ERL Coherent Xray Applications Qun Shen Cornell High

ERL & Coherent X-ray Applications Qun Shen Cornell High Energy Synchrotron Source (CHESS) Cornell University Talk Outline · Introduction to x-ray coherence · Coherent x-ray applications · Desired ERL properties · Options and improvements · Conclusions Shen 3/31/03

Source Emittance and Brilliance x x’ Þ Phase-space Emittance: EM wave: x’ sx’ E(r, t) = E 0 ei(k·r-wt) ex = sx sx’ sx Integrated total flux Fn y’ sy’ ey = sy sy’ x sy E s. E e t = st s. E / E y st t Þ Brilliance: photon flux density in phase-space Average B = Shen 3/31/03 Fn (2 p)2 ex ·ey ^= Peak B Fn (2 p)3 ex ·ey·et

Spatial (Transverse) Coherence 2 s 2 s q Dl = q · 2 s = l/2 2 s' => 2 q · 2 s ~ l q s' => X-ray beam is spatially coherent if phase-space area 2 ps’s < l/2 Diffraction limited source: 2 ps's = l/2 or e = l/4 p Almost diffraction limited: 2 ps's ~ l or e ~ l/2 p Shen 3/31/03

Temporal (Longitudinal) Coherence l l+Dl Coherence length: lc = l 2/Dl Coherence time: Dtc = lc/c lc = l 2/Dl Temporally coherent source: pulse length FWHM t £ Dtc For l = 1 Å, Dl/l = 10 -4 : lc = 1 mm, Dtc = 1 mm / 3 x 108 m/s = 3. 3 fs Þ uncertainty: t ·Dn £ 1 t ·DE £ h Degeneracy Parameter d. D X-ray optics can modify Dl/l, but extinction length (~100 mm) limits to Dl/l = 10 -6 => Dtc= 330 fs = Number of photons in coherent volume Þ ERL with st = 100 fs pulses coupled with 10 me. V x-ray monochromator could mean temporal coherence at 10 ke. V. = Number of photons within single quantum mode Shen 3/31/03

Transverse Coherence from Undulator d q L q = l/2 d Example: APS, L =2. 4 m, l =1. 5Å sr' = 13. 1 mrad dy = 2. 35 x 21 mm, sy' = 6. 9 mrad q = 1. 5 mrad, Q = 2. 35 x 14. 8 mrad => pc(vertical) = 4. 3% dx = 2. 35 x 350 mm, sx' = 23. 1 mrad q = 0. 091 mrad, Q = 2. 35 x 26. 6 mrad => pc(horizontal) = 0. 15% => pc (overall) = 0. 006% ERL: pc ~ 20% (45% in x or y) Shen 3/31/03 Þ A portion, q/Q in each direction, of undulator radiation is spatially coherent within central cone Þ Coherent fraction pc: depends only on total emittances

ERL Spatial Coherence Diffraction limited @ 8 ke. V (0. 123Å) ESRF emittance (4 nm x 0. 01 nm) ERL emittance (0. 015 nm=0. 15Å) Diffraction limited source: 2 ps's = l/2 or e = l/4 p Almost diffraction limited: 2 ps's ~ l or e ~ l/2 p Phase II ERL: diffraction-limited source E < 6. 6 ke. V almost diffraction-limited to 13 ke. V Shen 3/31/03

X-ray Coherence Workshop Program http: //www. chess. cornell. edu/Meetings Shen 3/31/03

X-ray Microscopy ESRF ID 21: TXM 3 -6 ke. V ERL hi-coherence ESRF ID 21: SXM 2 -10 ke. V & < 2 ke. V Þ transmission Þ fluorescence Þ XPEEM · Two types: full field & scanning · 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 Shen 3/31/03

Issues in Hard X-ray Microscopy · Phase contrast is x 104 higher than absorption contrast for protein in water @ 8 ke. V Only recently has Fresnel zone-plate (FZP) achieved <100 nm resolution at 8 ke. V (Yun, 1999) · High coherence sources: sources l 2/(e Coherence fraction ~ xey). => Requires 100 x smaller emittance product for 1 ke. V => 10 ke. V ERL would offer 102 -103 x better emittance product than present-day hard x-ray sources => Better coherence @10 ke. V than @1 ke. V at ALS C 94 H 139 N 24 O 31 S 1010 108 absorption contrast phase contrast 104 102 Refraction index: n = 1 - d - ib Shen 3/31/03 Kirz (1995): 0. 05 mm protein in 10 mm thick ice 106 · Absorption vs. phase contrast absorption contrast: mz = 4 pbz/l ~ l 3 phase contrast: f(z) = 2 pdz/l ~ l · Dose reduced to level comparable to using water-window in soft x-ray region Dose (Gr) · Focusing optics z 103 104 X-ray Energy (e. V) · In general, phase contrast requires: => coherent hard x-ray beams

Phase Imaging & Tomography l Cloetens et al. (1999): ESRF, ID 19, 18 ke. V Polystyrene foam 0. 7 x 0. 5 x 1 mm 3 1. 4 T wiggler, B~7 x 1014 ph/s/mr 2/mm 2/0. 1% @100 m. A 4 x 700 images at 25 sec/image · A form of Gabor in-line holography · Coherence over 1 st Fresnel zone (l. R)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

Far-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 Dl/l 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 Shen 3/31/03

Diffraction Microscopy recent results Miao et al. PRL (2002) l=2Å reconstructed image: to d~7 nm resolution Gold: 2. 5 mm x 2 mm x 0. 1 mm SPring-8 BL 29 XU: standard undulator 140 periods lu=3. 2 cm B=2 x 1019 ph/s/mr 2/mm 2/0. 1% @100 m. A For Au, exposure time 50 min, d~7 nm but: for Si, (ZSi/ZAu)2~1/32 => 26 hrs ! for C, (Zc/ZAu)2~1/173 => 6 days !! Shen 3/31/03 ERL high-coherence option: B=5 x 1022 ph/s/mr 2/mm 2/0. 1% @10 m. A Exposure time for Si & d~7 nm: 0. 6 min. for C & d~7 nm: 3. 5 min. => could achieve higher resolution, limited only by radiation damage

Miao et al. , Proc. Nat. Acad. Sci. (2003) E. Coli bacteria ~ 0. 5 mm by 2 mm SPring-8, l = 2 Å, pinhole 20 mm Total dose to specimen ~ 8 x 106 Gray Diffraction image to ~30 nm resolution Shen 3/31/03

X-ray Photon Correlation Spectroscopy Dierker (2000), ERL Workshop Shen 3/31/03

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 Shen 3/31/03

Coherent X-ray Patterning & Lithography (invited talk X-ray Coherence 2003) Maskless pattern DOE: diffractive optics element Lithography X-ray CVD Coherent X-rays Shen 3/31/03

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 Dl/l for high resolution small beam (some cases) large coherent area (some cases) CW operation: long pulses okay Basic Requirement: Þ low transverse emittances D 1 D 2 Þ X-ray optical slope error dq << sx/D 1 ~ 4 mm/40 m ~ 0. 1 mrad Shen 3/31/03 Þ long undulators (large Nu) Þ low machine energy spread Þ coherence preserving x-ray optics

Phase II ERL Coherent Flux · Time-averaged coherent flux comparable to LCLS XFEL · Coherent fraction ~100 x greater than 3 rd SR sources · Peak coherent flux (coherent flux per pulse) ~1000 x greater than 3 rd SR sources ? ? ? Shen 3/31/03

CHESS Tech Memo 01 -002: 3/8/01 http: //erl. chess. cornell. edu/papers Shen 3/31/03

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 s. E Shen 3/31/03 transverse exey scale with q

Phase II ERL Properties Shen 3/31/03

Options for Improvements · Injector emittance ? 0. 015 nm-rad ? ? · Separate running modes for hi-coherence & ultra-fast ? · Bunch decompression longer pulse but smaller s. E/g ? ? on-crest Df = 0 Shen 3/31/03 No Compression st ~ 2 ps s. E/g ~ 2 x 10 -4 off-crest Df > 0 st ~ 0. 1 ps s. E/g ~ 2. 7 x 10 -3 off-crest Df < 0 st ~ ? ? ps s. E/g ~ 1 x 10 -4 ?

Improved Coherence Properties by reducing machine energy spread Operation Mode: Shen 3/31/03 on-crest Df=0 off-crest Df<0 ? off-crest Df>0

Other Properties Shen 3/31/03

Short-Pulse Source Comparison fat bunch Shen 3/31/03

Conclusions · Phase II ERL would offer 100 x 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 Shen 3/31/03