew quads via coupling measurements• feedback: V emittance – skew quads via C- driving terms

Spectral line (-1, 1) in V associated with the sextupole resonance (-1,2)

Spectral line (-1,1) from tracking data observed at all BPMs

Comparison spectral line (-1,1) from tracking data and measured (-1,1)

observed at all BPMs

BPM number

model model; measured

BPM number


Frequency Analysis of Betatron Motion and Frequency Analysis of Betatron Motion and Lattice Model ReconstructionLattice Model Reconstruction

Accelerator Model

• tracking data at all BPMs

• spectral lines from model (NAFF)

• beam data at all BPMs

• spectral lines from BPMs signals (NAFF)

Accelerator

............... )2()2(1

)2()2(1

)1()1(1

)1()1(1 NBPMNBPMNBPMNBPM aaaaA

Define the distance between the two vector of Fourier coefficients

k

MeasuredModel jAjA 22 )()(

e.g. targeting more than one line

Least Square Fit of the sextupole gradients to minimise the distance χ2 of the two Fourier coefficients vectors

Using the measured amplitudes and phases of the spectral lines of the betatron motion we can build a fit procedure to calibrate the nonlinear model of the ring

FLS2010, SLAC, 02 March 2010

Simultaneous fit of (-2,0) in H and (1,-1) in V

start

iteration 1

iteration 2

Both resonance driving terms are decreasing

(-1,1) (-2,0) sextupoles

Sextupole variation

Now the sextupole variation is limited to < 5%

Both resonances are controlled

We measured a slight improvement in the lifetime (10%)


SOLEIL’s – off momentum FM


Simulations

Measurements

Agreement few % up to dp/p 4 %

Courtesy L. Nadolski

can be used for a Least Square Fit of the sextupole gradients to minimise the distance χ2 of the two vectors

Frequency map and detuning with momentum Frequency map and detuning with momentum comparison machine vs model (I)comparison machine vs model (I)

Using the measured Frequency Map and the measured detuning with momentum we can build a fit procedure to calibrate the nonlinear model of the ring

);...(Q),...,(Q),(Q),...,(Q(A my1ymx1xetargt

The distance between the two vectors

]))y,x[(Q,...,],)y,x[(Q],)y,x[(Q],...,)y,x[(Q...., ny1ynx1x

k

MeasuredModel jAjA 22 )()(

Accelerator Model Accelerator

• tracking data

• build FM and detuning with momentum

• BPMs data with licked beams

• measure FM and detuning with momentum

FM measured FM modeldetuning with momentum

model and measured

Frequency map and detuning with momentum Frequency map and detuning with momentum comparison machine vs model (II)comparison machine vs model (II)

Sextupole strengths variation less than 3%

The most complete description of the nonlinear model is mandatory !

Measured multipolar errors to dipoles, quadrupoles and sextupoles (up to b10/a9)

Correct magnetic lengths of magnetic elements

Fringe fields to dipoles and quadrupoles

Substantial progress after correcting the frequency response of the Libera BPMs

DA measured DA model Synchrotron tune vs RF frequency

Frequency map and detuning with momentum Frequency map and detuning with momentum comparison machine vs model (III)comparison machine vs model (III)

The fit procedure based on the reconstruction of the measured FM and detuning with momentum describes well the dynamic aperture, the resonances excited and the

dependence of the synchrotron tune vs RF frequency


R. Bartolini et al. Phys. Rev. ST Accel. Beams 14, 054003

Combining the complementary information from FM and spectral line should allow the calibration of the nonlinear model and a full control of the nonlinear resonances

FLS2010, SLAC, 02 March 2010

Closed Orbit Response Matrix

from model

Closed Orbit Response Matrix

measured

fitting quadrupoles, etc

Linear lattice correction/calibration

LOCO

Spectral lines + FMA

from model

Spectral Lines + FMA

measured

fitting sextupoles and higher order

multipoles

Nonlinear lattice correction/calibration

R. Bartolini and F. Schmidt in PAC05

Frequency Maps and amplitudes and phases of the spectral line of the betatron motion can be used to compare and correct the real accelerator with the model

Comparison real lattice to modelComparison real lattice to modellinear and nonlinear opticslinear and nonlinear optics

Damping rings (CLIC – ILC), third generation light sources and recently proposed B-factories have many similarities and they all push their design to ultra low emittance

These three worlds can profit from each others’ work

Modeliing has reached impressive precision in the linear optics and significant progress has been made in the modelisation and correction of the nonlinear optics

Standard tools like FMA and driving terms analysis, possibly complemented with MOGA-type apporaches seem adequate to generate sufficient DA and MA

with MBA

Emittance should be stable also wrt to orbit pertubations and collective effects

ConclusionsConclusions


review of lattice design for low emittance ring

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