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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(
Low Emittance Rings Workshop, Crete 3rd October 2011
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)
Low Emittance Rings Workshop, Crete 3rd October 2011
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)
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
Design challengesDesign challenges
Low Emittance Rings Workshop, Crete 3rd October 2011
• 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
33rdrd generation storage ring light sources generation storage ring light sources
under construction or planned NLSL-II
Max-IV
Low Emittance Rings Workshop, Crete 3rd October 2011
33rdrd generation storage ring light sources generation storage ring light sources
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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 Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
Cancellation of resonancesCancellation of resonances
Low Emittance Rings Workshop, Crete 3rd October 2011
All Geometrical 3rd and 4th Resonances Driven by Strong Sextupoles except 2x-2y
Third Order Fourth Order
Courtesy Min-Huey Wang, B. Hettel, Y. Cai
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).
Low Emittance Rings Workshop, Crete 3rd October 2011
Courtesy Min-Huey Wang, B. Hettel, Y. Cai
Optimisation with parallel computing and ELEGANTOptimisation with parallel computing and ELEGANT
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Courtesy Min-Huey Wang, B. Hettel, Y. Cai
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
Courtesy S. Guiducci
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
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
Low Emittance Rings Workshop, Crete 3rd October 2011
Courtesy S. Guiducci
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
Courtesy S. Guiducci
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
Low Emittance Rings Workshop, Crete 3rd October 2011
Courtesy S. Guiducci
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 %
Low Emittance Rings Workshop, Crete 3rd October 2011
MOGA DA studies for NSLS-IIMOGA DA studies for NSLS-II
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
• 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
Low Emittance Rings Workshop, Crete 3rd October 2011
ESRF coupling correction with spectral lines (I)ESRF coupling correction with spectral lines (I)
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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%)
Low Emittance Rings Workshop, Crete 3rd October 2011
SOLEIL’s – off momentum FM
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011
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
Low Emittance Rings Workshop, Crete 3rd October 2011