ERL & Coherent X-ray Applications Qun Shen Cornell High Energy Synchrotron Source (CHESS) Cornell University Talk Outline Introduction to x-ray coherence In this last talk of the morning, I will be focusing on coherent imaging and diffraction applications using the eventual phase-2 ERL machine. Coherent x-ray applications Desired ERL properties Options and improvements Conclusions

Source Emittance and Brilliance x x’ Integrated total flux Fn Phase-space Emittance: EM wave: E(r, t) = E0 ei(k·r-wt) x x’ sx sx’ ex = sx sx’ y y’ sy sy’ ey = sy sy’ t E st sE et = st sE / E Brilliance: photon flux density in phase-space B = Fn (2p)2 ex ·ey Average B = Fn (2p)3 ex ·ey·et ^ Peak

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

Temporal (Longitudinal) Coherence l+Dl Coherence length: lc = l2/Dl Coherence time: Dtc = lc/c Temporally coherent source: pulse length FWHM t £ Dtc lc = l2/Dl uncertainty: t ·Dn £ 1 t ·DE £ h For l = 1 Å, Dl/l = 10-4 : lc = 1 mm, Dtc = 1 mm / 3x108 m/s = 3.3 fs Degeneracy Parameter dD = Number of photons in coherent volume = Number of photons within single quantum mode X-ray optics can modify Dl/l, but extinction length (~100mm) limits to Dl/l = 10-6 => Dtc= 330 fs ERL with st = 100 fs pulses coupled with 10 meV x-ray monochromator could mean temporal coherence at 10 keV.

Transverse Coherence from Undulator q L q = l/2d Example: APS, L =2.4m, l =1.5Å sr' = 13.1 mrad dy = 2.35x21mm, sy' = 6.9 mrad q = 1.5 mrad, Q = 2.35x14.8 mrad => pc(vertical) = 4.3% dx = 2.35x350mm, sx' = 23.1 mrad q = 0.091 mrad, Q = 2.35x26.6 mrad => pc(horizontal) = 0.15% => pc (overall) = 0.006% A portion, q/Q in each direction, of undulator radiation is spatially coherent within central cone Coherent fraction pc: depends only on total emittances ERL: pc ~ 20% (45% in x or y)

ERL Spatial Coherence Diffraction limited @ 8keV (0.123Å) ESRF emittance (4nm x 0.01nm) ERL emittance (0.015nm=0.15Å) As we 've heard this morning that, the phase-2 ERL is high-brilliance hard x-ray source with high degree of spatial coherence. Let 's just take a closer look at what this really means. Here I show the same schematic as you 've seen earlier, of the transverse emittances or the ERL source, as compared to a typical third-generation synchrotron source such as the ESRF. Let us just focus on the high-coherence option, which is represented by the small red dot in the middle here. If I magnify this region, then you would see the ERL emittances represented by this red circle. In the middle of this circle, I 've plotted on the same scale the diffraction-limit for 8 keV photons. So what this shows is that the 8keV photons from the ERL are almost diffracted limited. If we use the more precise definitions of diffraction limit based electron beam phase-space areas, then we can say that the phase-2 ERL is a diffraction limited source for x-rays photons below 6.6 keV and is almost diffraction limited all the way to 13 keV. Diffraction limited source: 2ps's = l/2 or e = l/4p Almost diffraction limited: 2ps's ~ l or e ~ l/2p Phase II ERL: diffraction-limited source E < 6.6 keV almost diffraction-limited to 13 keV

X-ray Coherence Workshop Program http://www.chess.cornell.edu/Meetings So what types of experiments can we do using this type of coherent source? We have thought about about several areas of coherence experiments. The first area, as you 've just heard from Joel's talk, is the photon correlation spectroscopy or speckle experiments. This of course requires a fully coherent beam. By the way here is my color coded arrow that show the different degree of coherence requirements. So this is something Joel had covered already, so I won't repeat that area. What I am going focus on is the area of x-ray imaging microscopy. I should state at the very start, that not every form of x-ray microscopy requires a fully coherent beam. So what I am going to talk about are really those types that do require a high degree of coherence. These include phase-contrast imaging and microscopy, far-field diffraction microscopy, and holographic techniques development. For any of these full-field microscopies, one incorporate the timing aspect in an experiment, which would lead to so called flash imaging studies of time evolution of the specimen. But I don't think I 'll have time to elaborate on that, so I just want to mention it in this introduction. In principle, x-ray imaging and microscopy can only provide 2D information. So in order to obtain 3D structural information, one usually needs to rotate the sample and take multiple images at different sample orientations. This is the so-called tomography technique, so the natural extension of the phase imaging techniques would be the phase-contrast tomography for 3D structure images. Finally, at the end of my talk, I will show a few ideas of using coherence in crystalline materials, or in crystallography.

X-ray Microscopy Two types: full field & scanning ESRF ID21: TXM 3-6 keV ESRF ID21: SXM 2-10 keV & < 2keV transmission fluorescence ERL hi-coherence XPEEM Two types: full field & scanning I 'd like to start with some background on x-ray microscopy, because I don't know whether everyone is familiar with it. This picture shows a typical x-ray microscopy setup at a synchrotron beam line. It consists of an x-ray beam passing through a monochromator and gets focused by a Fresnel zone plate onto a sample. The transmitted or scattered x-rays are collected by another zoneplate which serves as the objective lens for the microscope. The enlarged image is then projected onto a CCD. One can study all kinds of materials with this type of setup, ranging from biological to magnetic materials. If you look through the literature, you can find many many examples, but I won't have time to go through them. In recent years there have been an increasing number of synchrotron based x-ray microscopes worldwide. And that's because of two things that are available recently: one is the high-resolution lens-like optics such as zone plates, and the other is the high-brilliance synchrotron x-ray sources. However, most of these x-ray microscopes are based on soft x-rays, only a few, maybe 3 or 4 of them use x-rays beyond 3 keV. So you may want to ask why that is the case? 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

Issues in Hard X-ray Microscopy Phase contrast is x104 higher than absorption contrast for protein in water @ 8keV Focusing optics Only recently has Fresnel zone-plate (FZP) achieved <100nm resolution at 8keV (Yun, 1999) Dose reduced to level comparable to using water-window in soft x-ray region High coherence sources: Coherence fraction ~ l2/(exey). => Requires 100x smaller emittance product for 1keV => 10 keV ERL would offer 102-103x better emittance product than present-day hard x-ray sources => Better coherence @10 keV than @1 keV at ALS C94H139N24O31S 1010 108 106 104 103 102 Kirz (1995): 0.05mm protein in 10mm thick ice X-ray Energy (eV) Dose (Gr) absorption contrast phase contrast Well, I think there are three reasons. First, only recently have the optics been good enough for hard x-rays. Right now the state of the art is about 100nm for hard x-rays as reported a couple of years. So that' s one reason. The second reason is the lack of high coherence hard x-ray sources. If you really think about it, the coherence requirement has a very stringent demand on the source emittances, because coherent fraction is proportional to wavelength squared. So suppose you have good coherent beam at 1 keV, and you would like to have the same good coherence at 10 keV, then you have to decrease the source emittance product by a factor 100. That is actually very difficult to do with the current 3rd generation synchrotron sources. So this is where we believe the ERL would really play an important role. It would offer 100 to 1000 times smaller emittance product than the present-day storage-ring based sources. So potentially it would provide better or similar coherence for hard x-rays than the soft x-rays that is currently available at for example the advanced light source in Berkeley. So that 's the second reason. The third reason is actually a scientific question. As we know the absorption is much lower for hard x-rays than soft x-rays. Another way of looking at it is the required dose or exposure time for a given contrast. This is shown in this figure which I took from Janos' review article in 1995. It shows the calculated Absorption vs. phase contrast Refraction index: n = 1 - d - ib absorption contrast: mz = 4pbz/l ~ l3 phase contrast: f(z) = 2pdz/l ~ l z In general, phase contrast requires: => coherent hard x-ray beams

Phase Imaging & Tomography l Cloetens et al. (1999): ESRF, ID19, 18 keV Polystyrene foam 0.7x0.5x1mm3 1.4T wiggler, B~7x1014 ph/s/mr2/mm2/0.1% @100mA 4x700 images at 25 sec/image A form of Gabor in-line holography Coherence over 1st Fresnel zone (lR)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.

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 Key development: oversampling phasing method coherent flux!! Coherent X-rays Miao et al. (1999) >>> soft x-rays, reconstruction to 75 nm

Diffraction Microscopy recent results Miao et al. PRL (2002) reconstructed image: to d~7nm resolution l = 2 Å Gold: 2.5mm x 2mm x 0.1mm SPring-8 BL29XU: standard undulator 140 periods lu=3.2 cm B=2x1019 ph/s/mr2/mm2/0.1% @100mA For Au, exposure time 50 min, d~7nm but: for Si, (ZSi/ZAu)2~1/32 => 26 hrs ! for C, (Zc/ZAu)2~1/173 => 6 days !! => could achieve higher resolution, limited only by radiation damage ERL high-coherence option: B=5x1022 ph/s/mr2/mm2/0.1% @10mA Exposure time for Si & d~7nm: 0.6 min. for C & d~7nm: 3.5 min.

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 ~ 8x106 Gray Diffraction image to ~30nm resolution

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

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

Coherent X-ray Patterning & Lithography (invited talk X-ray Coherence 2003) Maskless pattern DOE: diffractive optics element Lithography  X-ray CVD  Coherent X-rays

Desired ERL Properties 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 X-ray photon correlation spectroscopy Phase-contrast imaging & microscopy Coherent far-field diffraction Coherent crystallography X-ray holography Coherent x-ray lithography D1 D2 Basic Requirement: low transverse emittances long undulators (large Nu) low machine energy spread X-ray optical slope error dq << sx/D1 ~ 4mm/40m ~ 0.1mrad coherence preserving x-ray optics

Phase II ERL Coherent Flux 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 Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source. This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source. Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux. So we see the ERL is highly coherent source with a very high coherent flux. ???

CHESS Tech Memo 01-002: 3/8/01 http://erl.chess.cornell.edu/papers Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source. This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source. Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux. So we see the ERL is highly coherent source with a very high coherent flux.

Desired Changes to Memo Performance numbers for micro-beam undulator transverse exey scale with q Separate ultra-fast mode: less frequent fat bunch q Inclusion of effects of machine energy spread sE Of course, being a diffraction limited source doesn't mean anything if there is not enough photons emitted from that source. This next slide shows the time averaged coherent flux from the phase-2 ERL as compared to several other existing and proposed sources, including the free-electron laser source that is being considered at Stanford. So this shows that the time-averaged coherent flux is comparable to what is available at the LCLS free electron laser source. Compared to third generation sources, the ERL could offer about a hundred times better coherent fraction and about 100 to 1000 times better coherent flux per pulse or the so-called peak coherent flux. So we see the ERL is highly coherent source with a very high coherent flux.

Phase II ERL Properties

Options for Improvements Injector emittance ? 0.015 nm-rad  ?? Separate running modes for hi-coherence & ultra-fast ? Bunch decompression  longer pulse but smaller sE/g ?? No Compression st ~ 2 ps sE/g ~ 2x10-4 on-crest Df = 0 st ~ 0.1 ps sE/g ~ 2.7x10-3 off-crest Df > 0 st ~ ?? ps sE/g ~ 1x10-4 ? off-crest Df < 0

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

Other Properties

Short-Pulse Source Comparison fat bunch

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