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WIRSCHAFFENWISSEN–HEUTEFÜRMORGEN
Diffraction Limited Storage Rings JointUniversitiesAcceleratorSchool
RasmusIschebeck
RasmusIschebeck>JUAS2020>DLSRs
• 1stGeneration:storageringsbuiltforparticlephysics,andusedparasiticallyforsynchrotronradiation
• 2ndGeneration:storageringsbuiltforthepurposeofgeneratingsynchrotronradiation
• 3rdGeneration:optimizedringsforlowemittance;insertiondevices(wigglersandundulators),top-upoperation
• Generation4a:freeelectronlasers• Generation4b:diffractionlimitedstoragerings
Synchrotron X-Ray Sources
2
RasmusIschebeck>JUAS2019>SynchrotronRadiaOon
Since we Have FELs, Why do we Still Need Synchrotrons?
3
TheaveragebrillianceinallexistingFELsislow
SynchrotronshavemanymorebeamlinesthanFELs
Synchrotronsoffergreaterstabilityinpointingandpulseenergy
Alloftheabove
RasmusIschebeck>JUAS2020>DLSRs
DLSR = diffraction limited storage ring
4Andreas Streun
“diffractionlimited”meanssource(=electronbeam)phasespace<<diffractionphasespace⇨ maximumbrightnesstheoreticallypossible⇨ fullspatialcoherence(point-likesource)Photonbeamphasespace=convolutionofdiffractionphasespaceandelectronbeamphasespace
2-dphasespace(nocorrelation, 〈xx’〉 = 0)
Area: emittance εx = σx⋅ σxʹ
Aspectratio: beta-function βx = σx /σxʹ
[rms] size σx2 = εx⋅ βx
[rms]divergence σxʹ 2 = εx /βx
x
xʹ
RasmusIschebeck>JUAS2020>DLSRs
MAX-IV
5MAX IV
RasmusIschebeck>JUAS2020>DLSRs
Swiss Light Source
6PSI Bildarchiv
RasmusIschebeck>JUAS2020>DLSRs
The New X-Ray Source Generation
7Andreas Streun
Emittancenormalizedtoenergyvs.circumferenceεx ∝ (Energy)2 / (Circumference)3
TheoreticalEmittancescalingε ∝ γ 2 C −3
K ≈ 2 → ≈ −1 improvement×20
CK ln3ln 2 ⋅−=γ
ε
SLS2.0
upgradeprojects
RasmusIschebeck>JUAS2020>DLSRs
Emittance
8Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 4
= size ´ divergence - correlation
@ phase space areaunit = m·rad, nm·rad, pm·radas 2-D quantity presumes decoupling
horizontal « vertical « longitudinalis an invariant of motion
gx/y of photon beam is convolution of§ electron-ex/y : property of storage ring§ diffraction-er = l/4p (l = wavelength)
angle
position
x × d ~ l/2
area is invariant
Foundations
RasmusIschebeck>JUAS2020>DLSRs
Photon Beam Emittance
9Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 5
Photon beam emittance
w ex/y electron beam emittances (at dispersion free locations)§ SLS: ex/y = 5500 / 5 pm ð : ex/y = / pm ( )
w er = l/4p diffraction emittance ® 8 pm for l =1 Å (@ 12.4 keV)w b ~ beam size / beam divergence ® phase space orientationw bx/y electron beam
§ SLS short straights: bx/y = 1.4 / 1.0 m§ SLS [super]bends: bx/y = 0.45 / 14.0 m
w br diffraction § Undulator: br » L / 2p ® » 0.3 m for L = 2 m§ [super]bend: br » 0.014 m / B [T] ® » 0.0045 m for B = 3 T
w Convoluted photon beam emittances§ Undulator @ SLS: egx/y = 5520 / 15 pm ð : egx/y = / pm§ Superbend @ SLS: egx/y = 5900 / 350 pm ð : egx/y = / pm
rxr
x
x
rrxrxrxx
rx eebb
bbeeeeeee bb
g +¾¾ ®¾÷÷ø
öççè
æ-+++=Å= =2)( 2
(same for y)
Foundations
RasmusIschebeck>JUAS2020>DLSRs
Brightness and Coherence
10Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 6
N(l) spectral photon flux
BW bandwidth of experiment
Brightness and coherence
( )îíì
´´
=þýü
2)(/)(
)()(1
)()(
lel
lelell
gg ryx
NCFB BW! •
Possible increase of brightness and coherent fraction for the SLS photon energy range (0.09...45 keV @ 0.25...140 Å )
[undulator beam lines only]
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
0.25 2.50 25.00
CF SLS
CF SLS-2
Wavelength [Å]
Coherent fraction for SLS-2 and SLS
0.00
10.00
20.00
30.00
40.00
0.25 2.50 25.00
Brightness increase SLS-2/SLS
Wavelength [Å]
Foundations
RasmusIschebeck>JUAS2019>SynchrotronRadiaOon
Which Experiments Need Transverse Coherence?
11
Holography
SingleCrystalDiffraction
PhaseContrastImaging
Alloftheabove
Nick Veasey
I Have Heard that Users Perform All of These Experiments at Synchrotrons. How Do They Achieve the Required Coherence?
RasmusIschebeck>JUAS2020>DLSRs
Electron Beam Emittance
13Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 7
Electron beam emittance 1
Horizontal emittance in electron storage ring: ¯radiation damping¯ Þ equilibrium Üquantum excitation
independent from initial conditions !
òhow to
ñ maximize this -- and -- minimize this ñ
Foundations
RasmusIschebeck>JUAS2020>DLSRs
Electron Beam Emittance
14Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 8
Electron beam emittance 2w Maximum radiation damping
§ increase radiated power ð pay with RF-power
- e.g. PETRA III: Power 1.1 ® 4.9 MW ð ex 4.4 ® 1.0 nm
w Minimum quantum excitation§ keep off-momentum orbit close to nominal orbit
ð minimize dispersion at locations of radiation (bends) • strong horizontal focusing into bends.
many short (= small deflection angle) bends to limit dispersion growth.
highest radiation at region of lowest dispersion and v.v.
ppX
D==
momentumorbitDispersion
Foundations
RasmusIschebeck>JUAS2020>DLSRs
Electron Beam Emittance
15Andreas StreunA. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 9
Electron beam emittance 3Minimum horizontal emittanceex» 1/6 pm (E[GeV])2 (F[°])3 F
ð many (n) small dipoles: F = 360°/nð focus to magnet center: F » 2..5 ´ Fmin
end bend center bend longitudinal gradient
dispersion
Beam energyDeflection angle per dipoleBeam optics...
Vertical emittance (of a flat lattice)• equilibrium emittance small by nature SLS : 0.2 pm• determined by lattice imperfections SLS : 1...10 pm
SLS: 5500 pm
Foundations
RasmusIschebeck>JUAS2020>DLSRs
• Vacuumtechnology:distributedpumping• Highprecisionmachining• Newinjectionschemes• Solid-stateRFsystems
Technological Advances
16from left to right: Agilent, Wikimedia Commons, PSI Bildarchiv
RasmusIschebeck>JUAS2020>DLSRs
Multi-Bend Achromats
17MAX IV
RasmusIschebeck>JUAS2020>DLSRs
Newconcept• Longitudinalgradientbends(LGB):fieldvariationBy = By (s)
− ε∝∫ (dispersion2...)×(B-field)3ds→highfieldatlowdispersionandv.v.
• Anti-bends(AB):By < 0 − matchingofdispersiontoLGB
(disentanglehorizontalfocusingfromdispersionmatching)
⇨Factor≈ 5loweremittancecomparedtoaconventionallattice
⇨MBA+LGB/AB:factor≈ 25!
Compact low emittance lattice concept
18
B[T]
0.00
1.50
3.00
4.50
6.00
0.00 0.10 0.20 0.30 0.40
Disp.
! AS&A.Wrulich,NIMA770(2015)98–112! AS,NIMA737(2014)148–154
SLSupgrade
RasmusIschebeck>JUAS2020>DLSRs
• Conventionalcellvs.longitudinal-gradientbend/anti-bendcell− both:angle6.7°, E = 2.4 GeV, L = 2.36 m, Δµx = 160°, Δµy = 90°, Jx ≈ 1
conventional: ε = 990 pm LGB/AB:ε = 200 pm
The LGB/AB cell for low emittance
19Andreas Streun
βx βy βx βy
dipolefieldquadfieldtotal|field|
}atR = 13 mmlongitudinalgradientbend
anti-bend
Disp.η Disp.η
SLSupgrade
RasmusIschebeck>JUAS2020>DLSRs
• HardX-rays(≈ 80 keV)fromhighB-fieldpeak(4..6 Tesla):
• ε-reductionduetoincreasedradiatedpowerfromhighfieldandfromΣ|deflectionangle| > 360° (“wigglerlattice”).
• Beamdynamics:potentialsforeaseofchromaticitycorrection
− ratherrelaxedopticsforalowemittancelattice.
− negativemomentumcompaction(likeprotonsynchrotronbelowtransitionenergy):suppressionofhead-tailinstabilityatnegativechromaticity.(chromaticityisnegativebynature)
Additional benefits of the LGB/AB cell
20Andreas Streun
SLSnormalbendSLSsuperbend
SLS-2LGsuperbend
Photonenergy[keV]
Dipole Flux [ph/mr^2/sec/0.1%bw]
0.00E+00
1.25E+13
2.50E+13
3.75E+13
5.00E+13
0 25 50 75 100
1.4 T 2.95 T5.7 T
SLSupgrade
RasmusIschebeck>JUAS2020>DLSRs
• Anewon-axisinjectionscheme− copewithreducedaperture
(physicalordynamic)− useinterplayofradiationdampingand
synchrotronoscillationinlongitudinalphasespacetoinjectoff-energy,off-phasebuton-axis.
Advanced options
21Andreas Streun
! M.Aiba,M.Böge,Á.SaáHernández,F.Marcellini&AS,PRSTAB18,020701(2015)
Figureta
kenfrom
R.H
ettel,JSR21
(201
4)p.843
◆Roundbeamscheme▪ Wishfromusers▪ Maximumbrightness&coherence▪ Mitigationofintrabeamscatteringblow-up▪ “Möbiusaccelerator”:
beamrotationoneachturntoexchangetransverseplanes ! R.Talman(CornellUniv.),PRL74.9
(1995)1590
SLSSLS-2SLS-2RB
SLSupgrade
RasmusIschebeck>JUAS2020>DLSRs
Undulator brightness
22Andreas Streun
BrightnessofU19atSLSandSLS-2
Parametersforsimplemodel:Nu = 100periodsλu = 19 mm periodgapg :¼¾ λu uptoh = 33rdharmonicradiationintoconeof
Brightnessscaleswithphotonbeamemittance(=electrons⊕ diffraction)
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−−≈=
+=⎟⎟
⎠
⎞⎜⎜⎝
⎛−⎟
⎠
⎞⎜⎝
⎛= +−uu
ouo
uu
uhhu
ggB
emccB
KK
hKJJ
eI
NNλλπ
λξξξξπα 8.147.5exp33.3
2)/(24)()()0.1%BW(4 22
2
21
21
!
( )221
2
'
12 u
u
uuuu
r
Kh
NLL
+=
=≈
γ
λλ
λλ
σ
×12
×20
RasmusIschebeck>JUAS2020>DLSRs
Fanopeningangle±0.5 mrad convolutedintoeffectiveemittanceCave• Gaussianapproximationofnon-Gaussian• onlyrelevantformicro-focusingexperiments,notforfull
fieldimaging
Superbend flux and brightness
23Andreas Streun
Brightnessincreasesuperbend 2.9 TatSLS→ 6.0 TatSLS-2 20 keV → × 17 50 keV → × 67 100 keV → × 640
Questions?
Nick Veasey