ERL & Coherent X-ray X. applications. Talk Outline. Introduction to x-ray x. coherence. Desired ERL properties Options and improvements Conclusions

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1 ERL & Coherent X-ray X Applications Qun Shen Cornell High Energy Synchrotron Source (CHESS) Cornell University Talk Outline Introduction to x-ray x coherence Coherent x-ray x applications Desired ERL properties Options and improvements Conclusions

2 Source Emittance and Brilliance Phase-space space Emittance: EM wave: E(r, t) = E 0 e i(k r ωt) x x Integrated total flux F n x ε x = σ x σ x σ x y ε y = σ y σ y σ y σ E E ε τ = σ τ σ E / E σ x x σ y y σ τ t Brilliance: : photon flux density in phase-space space Average B = F n (2π) 2 ε x ε y Peak B ^ = F n (2π) 3 ε x ε y ε τ

3 Spatial (Transverse) Coherence 2σ 2σ θ 2σ' θ σ' l = θ 2σ = λ/2 => 2θ 2σ ~ λ => X-ray beam is spatially coherent if 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

4 Temporal (Longitudinal) Coherence λ λ+ λ Coherence length: l c = λ 2 / λ Coherence time: t c = l c /c l c = λ 2 / λ For λ = 1 Å, λ/λ = 10-4 : l c = 1 µm, t c = 1 µm / 3x10 8 m/s = 3.3 fs X-ray optics can modify λ/λ, but extinction length (~100µm) limits to λ/λ = 10-6 => t c = 330 fs Temporally coherent source: pulse length FWHM τ t c uncertainty: τ ν 1 τ Ε h Degeneracy Parameter δ D = Number of photons in coherent volume ERL with σ t = 100 fs pulses coupled with 10 mev x-ray monochromator could mean temporal coherence at 10 kev. = Number of photons within single quantum mode

5 Transverse Coherence from Undulator d θ Example: APS, L =2.4m, λ =1.5Å σ r' = 13.1 µrad d y = 2.35x21µm, σ y' = 6.9 µrad θ = 1.5 µrad, Θ = 2.35x14.8 µrad => p c (vertical) = 4.3% d x = 2.35x350µm, σ x' = 23.1 µrad θ = µrad, Θ = 2.35x26.6 µrad => p c (horizontal) = 0.15% => p c (overall) = 0.006% ERL: p c ~ 20% (45% in x or y) θ = λ/2d Θ = 2.35 σ r ' = L σ 2 r ' λ 2L + σ ' A portion, θ/θ in each direction, of undulator radiation is spatially coherent within central cone Coherent fraction p c : depends only on total emittances p c = F F c n ( λ/2) = F n 2 B = λ2 (4 2 π ) ε x ε y 2

6 ERL Spatial Coherence ESRF emittance (4nm x 0.01nm) Diffraction 8keV (0.123Å) 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 ERL: : diffraction-limited source E < 6.6 kev almost diffraction-limited to 13 kev

7 X-ray Coherence Workshop Program Friday, 22 August, :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 Saturday, 23 August, :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 15:00 Coffee Break 12:20 Lunch 15:20 Tetsuya Ishikawa (SPring8) Coherence preserving reflecting and crystal optics 15:50 Christian David (PSI) Diffractive optics and shearing interferometer 14:00 David Sayre (SUNY-SB) Crystallography applied to noncrystalline materials 16:20 David Paterson (APS) X-ray coherence measurements 14:30 John Miao (SSRL, SLAC) Imaging with single molecule diffraction 16:50 Discussion on coherent optics 15:00 Malcolm Howells (LBNL) Holography by phase retrieval 15:30 Discussion on coherent scattering II: structure determination

8 X-ray Microscopy ESRF ID21: TXM 3-6 kev ESRF ID21: SXM 2-10 kev & < 2keV ERL hi-coherence Two types: full field & scanning transmission fluorescence XPEEM All types of materials are studied, from biological to magnetic 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

9 Issues in Hard X-ray X Microscopy Focusing optics Only recently has Fresnel zone-plate (FZP) achieved <100nm resolution at 8keV (Yun, 1999) High coherence sources: Coherence fraction ~ λ 2 /(ε x ε y ). => Requires 100x smaller emittance product for 1keV => 10 kev ERL would offer x better emittance product than present-day hard x-ray sources => Better kev kev at ALS Phase contrast is x10 4 higher than absorption contrast for protein in 8keV Dose reduced to level comparable to using water-window in soft x-ray region Dose (Gr) Kirz (1995): 0.05µm protein in 10µm thick ice C 94 H 139 N 24 O 31 S absorption contrast Absorption vs. phase contrast 10 6 phase contrast Refraction index: n = 1 δ iβ absorption contrast: µz = 4πβz/λ λ 3 phase contrast: φ(z) = 2πδz/λ λ z X-ray Energy (ev) In general, phase contrast requires: => coherent hard x-ray beams

10 Phase Imaging & Tomography λ Cloetens et al. (1999): ESRF, ID19, 18 kev Polystyrene foam 0.7x0.5x1mm 3 1.4T wiggler, B~7x10 14 ph/s/mr 2 /mm 2 4x700 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.

11 Far-Field Field Diffraction Microscopy Diffraction microscopy is analogous to crystallography, but for noncrystalline materials Coherent diffraction from noncrystalline specimen: => continuous Fourier transform Spatial resolution: essentially no limit. (only limited by λ/λ and weak signals at large angles) Coherence requirement: coherent illumination of sample Coherent X-rays Key development: oversampling phasing method coherent flux!! Miao et al. (1999) >>> soft x-rays, reconstruction to 75 nm

12 Diffraction Microscopy recent results Miao et al. PRL (2002) λ = 2 Å reconstructed image: to d~7nm resolution Gold: 2.5µm x 2µm x 0.1µm SPring-8 BL29XU: standard undulator 140 periods λ u =3.2 cm B=2x10 19 ph/s/mr 2 /mm 2 For Au, exposure time 50 min, d~7nm but: for Si, (Z Si /Z Au ) 2 ~1/32 => 26 hrs! for C, (Z c /Z Au ) 2 ~1/173 => 6 days!! ERL high-coherence option: B=5x10 22 ph/s/mr 2 /mm 2 Exposure time for Si & d~7nm: 0.6 min. for C & d~7nm: 3.5 min. => could achieve higher resolution, limited only by radiation damage

13 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 ~ 8x10 6 Gray Diffraction image to ~30nm resolution

14 X-ray Photon Correlation Spectroscopy Dierker (2000), ERL Workshop

15 X-ray Holography with Reference Wave Leitenberger & Snigirev (2001) Wilhein et al. (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

16 Coherent X-ray X Patterning & Lithography SHAPING X-RAYS BY DIFFRACTIVE CODED NANO-OPTICS (invited talk X-ray Coherence 2003) Maskless pattern Enzo Di Fabrizio TASC-NNL-INFM (National Institute for the Physics of Matter) Elettra Synchrotron Light Source DOE: : diffractive optics element Lithography X-ray CVD Coherent X-raysX

17 Desired ERL Properties X-ray photon correlation spectroscopy Phase-contrast imaging & microscopy Coherent far-field diffraction Coherent crystallography X-ray holography Coherent x-ray lithography full transverse coherence high coherent flux / coh. fraction high λ/λ for high resolution small beam (some cases) large coherent area (some cases) CW operation: long pulses okay Basic Requirement: low transverse emittances D 1 D 2 X-ray optical slope error δθ << σ x /D 1 ~ 4µm/40m ~ 0.1µrad long undulators (large N u ) low machine energy spread coherence preserving x-ray x optics

18 Phase II ERL Coherent Flux Coherent Flux (photons/s/0.1%) LCLS SASE APS 4.8m ESRF U35 APS 2.4m ERL 25m 0.015nm 10mA Sp8 25m 0.15nm 100mA Sp8 5m 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 10 9??? Photon Energy (kev)

19 CHESS Tech Memo : 002: 3/8/01 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 E G (GeV) Machine design Current I (ma) Charge q (nc/bunch) ε x (nm-rad) ε y (nm-rad) Bunch fwhm τ (ps) # of bunches f (Hz) Insertion device Undulator L (m) Period λ u (cm) # of period N u DC experiments Pulsed expts. Ave. flux F n (p/s/0.1%) Ave. brilliance B (p/s/0.1%/mm 2 /mr 2 ) Coh flux F c (p/s/0.1%) Coh. fraction p c (%) Photons / bunch Peak brilliance (p/s/0.1%/mm 2 /mr 2 ) Peak flux (p/s/0.1%) Pk coh. flux (p/s/0.1%) Peak degen. par. δ D

20 Desired Changes to Memo Performance numbers for micro-beam undulator Separate ultra-fast mode: less frequent fat bunch q Inclusion of effects of machine energy spread σ E transverse ε x ε y scale with q Relative Flux Gain Relative Gain in Undulator Flux Decrease due to Energy Spread σ E Undulator Length N u / N EG[GeV] E1[keV] = 2 (1 + K / 2) λ [cm] E E 1 1 E = 2 E 1 G G E = E 2 u = σ 1 1 N 0 E 1 = E N u E

21 Phase II ERL Properties Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II Shen 3/31/03 Machine energy E (GeV) Charge per bunch q (nc) Repetition rate f (MHz) Machine current I (ma) Horizontal emittance εx (nm-rad) Vertical emittance εy (nm-rad) Rms bunch length σt (ps) Energy spread σe/e Limit on number of periods N Diffraction-limited to Ed (kev) Undulator length L (m) Undulator period λu (cm) Number of periods Nu Effective number of periods Neff Horizontal beta βx (m) Vertical Average beta flux Fn βy (m) (p/s/0.1%) 8.81E E E E E E+11 Deflection Average parameter brilliance Bn K (std units) 7.74E E E E E E Average flux density field 1:1 (p/s/0.1%/µm2) B (T) 7.30E E E E E E Fundamental Peak energy flux E1 Fp (p/s/0.1%) (kev) 1.27E E E E E E Fundamental Peak wavelength brilliance Bp λ1 (A) (std units) 1.11E E E E E E Photons Parameter per pulse np K2/4/(1+K2/2) (p/0.1%) 6.78E E E E E E Coherent Parameter flux Fc Qn (p/s/0.1%) (n=1) 4.35E E E E E E Total source size x σx (µm) Total source divergence x σx' (µrad) Total source size y σy (µm) Total source divergence y σy' (µrad)

22 Options for Improvements Injector emittance? nm-rad?? Separate running modes for hi-coherence & ultra-fast? Bunch decompression longer pulse but smaller σ E /γ?? on-crest φ = 0 No Compression σ t ~ 2 ps σ E /γ ~ 2x10-4 off-crest φ > 0 σ t ~ 0.1 ps σ E /γ ~ 2.7x10-3 off-crest φ < 0 σ t ~?? ps σ E /γ ~ 1x10-4?

23 Improved Coherence Properties by reducing machine energy spread Operation Mode: on-crest φ=0 off-crest φ<0? off-crest φ>0 Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II Shen 3/31/03 Machine energy E (GeV) Charge per bunch q (nc) Repetition rate f (MHz) Machine current I (ma) Horizontal emittance εx (nm-rad) Vertical emittance εy (nm-rad) Rms bunch length σt (ps) Energy spread σe/e Limit on number of periods N Diffraction-limited to Ed (kev) Undulator length L (m) Undulator period λu (cm) Number of periods Nu Effective number of periods Neff Average brilliance Bn (std units) 7.74E E E E E E+16 Average flux 1:1 (p/s/0.1%/µm2) 7.30E E E E E E+07 Peak flux Fp (p/s/0.1%) 1.27E E E E E E+19 Peak brilliance Bp (std units) 1.11E E E E E E+25 Coherent flux Fc (p/s/0.1%) 4.35E E E E E E+08

24 Other Properties Type of experiments Hi-flux Hi-coh I Hi-coh II µ-beam Ultra fast I Ultra fast II Machine energy E (GeV) Charge per bunch q (nc) Repetition rate f (MHz) Machine current I (ma) Horizontal emittance εx (nm-rad) Vertical emittance εy (nm-rad) Rms bunch length σt (ps) Energy spread σe/e Bandpass for pink beam λ/λ (%) Coherent flux in pink beam Fc (p/s) 5.05E E E E E E+09 Average flux in pink beam Fn (p/s) 1.02E E E E E E+12 Peak flux in pink beam Fp (p/s) 1.47E E E E E E+20 Photons per pulse in pink beam np (photons) 7.87E E E E E E+08 Coherent flux fraction pc (%) Coherent Ω fraction in ctr cone pc (%) Coherence width wc (mm) Coherence length for pink beam lc (µm) Photons per coherent volume δd Average total power P0 (W) 31,679 3,168 3, On-axis power dp/da (W/mm2) Peak total power Pp (MW) Peak electric exit E0 (V/m) 5.34E E E E E E+10

25 Short-Pulse Source Comparison fat bunch

26 Conclusions 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 if injector emittance can be further reduced Ultra-fast mode of ERL can still be a leader in peak brilliance for short-pulses. Further improvement is determined by how much charge in a single bunch and by energy spread from bunch compressor