Shen 3/31/03

ERL & Coherent XERL & Coherent X--ray Applicationsray Applications

Qun ShenCornell High Energy Synchrotron Source (CHESS)

Cornell University

Talk OutlineTalk Outline

•• Introduction to xIntroduction to x--ray coherenceray coherence

•• Coherent xCoherent x--ray applications ray applications

•• Desired ERL propertiesDesired ERL properties

•• Options and improvements Options and improvements

•• Conclusions Conclusions

Shen 3/31/03

SourceSource EmittanceEmittance and Brillianceand Brilliance

xx’

Integrated total flux Fn

⇒ PhasePhase--space space EmittanceEmittance::

EM wave: E(r, t) = E0 ei(k·r−ωt)

t

E

στ

σE

ετ = στ σE / E

y

y’

σy

σy’

εy = σy σy’

x

x’

σx

σx’

εx = σx σx’

⇒ BrillianceBrilliance: photon flux density in phase: photon flux density in phase--spacespace

B =Fn

(2π)3 εx ·εy·ετ

^PeakB =Fn

(2π)2 εx ·εyAverage

Shen 3/31/03

Spatial (Transverse) CoherenceSpatial (Transverse) Coherence

2σ

θ2σ

2σ' ∆l = θ • 2σ = λ/2

=> 2θ • 2σ ~ λ

θ σ'

X-ray beam is spatially coherentif phase-space area 2πσ’σ < λ/2

=>

Diffraction limited source: 2πσ'σ = λ/2 or ε = λ/4π

Almost diffraction limited: 2πσ'σ ~ λ or ε ~ λ/2π

Shen 3/31/03

Temporal (Longitudinal) CoherenceTemporal (Longitudinal) Coherence

λ λ+∆λ Coherence length: lc = λ2/∆λ

Coherence time: ∆tc = lc/c

Temporally coherent source: pulse length FWHM τ ≤ ∆tclc = λ2/∆λ

⇒ uncertainty: τ ·∆ν ≤ 1τ ·∆Ε ≤ hFor λ = 1 Å, ∆λ/λ = 10-4 :

lc = 1 µm, ∆tc = 1 µm / 3x108 m/s = 3.3 fsDegeneracy Parameter δD

= Number of photons incoherent volume

= Number of photons within single quantum mode

X-ray optics can modify ∆λ/λ, but extinction length (~100µm) limits to ∆λ/λ = 10-6 => ∆tc= 330 fs

⇒ ERL with σt = 100 fs pulses coupled with 10 meV x-ray monochromator could mean temporal coherence at 10 keV.

Shen 3/31/03

Transverse Coherence from Transverse Coherence from UndulatorUndulator

θd Lθθ = = λλ/2d/2d

Example: APS, L =2.4m, λ =1.5Åσr' = 13.1 µrad

dy = 2.35x21µm, σy' = 6.9 µradθ = 1.5 µrad, Θ = 2.35x14.8 µrad

=> pc(vertical) = 4.3%

dx = 2.35x350µm, σx' = 23.1 µrad θ = 0.091 µrad, Θ = 2.35x26.6 µrad

=> pc(horizontal) = 0.15%

=> pc (overall) = 0.006%

Lr

r

2

'35.2

'

22'

λσ

σσ

=

+=Θ

⇒ A portion, θ/Θ in each direction, of undulator radiation is spatially coherent within central cone

⇒ Coherent fraction pc: depends only on total emittances

yxnn

cc F

BFF

pεεπ

λλ2

22

)4()2/(

=⋅

==ERL: pc ~ 20% (45% in x or y)

Shen 3/31/03

ERL Spatial CoherenceERL Spatial Coherence

Diffraction limited @ 8keV (0.123Å)ESRF emittance(4nm x 0.01nm) ERL emittance (0.015nm=0.15Å)

Diffraction limited source: 2πσ'σ = λ/2 or ε = λ/4π

Almost diffraction limited: 2πσ'σ ~ λ or ε ~ λ/2π

Phase II ERLPhase II ERL: diffraction: diffraction--limited source limited source E < 6.6 E < 6.6 keVkeValmostalmost diffractiondiffraction--limited tolimited to 13 13 keVkeV

Shen 3/31/03

XX--ray Coherence Workshop Programray Coherence Workshop Programhttp://www.chess.cornell.edu/Meetings

Friday, 22 August, 2003

8:30 Qun Shen (CHESS) Welcome

8:35 Sol Gruner (Cornell) Energy recovery linac source properties

8:55 Jerry Hastings (SLAC) XFEL source properties

9:15 Bruno Lengeler (Aachen) Tutorial on X-ray coherence

10:05 Coffee Break

10:30 Mark Sutton (McGill) X-ray photon correlation spectroscopy

11:00 Gerhard Gruebel (ESRF) Coherent SAXS

11:30 Jeroen Goedkoop (WZI) Magnetic speckle

12:00 Discussion on coherent scattering I: time correlation

12:15 Lunch

14:00 Ian Robinson (UIUC) Crytallography on nanocrystallites

14:30 John Spence (ASU) Ptychography and diffractive imaging: How it works, with electrons and x-rays

15:00 Coffee Break

15:20 Tetsuya Ishikawa (SPring8) Coherence preserving reflecting and crystal optics

15:50 Christian David (PSI) Diffractive optics and shearing interferometer

16:20 David Paterson (APS) X-ray coherence measurements

16:50 Discussion on coherent optics

Saturday, 23 August, 2003

8:30 Chris Jacobsen (SUNY-SB) Overview on coherent x-ray microscopy

9:00 Keith Nugent (Melbourne) Phase imaging and phase retrieval

9:30 Peter Cloetens (ESRF) 3D phase tomography

10:00 Discussion on phase contrast microscopy

10:15 Coffee Break

10:35 Enzo Di Fabrizio (Eletra) Wavefront shaping & lithography

11:05 Anatoly Snigirev (ESRF) Fourier transform holography

11:35 Makina Yabashi (SPring8) Two-photon interferometry

12:05 Discussion on holography and interferometry

12:20 Lunch

14:00 David Sayre (SUNY-SB) Crystallography applied to noncrystalline materials

14:30 John Miao (SSRL, SLAC) Imaging with single molecule diffraction

15:00 Malcolm Howells (LBNL) Holography by phase retrieval

15:30 Discussion on coherent scattering II: structure determination

Shen 3/31/03

XX--ray Microscopyray Microscopy

ESRF ID21: TXMTXM 3-6 keV

• Increasing number of SR imaging microscopes worldwide due to availability of => lens-like optics: zone plates, KB mirrors, CRLs=> high-brilliance & high-energy synchrotron sources

• All types of materials are studied, from biological to magnetic

• Two types: full field & scanning

⇒ transmission⇒ fluorescence⇒ XPEEMERL hi-coherence

ESRF ID21: SXM 2-10 keV & < 2keVSXM

Shen 3/31/03

Issues in Hard XIssues in Hard X--ray Microscopyray Microscopy

• Focusing opticsFocusing optics

• High coherence sourcesHigh coherence sources:

Coherence fraction ~ λ2/(εxεy). => Requires 100x smaller emittance product for

1keV => 10 keV

ERL would offer 102-103x better emittanceproduct than present-day hard x-ray sources

=> Better coherence @10 keV than @1 keV at ALS

• Absorption vs. phase contrastAbsorption vs. phase contrast

Only recently has Fresnel zone-plate (FZP) achieved <100nm resolution at 8keV (Yun, 1999)

Refraction index: n = 1 − δ − iβ

absorption contrast: µz = 4πβz/λ ∼ λ3

phase contrast: φ(z) = 2πδz/λ ∼ λz

C94H139N24O31S

1010

108

106

104

103102 104

Kirz (1995): 0.05µm protein in 10µm thick ice

X-ray Energy (eV)

Dos

e (G

r) absorption contrast

phase contrast

• In general, phase contrast requires:=> coherent hard x-ray beams

• Phase contrast is x104 higher than absorption contrast for protein in water @ 8keV

• Dose reduced to level comparable to using water-window in soft x-ray region

Shen 3/31/03

Phase Imaging &Phase Imaging & TomographyTomography

λ

Cloetens et al. (1999): ESRF, ID19, 18 keVPolystyrene foam 0.7x0.5x1mm3

1.4T wiggler, B~7x1014 ph/s/mr2/mm2/0.1% @100mA4x700 images at 25 sec/image

• A form of Gabor in-line holography• Coherence over 1st Fresnel zone (λR)1/2

• Image reconstruction (phase retrieval)• Spatial resolution limited by pixel size

• With ERL: it would be possible to reduce the exposure times by orders of magnitude.

• It offers great potential for flash imaging studies of biological specimens, at ID beam lines.

Shen 3/31/03

FarFar--Field Diffraction MicroscopyField Diffraction Microscopy

• Spatial resolution: essentially no limit.(only limited by ∆λ/λ and weak signals at large angles)

• Key development: oversampling phasing methodcoherent flux!!

• Coherent diffraction from noncrystalline specimen:=> continuous Fourier transform

• Diffraction microscopy is analogous to crystallography, but for noncrystalline materials

• Coherence requirement: coherent illumination of sample

Coherent X-rays

Miao et al. (1999) >>>soft x-rays, reconstruction to 75 nm

Shen 3/31/03

Diffraction MicroscopyDiffraction Microscopyrecent resultsrecent results

reconstructed image: to d~7nm resolution

Miao et al. PRL (2002) λ = 2 Å

Gold: 2.5µm x 2µm x 0.1µm

=> could achieve higher resolution,limited only by radiation damage

ERL high-coherence option:B=5x1022 ph/s/mr2/mm2/0.1% @10mAExposure time for Si & d~7nm: 0.6 min.

for C & d~7nm: 3.5 min.

SPring-8 BL29XU:standard undulator 140 periods λu=3.2 cmB=2x1019 ph/s/mr2/mm2/0.1% @100mAFor Au, exposure time 50 min, d~7nmbut: for Si, (ZSi/ZAu)2~1/32 => 26 hrs !

for C, (Zc/ZAu)2~1/173 => 6 days !!

Shen 3/31/03

Imaging Whole Escherichia Coli Bacteria Using Single Particle X-ray Diffraction

Jianwei Miao*†, Keith O. Hodgson*‡, Tetsuya Ishikawa§,

Carolyn A. Larabell¶?, Mark A. LeGros**, and Yoshinori Nishino§

Miao et al., Proc. Nat. Acad. Sci. (2003)

E. Coli bacteria ~ 0.5 µm by 2 µm

SPring-8, λ = 2 Å, pinhole 20 µm

Total dose to specimen ~ 8x106 Gray

Diffraction image to ~30nm resolution

Shen 3/31/03

XX--ray Photon Correlation Spectroscopyray Photon Correlation Spectroscopy

Dierker (2000), ERL Workshop

Shen 3/31/03

XX--ray Holography with Reference Waveray Holography with Reference Wave

Wilhein et al. (2001).Leitenberger & Snigirev (2001)

Howells et al. (2001); Szoke (2001).

Illumination of two objects, one as reference, e.g. pin-hole arrays

• X-ray holography is exciting but not ready for applications

• ERL is an ideal source for further research in this area

Shen 3/31/03

Coherent XCoherent X--ray Patterning & Lithographyray Patterning & Lithography

DOEDOE: diffractive : diffractive optics elementoptics element

Coherent XCoherent X--raysrays

SHAPING X-RAYS BY DIFFRACTIVE CODED NANO-OPTICS

Enzo Di Fabrizio TASC-NNL-INFM (National Institute for the Physics of Matter) Elettra Synchrotron Light Source

(invited talk X-ray Coherence 2003)

Lithography Lithography XX--ray CVD ray CVD

MasklessMaskless patternpattern

Shen 3/31/03

Desired ERL PropertiesDesired ERL Properties

X-ray photon correlation spectroscopyPhase-contrast imaging & microscopy

Coherent far-field diffractionCoherent crystallography

X-ray holographyCoherent x-ray lithography

full transverse coherencehigh coherent flux / coh. fractionhigh ∆λ/λ for high resolutionsmall beam (some cases)large coherent area (some cases)CW operation: long pulses okay

D1 D2

Basic Requirement:Basic Requirement:

⇒⇒ low transverse low transverse emittancesemittances

⇒⇒ long long undulators undulators (large (large NNuu))

⇒⇒ low machine energy spreadlow machine energy spread⇒ X-ray optical slope error

δθ << σx/D1 ~ 4µm/40m ~ 0.1µrad ⇒⇒ coherence preserving xcoherence preserving x--ray opticsray optics

Shen 3/31/03

Phase II ERL Coherent FluxPhase II ERL Coherent Flux

3 4 5 6 7 8 910 20 30 40 50

109

1010

1011

1012

1013

1014

1015LCLS SASE

APS 2.4m

ESRF U35

APS 4.8m

Sp8 5m

Sp8 25m

0.15nm 100mA

ERL 25m0.015nm 10mA

Coh

eren

t Flu

x (p

hoto

ns/s

/0.1

%)

Photon Energy (keV)

• Time-averaged coherent flux comparable to LCLS XFEL

• Coherent fraction ~100x greater than 3rd SR sources

• Peak coherent flux (coherent flux per pulse) ~1000x greater than 3rd SR sources

???

Shen 3/31/03

CHESS Tech Memo 01CHESS Tech Memo 01--002: 3/8/01002: 3/8/01http://erl.chess.cornell.edu/papers

Ave. flux Fn (p/s/0.1%) 1.5· 1016 1.5· 1015 7.0· 1014 4.2· 1015 1.3· 1015 2.4· 1015 9.0· 1015 3.3· 1010 2.4· 1014 6.4· 1012 4· 1017 Ave. brilliance B

(p/s/0.1%/mm2/mr2) 1.3· 1022 5.2· 1022 1.5· 1019 1.5· 1021 3.1· 1020 5.0· 1020 2.2· 1021 1.6· 1017 4.2· 1022 3.6· 1019 8· 1025

Coh flux Fc (p/s/0.1%) 8.1· 1013 3.1· 1014 0.9· 1011 9.0· 1012 1.8· 1012 3.0· 1012 1.3· 1013 9.0· 108 2.4· 1014 1.4· 1011 4· 1017

DC

exp

erim

ents

Coh. fraction pc (%) 0.52 20 0.013 0.22 0.14 0.13 0.14 2.7 100 2.1 100

Photons / bunch 1.2· 107 1.2· 106 9.6· 107 1.9· 108 5.7· 106 7.1· 106 2.7· 107 2.8· 108 2· 1012 1.1· 108 7· 1012 Peak brilliance

(p/s/0.1%/mm2/mr2) 3.0· 1025 1.2· 1026 2.5· 1022 8.3· 1023 3.3· 1022 3.6· 1022 1.6· 1023 4.8· 1027 1.2· 1033 3.4· 1027 7· 1033

Peak flux (p/s/0.1%) 3.9· 1019 3.9· 1018 1.3· 1018 2.6· 1018 1.6· 1017 1.9· 1017 7.4· 1017 1.2· 1021 7.2· 1024 6.0· 1020 3· 1025

Pk coh. flux (p/s/0.1%) 2.1· 1017 7.9· 1017 1.7· 1014 5.6· 1015 2.2· 1014 2.5· 1014 1.1· 1015 2.7· 1019 7.2· 1024 1.4· 1019 3· 1025 Puls

ed e

xpts

.

Peak degen. par. δD 95 368 0.078 2.6 0.103 0.113 0.49 1.3· 104 3.3· 109 4.7· 103 8· 109

Assuming high duty-cycle operations

ERL hi-flux

ERL hi-coh.

APS und. A

APS upgrade

ESRF U35

Spring8 5m

Spring8 25m

LCLS spont.

LCLS SASE

TESLA spont.

TESLA SASE

Energy EG (GeV) 5.3 5.3 7 7 6 8 8 15 15 25 25

Current I (mA) 100 10 100 300 200 100 100 72· 10-6 72· 10-6 0.063 0.063

Charge q (nC/bunch) 0.077 0.008 14 14 0.85 0.29 0.29 1 1 1 1

εx (nm-rad) 0.15 0.015 8 3.5 4 6 6 0.05 0.05 0.02 0.02

εy (nm-rad) 0.15 0.015 0.08 0.0035 0.01 0.003 0.003 0.05 0.05 0.02 0.02

Bunch fwhm τ (ps) 0.3 0.3 73 73 35 36 36 0.23 0.23 0.188 0.090

Mac

hine

des

ign

# of bunches f (Hz) 1.3· 109 1.3· 109 7.3· 106 22· 106 2.3· 108 3.4· 108 3.4· 108 120 120 56575 56575

Undulator L (m) 25 25 2.4 4.8 5 4.5 25 100 100 30 87

Period λu (cm) 1.7 1.7 3.3 3.3 3.5 2.4 3.2 3 3 3.81 5

Inse

rtion

de

vice

# of period Nu 1470 1470 72 145 142 187 781 3300 3300 787 1740

Shen 3/31/03

Desired Changes to MemoDesired Changes to Memo

•• Inclusion of effects of machine energy spread Inclusion of effects of machine energy spread σσEE

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Decrease due to Energy Spread σE

Rel

ativ

e Fl

ux G

ain

Undulator Length Nu / N0

Relative Gain in Undulator Flux]cm[)2/1(

]GeV[95.0]keV[ 2

2

1u

G

KEE

λ+

⋅=

EG

G

EE

EE

σ35.2221

1 ×=

∆=

∆

01

1 1NE

E=

∆

uNEE 1

=∆

transverse transverse εεxxεεyyscale with scale with qq

•• Performance numbers for microPerformance numbers for micro--beam beam undulator undulator

•• Separate ultraSeparate ultra--fast mode: less frequent fat bunch fast mode: less frequent fat bunch qq

Shen 3/31/03

Phase II ERL PropertiesPhase II ERL Properties

Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II

Machine energy E (GeV) 5.3 5.3 5.3 5.3 5.3 5.3Charge per bunch q (nC) 0.077 0.0077 0.0077 0.0077 0.4 1.2

Repetition rate f (MHz) 1300 1300 1300 1300 0.01 0.01Machine current I (mA) 100 10 10 10 0.004 0.012

Horizontal emittance εx (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Vertical emittance εy (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Rms bunch length σt (ps) 2.0 2.0 2.0 2.0 0.1 0.1

Energy spread σE/E 0.0002 0.0002 0.0002 0.0002 0.0027 0.0027Limit on number of periods N0 1064 1064 1064 1064 79 79

Diffraction-limited to Ed (keV) 0.658 6.578 6.578 6.578 0.913 0.527Undulator length L (m) 25 25 30 3.4 2.2 2.2Undulator period λu (cm) 1.7 1.7 1.5 1.4 1.4 1.4

Number of periods Nu 1470 1470 2000 240 160 160Effective number of periods Ne ff 861.8 861.8 939.2 234.1 70.7 70.7

Horizontal beta βx (m) 12.5 4.0 4.8 0.5 1.0 1.0Vertical beta βy (m) 12.5 4.0 4.8 0.5 1.0 1.0

Deflection parameter K 1.34 1.34 1.52 1.6 1.9 1.9Magnetic field B (T) 0.84 0.84 1.08 1.22 1.45 1.45

Fundamental energy E1 (keV) 8.27 8.27 8.25 8.36 6.80 6.80Fundamental wavelength λ1 (A) 1.50 1.50 1.50 1.48 1.82 1.82

Parameter K2/4/(1+K2/2) 0.2365 0.2365 0.2680 0.2807 0.3217 0.3217Parameter Qn (n=1) 0.7139 0.7139 0.7733 0.7949 0.8559 0.8559

Total source size x σx (µm) 43.85 10.35 11.34 3.79 10.64 13.87Total source divergence x σx' (µrad) 3.87 2.60 2.38 7.08 12.20 15.10

Total source size y σy (µm) 43.85 10.35 11.34 3.79 10.64 13.87Total source divergence y σy' (µrad) 3.87 2.60 2.38 7.08 12.20 15.10

Average flux Fn (p/s/0.1%) 8.81E+15 8.81E+14 1.04E+15 2.67E+14 3.46E+10 1.04E+11Average brilliance Bn (std units) 7.74E+21 3.08E+22 3.63E+22 9.40E+21 5.20E+16 6.00E+16

Average flux density @ 1:1 (p/s/0.1%/µm2) 7.30E+11 1.31E+12 1.29E+12 2.96E+12 4.87E+07 8.59E+07Peak flux Fp (p/s/0.1%) 1.27E+18 1.27E+17 7.49E+16 3.84E+16 1.30E+19 3.89E+19

Peak brilliance Bp (std units) 1.11E+24 4.43E+24 2.61E+24 1.35E+24 1.95E+25 2.25E+25Photons per pulse np (p/0.1%) 6.78E+06 6.78E+05 8.00E+05 2.05E+05 3.46E+06 1.04E+07

Coherent flux Fc (p/s/0.1%) 4.35E+13 1.73E+14 2.05E+14 5.17E+13 4.33E+08 4.99E+08

Shen 3/31/03

Options for ImprovementsOptions for Improvements

•• Injector Injector emittance emittance ? 0.015 nm? 0.015 nm--rad rad ????

•• Separate running modes for hiSeparate running modes for hi--coherence & ultracoherence & ultra--fast ? fast ?

•• Bunch decompression Bunch decompression longer pulse but smaller longer pulse but smaller σσEE/γ /γ ????

No Compression σσtt ~ 2 ~ 2 pspsσσEE/γ/γ ~ 2x10~ 2x10--44

onon--crestcrest∆φ ∆φ = 0= 0

σσtt ~ 0.1 ~ 0.1 pspsσσEE/γ/γ ~ 2.7x10~ 2.7x10--33

offoff--crestcrest∆φ ∆φ > 0> 0

σσtt ~ ?? ~ ?? pspsσσEE/γ/γ ~ 1x10~ 1x10--4 4 ??

offoff--crestcrest∆φ ∆φ < 0< 0

Shen 3/31/03

Improved Coherence PropertiesImproved Coherence Propertiesby reducing machine energy spreadby reducing machine energy spread

Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II

Machine energy E (GeV) 5.3 5.3 5.3 5.3 5.3 5.3Charge per bunch q (nC) 0.077 0.0077 0.0077 0.0077 0.4 1.2

Repetition rate f (MHz) 1300 1300 1300 1300 0.01 0.01Machine current I (mA) 100 10 10 10 0.004 0.012

Horizontal emittance εx (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Vertical emittance εy (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Rms bunch length σt (ps) 2.0 2.0 4.0 2.0 0.1 0.1

Energy spread σE/E 0.0002 0.0002 0.0001 0.0002 0.0027 0.0027Limit on number of periods N0 1064 1064 2128 1064 79 79

Diffraction-limited to Ed (keV) 0.658 6.578 6.578 6.578 0.913 0.527Undulator length L (m) 25 25 25 3.4 2.2 2.2Undulator period λu (cm) 1.7 1.7 1.7 1.4 1.4 1.4

Number of periods Nu 1470 1470 1470 240 160 160Effective number of periods Ne ff 861.8 861.8 1209.4 234.1 70.7 70.7

Operation Mode: Operation Mode: offoff--crestcrest∆φ∆φ<0 ?<0 ?

offoff--crestcrest∆φ∆φ>0>0

onon--crestcrest∆φ∆φ=0=0

Average brilliance Bn (std units) 7.74E+21 3.08E+22 4.32E+22 9.40E+21 5.20E+16 6.00E+16Average flux density @ 1:1 (p/s/0.1%/µm2) 7.30E+11 1.31E+12 1.84E+12 2.96E+12 4.87E+07 8.59E+07

Peak flux Fp (p/s/0.1%) 1.27E+18 1.27E+17 8.91E+16 3.84E+16 1.30E+19 3.89E+19Peak brilliance Bp (std units) 1.11E+24 4.43E+24 3.11E+24 1.35E+24 1.95E+25 2.25E+25

Coherent flux Fc (p/s/0.1%) 4.35E+13 1.73E+14 2.43E+14 5.17E+13 4.33E+08 4.99E+08

Shen 3/31/03

Other PropertiesOther Properties

Bandpass for pink beam ∆λ/λ (%) 0.116 0.116 0.083 0.427 1.415 1.415Coherent flux in pink beam Fc (p/s) 5.05E+13 2.01E+14 2.01E+14 2.21E+14 6.12E+09 7.06E+09Average flux in pink beam Fn (p/s) 1.02E+16 1.02E+15 1.02E+15 1.14E+15 4.90E+11 1.47E+12

Peak flux in pink beam Fp (p/s) 1.47E+18 1.47E+17 7.36E+16 1.64E+17 1.83E+20 5.50E+20Photons per pulse in pink beam np (photons) 7.87E+06 7.87E+05 7.87E+05 8.76E+05 4.90E+07 1.47E+08

Coherent flux fraction pc (%) 0.49 19.62 19.62 19.39 1.25 0.48Coherent ∆Ω fraction in ctr cone pc (%) 0.56 22.32 22.32 22.06 1.42 0.55

Coherence width fwhm @100m wc (mm) 0.074 0.413 0.413 1.114 0.373 0.284Coherence length for pink beam lc (µm) 0.129 0.129 0.181 0.035 0.013 0.013

Photons per coherent volume δD 3 12 9 4 99 114

Average total power P0 (W) 31,679 3,168 3,168 895 0.336 1.009On-axis power density @20m dP/dA (W/mm2) 2655 266 266 62.9 0.0199 0.0597

Peak total power Pp (MW) 4.563 0.456 0.228 0.129 126.0 377.9Peak electric field @ exit E0 (V/m) 5.34E+08 7.15E+08 5.06E+08 1.04E+09 1.16E+10 1.54E+10

Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II

Machine energy E (GeV) 5.3 5.3 5.3 5.3 5.3 5.3Charge per bunch q (nC) 0.077 0.0077 0.0077 0.0077 0.4 1.2

Repetition rate f (MHz) 1300 1300 1300 1300 0.01 0.01Machine current I (mA) 100 10 10 10 0.004 0.012

Horizontal emittance εx (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Vertical emittance εy (nm-rad) 0.15 0.015 0.015 0.015 0.108 0.187Rms bunch length σt (ps) 2.0 2.0 4.0 2.0 0.1 0.1

Energy spread σE/E 0.0002 0.0002 0.0001 0.0002 0.0027 0.0027

Shen 3/31/03

ShortShort--Pulse Source ComparisonPulse Source Comparison

fat bunch

Shen 3/31/03

ConclusionsConclusions

• Phase II ERL would offer 100x more coherent flux and coherence fraction for hard x-rays than present-day sources, comparable to prototype XFEL source

• Many scientific applications benefit substantially, e.g. in coherent scattering & diffraction, and in x-ray holography and coherent patterning, possibly opening up new research areas

• Improvements in ERL coherent flux require long undulator, which in turn requires reducing machine energy spread by bunch decompression or by some other means

• Further improvements in coherence are possible only ifinjector emittance can be further reduced

• Ultra-fast mode of ERL can still be a leader in peak brilliancefor short-pulses. Further improvement is determined by how much charge in a single bunch and by energy spread from bunch compressor