rasmus ischebeck diffraction limited storage rings...rasmus ischebeck > juas 2020 > dlsrs...

$: Rasmus Ischebeck Diffraction Limited Storage Rings...Rasmus Ischebeck > JUAS 2020 > DLSRs Brightness and Coherence. A. Streun: SLS 2.0 Photon Science Seminar, Feb. 27, 2015 6 Andreas$
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


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


MAX-IV

5MAX IV


Swiss Light Source

6PSI Bildarchiv


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


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


Photon Beam Emittance


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


Brightness and Coherence


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?


Electron Beam Emittance


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




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




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


• Vacuumtechnology:distributedpumping• Highprecisionmachining• Newinjectionschemes• Solid-stateRFsystems

Technological Advances

16from left to right: Agilent, Wikimedia Commons, PSI Bildarchiv


Multi-Bend Achromats

17MAX IV


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


• 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


• 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


• 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


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


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

rasmus ischebeck diffraction limited storage rings...rasmus ischebeck > juas 2020 > dlsrs...

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