doi:10.1038/nature10721 Experimental Methods The experiment was performed at the AMO scientific instrument 31 at the LCLS XFEL at the SLAC National Accelerator Laboratory. The nominal electron bunch charge was 250 pc, the average electron-bunch duration was 80 fs. Two recent, independent experiments, however, estimated that the duration of the x-ray pulse might be smaller by a factor of two 28,32, which would result in x-ray pulses of approximately 40 fs. After exiting the undulators, the x-rays pass through a diagnostic and beam transport section consisting of three flat x-ray mirrors 33. Gas and solid attenuators are available, to attenuate the x-ray beam. The diagnostic consists of two N 2 luminescence detectors 34 measuring the x-ray pulse energies before and after the attenuators. Using the gas attenuator, the pulse energies were varied from 0.05 to 1.5 mj. The x-ray pulses were focused by Kirkpatrick-Baez mirrors 35,36 to an estimated focus spot of 1-2 µm radius in a gas cell filled with neon at 500 Torr pressure, situated at the center of the AMO interaction chamber. To reach this high pressure, the gas cell had double windows at both front and back ends, made by a 50 µm-thick polyimide film. The x-ray path through the cell was self-aligned in that the windows were drilled through by ablation from the focused XFEL beam 37. The rectangular hole size of ~50 µm (measured after the experiment) corresponds to the total beam size (including the low-intensity wings), defined by the mirror optics of the LCLS. The region between each set of windows was differentially pumped. Due to the leakage of neon gas through these holes, the effective length of the gain material was longer than the physical length of 1.4 cm. A flat-field grating spectrometer with a 600 grooves/mm varied line-spaced reflection gold grating was fielded at a distance of 4 meters downstream from the gas cell to record the spectra of both the transmitted XFEL and the atomic XRL line, with a resolution of 2 ev at1 kev photon energy. During our experiment the nominal photon energy was 960 ev with a single pulse bandwidth of 8 ev FHWM and a centroid jitter of ±7 ev. The transmission of the beam line was estimated to be approximately 0.18, by comparing the XFEL pulse energy, measured by the upstream pulse-energy detectors with the total number of photons detected with the inline spectrometer. This is in accordance with previous estimates 28,38. For the measurement the gas cell was empty and a combination of 4 µm Al / 0.9 µm Cu and 4 µm Al filters was used. A 5-mm slice of the transmitted XFEL and XRL beam, defined by the spectrometer slit, was monitored. Figure 5 shows the beam WWW.NATURE.COM/NATURE 1
RESEARCH SUPPLEMENTARY INFORMATION intensity profile along the slit for the XFEL and the XRL line. 1 0.8 atomic XRL transmitted XFEL Intensity [arb. units.] 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Position [mm] Figure 5: Slice of atomic XRL and XFEL beam intensity profile at the entrance of the spectrometer. Whereas the atomic XRL line shows a smooth spatial intensity profile, the transmitted XFEL features pronounced maxima and minima in the spatial intensity profile. The beam size of both XRL and XFEL was estimated by fitting a Gaussian to the beam profile and shows a beam waist diameter of 3 mm FWHM at the entrance of the spectrometer. Both XFEL and XRL have similar beam divergences of 1 mrad. Several filters were used in front of the spectrometer. These filters served to provide differential attenuation of the XFEL radiation with respect to the XRL radiation. When first searching for and detecting the XRL line, a filter composed of 0.65 µm Cu on 1 µm Al was used, to provide differential attenuation of the XFEL versus XRL line 39. After optimizing the XRL output by increasing the gas pressure, increasing the XFEL pulse energies by adding more undulators, and adjusting the focus position, we were able to dispense with the differential filter and used only a 0.2 µm Al Filter. Estimates of the XFEL and atomic line energies Spectra were recorded with the Princeton Instruments MTE-1300 CCD camera, with a gain of 1.7 electrons per count. The throughput of the spectrograph is determined by the transmissions of the slit, two grazing incidence gold mirrors and the grating and resulted in 7.5 10-5. The transmission through the slit was calculated by integrating a Gaussian fit of the profile of the Ne K- line to be 3.9 10-3 +/- 1 10-3, which had a beam waist diameter of 3 2 WWW.NATURE.COM/NATURE
RESEARCH profile of the Ne K-α line to be 3.9 10-3 +/- 1 10-3, which had a beam waist diameter of 3 mm at the plane of the 20 µm entrance slit of the spectrometer. The beam was not centered on the 5 mm wide slit and no fine adjustments were done to maximize the throughput of the spectrometer. The energy estimates are therefore a lower limit. Correcting for the transmission through the 200 nm Al filter (0.91) and the quantum efficiency of the CCD, the number of Ne K-α photons exciting the gas target per CCD count is 132 +/- 47. Theoretical modeling To estimate the gain properties of the XFEL pumped XRL, we developed a one dimensional, time-dependent, self-consistent gain model, based on kinetic rate equations for the occupancies of the different configuration states involved in the lasing process, coupled to the propagation of the x-ray flux (see reference 13). The presented XRL scheme is gain swept, meaning that the atomic population inversion in a specific region of the amplifier is almost instantaneously prepared at the arrival time of the pump pulse. The population inversion and hence the gain is characterized by a short rise time, followed by a decay due to the Auger process. The absorption of the pump pulse is strong. The gain coefficient of the laser g(z,t) hence depends strongly on time and on the propagation depth:!!,! =!!!!,!!!!,!!!!!!!"#$, (1) where!!!,! [!!!,! ] and!! [!! ] denote the time-dependent occupancies and statistical weights of the upper (1s 1 2s 2 2p 6 ) [lower (1s 2 2s 2 2p 5 )] lasing state,!!"#! is the cross section for stimulated emission and N is the atomic density. The level occupancies in equation (1) are determined by a set of rate equations, following the occupancies of 63 configuration states of neon in charge states up to 10+ during the interaction with the x-ray radiation. The processes taken into account are: photoionization of the valence and core shells (with cross sections from reference 40), Auger decay, spontaneous and stimulated radiative decay, and absorption (with decay rates from reference 41). The kinetic rate equations are self-consistently coupled to the equation determining propagation, absorption and amplification of the XFEL and XRL flux. We consider the forward propagation of the x-ray flux at two discrete energies, the pump energy at 960 ev and the XRL energy at 849 ev. We did not treat any dispersive effects and assume that both colors are propagating with the speed of light. The gain depends strongly on the temporal shape of the pump pulse. Since the XFEL WWW.NATURE.COM/NATURE 3
RESEARCH SUPPLEMENTARY INFORMATION The gain depends strongly on the temporal shape of the pump pulse. Since the XFEL pulses are based on self-amplified spontaneous emission (SASE), they have limited temporal coherence and high shot-to shot fluctuations in the temporal shape. We employed a Monte Carlo method 42 to generate a stochastic ensemble of SASE pulses. The variation in the smallsignal gain was studied for an ensemble of SASE pulses is characterized by an average flattop pulse envelope, a pulse duration of 40 fs, a photon energy of 960 ev, a pulse energy of 0.24 mj and a coherence time of 0.3 fs. Fluctuations in the pulse duration are not accounted for in this simple analysis. The self-consistent gain calculations, describing the absorption of the XFEL pump flux and the amplification of the XRL are performed for a flat-top pulse with a Gaussian ramp on/off of 0.5 fs, corresponding to the assumed averaged pulse shape of the SASE ensemble. To quantify the amplifier we defined a gain-length product by!!!! max!!!!! [!!,! ]!", (2) where T denotes the duration of the pump pulse, L the length of the amplifier and g(z,t) is determined self-consistently in our model. The amplification of the output energy as a function of length is well described by an exponential of GL. Due to strong absorption of the pump, the gain decreases as a function of propagation depth and the total growth turns out to be smaller than exponential. 1x10 10 Number of transmitted photons 1x10 9 1x10 8 1x10 7 1x10 6 100000 10000 0 0.05 0.1 0.15 0.2 0.25 0.3 Incoming XFEL pulse energy [mj] Figure 6: Pump-power dependence of transmitted XFEL and atomic XRL. Shown is a comparison of the experiment with theoretical results from the 1D self-consistent gain model. The blue dots represent the average number of photons detected in the Ne K-α XRL line at 849 ev, determined by integration over 10 consecutive SASE SFEL pulses. The average number of photons in the transmitted XFEL-pump line is shown by the green triangles. 4 WWW.NATURE.COM/NATURE
RESEARCH The measured output energy in both transmitted XFEL and atomic XRL as a function of the incoming XFEL pulse energy compare well in experiment and theory (see figure 6). For comparison with theory we assumed an average XFEL pulse duration of 40 fs (flat-top pulse with a Gaussian ramp on/off of 0.5 fs), a gas density of 1.6 10 19 atoms/cm 3 (corresponding to a pressure of 500 Torr), an interaction length of 1.8 cm and a focal radius of 2 µm. It should be noted, that a combination of a smaller focus and longer pulse duration, resulting in equivalent pump intensities, gives similar good agreement with the experiment. Estimate of the gain-length product We estimate the effective gain-length product (GL) by comparing measured values of the output energy to calculations, assuming exponential amplification of the spontaneous radiation emitted in the first gain length of the lasing medium 43. The spontaneous emission is assumed to be proportional to the incident XFEL energy. For a Lorentzian line profile, we get the calculated XRL energy!!!"#! =!!"#!"#!!!!!". (3)!!"#!!!" Here E FEL is the XFEL energy entering the Ne gas, ω XRL,FEL are the frequencies of the XRL and XFEL lines, b is the branching ratio for spontaneous radiative decay of the upper laser level, f is the fraction of XFEL photons absorbed by K-shell photoionization of neutral neon, Ω is the solid angle of the gain region, and GL is the effective line center gain-length. We use the following input parameters: E FEL = 0.18 1.4 mj, where the factor of 0.18 accounts for the losses before the Ne gas cell, b = 1.75 10-2, f = (0.1-0.2), and Ω = (0.6-1.2 10-6 ) sr. The solid angle has been estimated both from the measured width of the XRL radiation perpendicular to the spectral dispersion direction and from a theoretical model based on the focal spot area measured by beam imprints 44 and the length of the gain region. Finally, we determine the maximum gain-length by equating E calc to the maximum measured energy of 1.1+/- 0.4 µj (value already corrected for absorption in the neon gas in the region beyond the XFEL attenuation length). We find values of GL ranging from 19.2 to 21.3. References 31 Bozek, J. D. AMO instrumentation for the LCLS X-ray FEL. Eur. Phys. J. Spec. Top. 169, WWW.NATURE.COM/NATURE 5
RESEARCH SUPPLEMENTARY INFORMATION References 31 Bozek, J. D. AMO instrumentation for the LCLS X-ray FEL. Eur. Phys. J. Spec. Top. 169, 129 132 (2009) 32 S. Düsterer et al., Femtosecond X-ray Pulse Length Characterization at the Linac Coherent Light Source Free Electron Laser. New J. Phys. 13, 093024 (2011). 33 Soufli R. et al. Morphology, microstructure, stress and damage properties of thin film coatings for the LCLS x-ray mirrors, Proceedings of the SPIE 7361, 73610U (2009) 34 Hau-Riege, S. P. et al. Near-Ultraviolet Luminescence of N2 Irradiated by Short X-Ray Pulses, Phys. Rev. Lett. 105, 043003 (2010) 35 Kelez, N. et al. in Proc. FEL2009 paper WEPC20 546 549 (2009); http://accelconf.web.cern.ch/accelconf/fel2009/papers/wepc20.pdf. 36 Barty A., Soufli R. McCarville T., Baker S. L., Pivovaroff M. J., Stefan P. & Bionta R., Predicting the coherent x-ray wavefront focal properties at the Linac Coherent Light Sources (LCLS) x-ray free electron laser, Optics Express 17, 15508 (2009) 37 Hau-Riege S. P. et al. Interaction of short x-ray pulses with low-z x-ray optics materials at the LCLS free-electron laser, Optics Express 18, 2393 (2010) 38 Richter M. Private communication. 39 Dunn J. et al. Design and measurement of a Cu L-edge x-ray filter for free electron laser pumped x-ray laser experiments. Rev. Sci. Instr. 81, 10E330 (2010) 40 Los Alamos Atomic Physics Codes, http://aphysics2.lanl.gov/tempweb/, based on R.D. Cowan R.D. Theory of Atomic Spectra, (University of California Press, Berkeley, 1981) 41 Bhalla C.P., Folland N. O. & Hein M. A. Theoretical K-Shell Auger Rates, Transition Energies, and Fluorescence Yields for Multiply Ionized Neon, Phys. Rev. A 8, 649 (1973) 42 6 WWW.NATURE.COM/NATURE
RESEARCH 42 Vannucci G. & Teich M. C. Computer simulation of superposed coherent and chaotic radiation, Appl. Opt. 19, 548 (1980) 43 Pert G. J. Output characteristics of amplified-stimulated-emission lasers. J. Opt. Soc. Am. B 11, 1425 (1994). 44 Krzywinski J. private communication; Chalupský J. et al. Spot size characterization of focused non-gaussian X-ray laser beams. Optics Express 18, 27836 (2010) WWW.NATURE.COM/NATURE 7