Echo-Enabled Harmonics up to the 75Th Order from Precisely Tailored Electron Beams E

LETTERS PUBLISHED ONLINE: 6 JUNE 2016 | DOI: 10.1038/NPHOTON.2016.101

Echo-enabled harmonics up to the 75th order from precisely tailored electron beams E. Hemsing1*,M.Dunning1,B.Garcia1,C.Hast1, T. Raubenheimer1,G.Stupakov1 and D. Xiang2,3*

The production of coherent radiation at ever shorter wave- phase-mixing transformation turns the sinusoidal modulation into lengths has been a long-standing challenge since the invention a filamentary distribution with multiple energy bands (Fig. 1b). 1,2 λ of lasers and the subsequent demonstration of frequency A second laser ( 2 = 2,400 nm) then produces an energy modulation 3 ΔE fi doubling . Modern X-ray free-electron lasers (FELs) use relati- ( 2) in the nely striated beam in the U2 undulator (Fig. 1c). vistic electrons to produce intense X-ray pulses on few-femto- Finally, the beam travels through the C2 chicane where a smaller 4–6 R(2) second timescales . However, the shot noise that seeds the dispersion 56 brings the energy bands upright (Fig. 1d). amplification produces pulses with a noisy spectrum and Projected into the longitudinal space, the echo signal appears as a λ λ h limited temporal coherence. To produce stable transform- series of narrow current peaks (bunching) with separation = 2/ limited pulses, a seeding scheme called echo-enabled harmonic (Fig. 1e), where h is a harmonic of the second laser that determines generation (EEHG) has been proposed7,8, which harnesses the character of the harmonic echo signal. the highly nonlinear phase mixing of the celebrated echo EEHG has been examined experimentally only recently and phenomenon9 to generate coherent harmonic density modu- at modest harmonic orders, starting with the 3rd and 4th lations in the electron beam with conventional lasers. Here, harmonics18,19, the 7th harmonic20 and most recently at the we report on a demonstration of EEHG up to the 75th harmonic, 15th harmonic21 of infrared lasers. These studies demonstrated where 32 nm light is produced from a 2,400 nm laser. We also that the EEHG harmonics are generated with small relative demonstrate that individual harmonic amplitudes are con- increases in the beam energy spread compared with high-gain trolled by simple adjustment of the phase mixing. Results harmonic-generation (HGHG) schemes22–24 and also that the show the potential of laser-based manipulations to achieve spectrum is much less sensitive to initial electron-beam phase- precise control over the coherent spectrum in future X-ray space distortions. However, to reach from ultraviolet seed FELs for new science10,11. lasers to the soft X-ray wavelengths where the most compelling The well-known echo effect is a highly nonlinear process that was scientific applications are found, harmonic numbers h ≥ 50 are originally described in 1950 by E.L. Hahn in the context of precessing required, which in turn requires exquisite preservation of the nuclear spins9. Echoes have been observed in many areas of physics, fine-scale phase-space memory. including cyclotron beams12, plasma waves13, photons14, hadron Here, we report the first results of EEHG experiments in the colliders15, molecular rotors in gas16 and in classical mechanical h = 60 and h = 75 harmonic regimes, which also highlight the fine systems17. Broadly described, echoes arise in a medium that is first and unique control the echo mechanism provides over the coherent excited by a perturbation that then damps completely due to dephas- emission spectrum. The results suggest the possibility to precisely ing. The inherent damping mechanism is non-dissipative, however, tailor the pulses in future X-ray FELs for new science applications10,11. and the perturbations remain deeply encoded as highly filamentary From EEHG theory, the optimal harmonic bunching bh is tuned h ≈ λ R(1) λ R(2) structures in the phase space. Following an excitation by a second and scales according to the ratio of dispersions, 2 56 / 1 56 . R(1) perturbation, the phase mixing is partially reversed as the system Accordingly, the C1 chicane was set to 56 = 12.5 mm, close to its evolves, and the echo signal appears as a recoherence effect. This is peak value. In the first experiment, the dispersion of the second R(2) μ the mechanism behind the proposed echo-enabled harmonic gener- chicane was approximately 56 = 600 m to produce bunching ation (EEHG) technique, used to produce fully coherent X-ray pulses near the 60th harmonic of the 2,400 nm laser. The bunched beam in a free-electron laser (FEL)7,8. EEHG exploits the fact that the was boosted to 192 MeV in a short linac (Fig. 1) such that the fine phase-coherent echo structures have much higher frequency λ ≈ 40 nm harmonic wavelengths were radiated at the 3rd harmonic content than the original perturbations, so the temporal coherence of the U3 emission spectrum (see Methods). Figure 2a shows the of modulations imprinted by conventional lasers can be passed to characteristic undulator radiation pattern seen in the quadratic shorter wavelengths, with the electrons serving as the harmonic dependence of the wavelength on the vertical forward angle (see upconversion medium. Methods), and the bright peaks are the coherent harmonic echo The EEHG concept is illustrated in the schematic of our exper- signals. The image is the average of over 200 consecutive shots, imental layout in Fig. 1. The E = 120 MeV relativistic electron but is representative of typical single shots. The spectrum of each λ beam co-propagates with a laser pulse ( 1 = 800 nm) in a magnetic shot, taken from the vertical projection, is shown in Fig. 2b. undulator, U1 (see Methods). The resonant interaction imprints a Analysis of the spectral stability over all shots gives a 0.025 nm ΔE sinusoidal energy modulation with amplitude 1 in the electron (r.m.s.) variation of the central wavelength of the 59th harmonic beam phase space (Fig. 1a). Linear longitudinal dispersion signal (0.063% relative). The observed bandwidth of each harmonic through the magnetic chicane C1, given by the transport matrix peak for each shot is equal to the measured 0.15 nm resolution of R(1) element 56 , allows electrons with different energies to move the extreme ultraviolet (EUV) spectrometer (see Methods), but relative to one another as they traverse different path lengths. This simulations indicate the true bandwidth to be 0.011 nm (full-width

1SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA. 2Key Laboratory for Laser Plasmas (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China. 3Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China. *e-mail: [email protected]; [email protected]

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Figure 3 | Echo in the 75th harmonic range. a,Measuredelectronbeamemissionspectrumwithecholaserson(singleshotsinlightblue,averageindark blue) and with lasers off (single shots in light red, average in dark red). b, Coherent signal with spontaneous emission spectrum subtracted (black) and the 2 harmonic amplitudes of |bh| from numerical simulations (red). at half-maximum, FWHM). Simulations also show that the 1 ps of modulations that produce an echo rather than HGHG bunching lasers produce echo bunching in a 0.4 ps (FWHM) portion of the from a single laser. ∼1 ps (FWHM) electron beam. The envelope of the average spec- To access the highest harmonics in our set-up, dispersion in the trum is shown in Fig. 2c (blue line), together with the spectrum second chicane was lowered towards its minimum value around R(2) = μ of incoherent spontaneous radiation from the beam when both seed 56 500 m and the EUV spectrometer was moved to view the lasers are blocked (red line), which has a small bump at the 3rd undu- 75th harmonic regime at 32 nm. Coherent emission in this case lator harmonic. Numerical simulations of the bunching indicate good is peaked at the 4th harmonic resonance of U3 and thus is ΔE agreement with the observed EEHG spectrum for 1 =38keVand emitted slightly off-axis by the nature of even harmonic undulator ΔE 2 = 84 keV. These energy modulation amplitudes are consistent emission. The measured spectra are shown in Fig. 3a. With lasers with those observed experimentally at the electron energy spectrometer. on, the echo harmonics are clearly visible (blue lines), and with the It is noted that, with laser 1 blocked, no harmonic signals were lasers off, only spontaneous radiation is observed (red). In Fig. 3b, observed, which conﬁrms that the signal is due to the combination the averaged spontaneous background (Fig. 3a, dark red) is

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λ R(2) Figure 4 | Tuning harmonics with dispersion. a, Individual echo harmonics of the 2 = 800 nm laser tuned as a function of the second dispersion 56 . b, At certain dispersion values, speciﬁc harmonics are dominant and nearby harmonics are almost completely suppressed. c,d, Matching results from 2 numerical simulations for |bh| , where the narrow bandwidth is resolved.

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© 2016 Macmillan Publishers Limited. All rights reserved NATURE PHOTONICS DOI: 10.1038/NPHOTON.2016.101 LETTERS subtracted from the averaged echo spectrum (Fig. 3a, dark blue), References and results from numerical simulations for the bunching are com- 1. Maiman, T. H. Stimulated optical radiation in ruby. Nature 187, 493–494 (1960). pared with the measured coherent spectrum. Simulations indicate 2. Schawlow, A. L. & Townes, C. H. Infrared and optical masers. Phys. Rev. ΔE ΔE 112, 1940–1949 (1958). that energy modulations of 1 = 61 keV and 2 = 104 keV 3. Franken, P. A., Hill, A. E., Peters, C. W. & Weinreich, G. Generation of optical produce a harmonic spectrum that is strikingly similar to the harmonics. Phys. Rev. Lett. 7, 118–119 (1961). data, both in the relative amplitudes of the harmonics and in 4. Emma, P. et al. First lasing and operation of an angstrom-wavelength the variation of the envelope of the harmonic peaks. Again, free-electron laser. Nature Photon. 4, 641–647 (2010). et al these values are consistent with experimental measurements. As 5. Ishikawa, T. . A compact X-ray free-electron laser emitting in the sub-angstrom region. Nature Photon. 6, 540–544 (2012). was also the case with the experiments on the 60th harmonic, 6. McNeil, B. W. J. & Thompson, N. R. X-ray free-electron lasers. Nature Photon. 4, the observed shot-to-shot amplitude fluctuations were due primar- 814–821 (2010). ily to charge fluctuations (as seen in the variation of the incoherent 7. Stupakov, G. Using the beam-echo effect for generation of short-wavelength signal) and systematic intensity fluctuations in the second laser radiation. Phys. Rev. Lett. 102, 074801 (2009). pulse (see Methods). With laser 1 blocked in this configuration, 8. Xiang, D. & Stupakov, G. Echo-enabled harmonic generation free electron laser. Phys. Rev. ST Accel. Beams 12, 030702 (2009). the harmonics of the optimized HGHG signal were fully sup- 9. Hahn, E. L. Spin echoes. Phys. Rev. 80, 580–594 (1950). pressed, which confirms the efficiency of the echo harmonic 10. Hemsing, E., Stupakov, G., Xiang, D. & Zholents, A. Beam by design: generation process. laser manipulation of electrons in modern accelerators. Rev. Mod. Phys. It is important to note that the coherent signal at these wave- 86, 897–942 (2014). Rev. Accel. Sci. lengths and at this beam energy is calculated to be strongly sup- 11. Schneider, J. R. Photon science at accelerator-based light sources. Technol. 3, 13–37 (2010). pressed by longitudinal smearing effects of beam betatron motion 12. Hill, R. M. & Kaplan, D. E. Cyclotron resonance echo. Phys. Rev. Lett. in U3, due to the finite beam emittance and the fixed U3 strong 14, 1062–1063 (1965). focusing channel. This probably accounts for the relative smallness 13. Gould, R. W., O’Neil, T. M. & Malmberg, J. H. Plasma wave echo. Phys. Rev. Lett. of the coherent signal compared to the spontaneous background in 19, 219–221 (1967). both the 60th and 75th harmonic experiments. This effect becomes 14. Kurnit, N. A., Abella, I. D. & Hartmann, S. R. Observation of a photon echo. Phys. Rev. Lett. 13, 567–568 (1964). stronger at shorter wavelengths, which precluded investigation of 15. Spentzouris, L. K., Ostiguy, J.-F. & Colestock, P. L. Direct measurement of still higher harmonics in our set-up, but is significantly reduced diffusion rates in high energy synchrotrons using longitudinal beam echoes. in optimized soft X-ray FELs with larger beta functions and Phys. Rev. Lett. 76, 620–623 (1996). higher energy beams (see Methods). 16. Karras, G. et al. Orientation and alignment echoes. Phys. Rev. Lett. 114, 153601 (2015). The variation of the harmonic envelope observed in Fig. 3b, 17. Chebotayev, V. P. & Dubetsky, B. Ya. A classical model of the photon echo. Appl. where certain harmonics are suppressed (for example, the 72nd) Phys. B 31, 45–52 (1983). while nearby harmonics are enhanced (for example, the 74th), is 18. Xiang, D. et al. Demonstration of the echo-enabled harmonic generation a newly observed and unique feature of the beam echo effect technique for short-wavelength seeded free electron lasers. Phys. Rev. Lett. 105, compared to HGHG. This effect is predicted from EEHG 114801 (2010). 19. Zhao, Z. et al. First lasing of an echo-enabled harmonic generation free-electron theory, which indicates that the individual harmonics can be pre- laser. Nature Photon. 6, 360–363 (2012). cisely tuned by the dispersion (see Methods). Results of a separate 20. Xiang, D. et al. Evidence of high harmonics from echo-enabled harmonic experiment to explore this harmonic tunability are presented in generation for seeding X-ray free electron lasers. Phys. Rev. Lett. Fig. 4, where the measured spectra in the neighbourhood of the 108, 024802 (2012). et al 20th harmonic from two 800 nm seed lasers are shown in 21. Hemsing, E. . Highly coherent vacuum ultraviolet radiation at the 15th ΔE harmonic with echo-enabled harmonic generation technique. Phys. Rev. ST Fig. 4a and b, respectively. Here, 2 was held stable while the Accel. Beams R(2) 17, 070702 (2014). value of 56 was varied. Individual harmonics within the envelope 22. Yu, L. H. Generation of intense UV radiation by subharmonically seeded single- are seen to be optimized at slightly different dispersion values. For pass free-electron lasers. Phys. Rev. A 44, 5178–5193 (1991). instance, at R(2) = 660 μm, bunching at 40 nm can be optimized 23. Allaria, E. et al. Highly coherent and stable pulses from the FERMI seeded free- 56 Nature Photon – while that at 42 nm can be suppressed; the 2 nm difference is electron laser in the extreme ultraviolet. . 6, 699 704 (2012). 24. Allaria, E. et al. Two-stage seeded soft-X-ray free-electron laser. Nature Photon. more than two orders of magnitude smaller than the wavelength 7, 913–918 (2013). of the lasers used to create the fine structure. This precise control over the coherent beam distribution is also reproduced Acknowledgements ΔE ΔE in simulations with 1 = 29 keV and 2 = 27 keV, as shown The authors thank D. McCormick, K. Jobe, I. Makasyuk, T. Beukers, C. Hudspeth, J. Cruz, in Fig. 4c,d. V. Yakimenko and the rest of the Test Facilities Group for their support. The authors also thank M. Guehr for his guidance with the design and construction of the EUV spectrometer The experiments thus show that the proposed beam echo effect and E. Johnson for the VISA undulator. This work was supported by the US DOE Office of can be used to produce ultrahigh harmonic bunching and that it Basic Energy Sciences under award no. 2012-SLAC-10032 using the SLAC NLCTA facility, enables precise control via practical means over the fine-scale which is partly supported by US DOE Office of High Energy Physics under contract bunching spectrum. Demonstration of EEHG at the 75th harmonic no. DE-AC02-76SF00515. The work of D.X. was supported by the Major State Basic suggests that it may be straightforward to use this technique to Research Development Program of China (grant no. 2015CB859700) and by the National Natural Science Foundation of China (grant no. 11327902). seed the amplification of fully coherent and tunable soft X-rays in the water window (2–4 nm) above the gigawatt level in a single Author contributions stage from ultraviolet lasers in future FELs. Furthermore, two- G.S. conceived the original EEHG theoretical concept, which, with D.X., was later stage EEHG, with soft X-rays from the first stage seeding the developed further. E.H., B.G. and M.D. carried out the experiments. B.G. and M.D. second stage, might eventually allow extension to hard X- designed and built the EUV spectrometer. E.H. and B.G. performed the data analysis and performed simulations. D.X., C.H. and T.R. provided guidance on the experiments and on ray wavelengths. potential applications. E.H. and D.X. wrote the paper, with contributions from all other authors. Methods Methods and any associated references are available in the online Additional information Reprints and permissions information is available online at www.nature.com/reprints. version of the paper. Correspondence and requests for materials should be addressed to E.H. and D.X. Received 18 March 2016; accepted 21 April 2016; Competing financial interests published online 6 June 2016 The authors declare no competing financial interests.

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Methods EUV spectrometer. Coherent EUV radiation emitted by the beam in U3 was Experiments were conducted at the Next Linear Collider Test Accelerator (NLCTA) measured with a high-resolution, custom-built, ultrahigh-vacuum spectrometer with at SLAC National Accelerator Laboratory. sensitivity in the 11–62 nm wavelength range26. Radiation was first reflected off an insertable gold-coated mirror at 15° incidence ∼0.5 m downstream of U3 and sent Electron beam. The NLCTA electron beam was generated in a photocathode RF gun through an extraction port off the beam line. The light then passed through a slit (RF frequency at 2.856 GHz) at a repetition rate of 10 Hz and was boosted to with independently adjustable blades and then struck a Hitachi 001-0640 – E = 120 MeV with two X-band linac structures (RF frequency at 11.424 GHz). Echo aberration-corrected concave grating with 1,200 G mm 1 at an incidence angle of manipulations were performed at this energy. The electron beam charge was ∼20 pC 4.7°. The blaze angle was 3.7° and the grating imaged the slit at a flat field focus in the experiment, the FWHM bunch length was ∼1 ps, the slice energy spread was 469 mm from the centre. The combined assembly allowed 60–80% efficiency over σE ≃ 1–2 keV, and the projected normalized transverse emittance was ∼1.7 μm. The the wavelengths of interest. This grating was fixed-mounted in a custom high- beam current was kept low to avoid lasing in the undulator, so that the undulator vacuum chamber connected to a large bellows that allowed the light to travel to the harmonics and off-axis emission angles provided a broadband diagnostic of the 40 mm MicroChannel Plate (MCP) detector (Model BOS-40, Beam Imaging harmonic bunching spectrum. The measured r.m.s. energy variation about the final Solutions, ≤2 kV power supply). Behind the MCP was a P-43 phosphor screen, ∼ R(1) ≤ 190 MeV central energy was 190 keV (0.1%). At this level, the 56 = 12.5 mm powered by a 5 kV power supply, which was then directly imaged with a CCD dispersion in the first chicane led to a 40 fs r.m.s. electron beam arrival time jitter in camera. The MCP/phosphor/camera assembly was mounted to a linear motion stage the downstream undulators. that allowed 120 mm of translation parallel to the grating focal plane to capture the full wavelength range, including the zeroth order. Calibration of the spectrometer Laser beam. The two seed lasers originated from a single 800 nm (∼1 ps FWHM) was carried out using the known grating equations in combination with the laser pulse that was sent through a beamsplitter. One pulse seeded the U1 undulator harmonic radiation spectrum from the undulator and the echo harmonics from the λ fi fi at 1 = 800 nm and the other pumped an optical parametric ampli er (OPA) to 800/2,400 nm and 800/800 nm laser seeding con gurations. The spectrometer can λ ∼ ≤ μ produce a 2 = 2,400 nm pulse ( 1psFWHM, 10 J) in the U2 undulator. The be set to capture different harmonic emissions of the U3 undulator. energy of the 2,400 nm laser had considerable fluctuations due to the pointing stability and long transport of the 800 nm laser, which led to relatively large shot-to-shot Simulations. Numerical simulations used measured realistic beam distributions, fluctuations of the echo signals in Figs 2 and 3. The OPA could also be bypassed to laser energy modulations and chicane dispersions. Electrons were tracked through allow modulation of the beam in U2 with the 800 nm seed laser. By using the two the echo beamline and the final beam distribution was used to calculate the R(1) 800 nm lasers, the echo signals in Fig. 4 had much better energy stability. bunching at various wavelengths. The dispersion in C1 was taken as 56 = 12.5 mm and the electron beam length was 0.43 ps r.m.s. for all simulations. For the Echo R(2) μ Echo beamline. The echo beamline consisted of three undulators (a series of 75 simulations in Fig. 3b, 56 = 484 m (in good agreement with the measured magnets with alternating fields), two chicanes (a series of bending magnets that value considering the uncertainty of the dispersion near the minimal value), ’ ΔE ΔE change the electron s path length according to its energy) and one accelerator 1 = 61 keV and 2 = 104 keV. With a seed laser pulse length of 1 ps FWHM, λ = λ h γ2 K2 structure. The resonant wavelength of each undulator was r ( u/2 u )(1 + /2 + simulations indicate that the coherent bunching extends over 0.4 ps of the electron θ2γ2 λ K h b 2 ), where u is the undulator period, is the normalized undulator parameter, u beam and that the FWHM bandwidth of | h| is 0.007 nm at 32 nm. In Fig. 4, γmc2 θ ΔE ΔE is the undulator harmonic, is the beam energy in the undulator, and is the the parameters used in the simulation are 1 = 29 keV, 2 = 27 keV and λ R(2) – μ forward emission angle. U1 had 10 periods, each with a length of u = 3.3 cm and an 56 = 590 730 m. undulator parameter of K = 1.82. The beam then transitted the C1 chicane, and then λ λ co-propagated with the second laser pulse ( 2 = 2,400 nm if from the OPA, 2 = 800 nm Bunching factor. From EEHG theory, the bunching amplitude at the bunching ω nω mω if the OPA was bypassed) inside the U2 undulator (10 periods with a period length frequency n,m = 1 + 2 is K of 5.5 cm and = 2.76). The tuning of U2 was such that the 2,400 nm laser pulse was γ h = 2 resonant with the 120 MeV ( = 235) beam at the 1st harmonic ( u 1) of the −ξ /2 (2) bh = e Jn −ξΔE /σE Jm −ωn mΔE R /cE (1) undulator and the 800 nm pulse was resonant with the 3rd harmonic. After passing 1 , 2 56 through the C2 chicane, the beam was accelerated up to a maximum of 192 MeV by ω πc λ ξ σ cE nω R(1) ω R(2) a 1.05-m-long x-band linac. Radiation was produced by the beam inside the U3 where 1,2 =2 / 1,2 are the seed laser frequencies, =( E / )( 1 56 + n,m 56 ) L J undulator (110 periods with a period length of 1.8 cm ( = 198 cm total length) and and n,m are Bessel functions. In practice, the modulations and dispersions are K = 1.26). The U3 was a 2 m section of the VISA-II Halbach-type pure-permanent tuned so that bh is maximized at the desired echo harmonic of the second laser h ω ω m n ω ω n m m n magnet undulator with eight distributed strong focusing focus, drift, defocus, drift = n,m/ 2 = + ( 1/ 2) for a given and , where is typically large and <0 (FODO) cells, each of 24.75 cm length25.AtE = 190 MeV (γ = 372), the on-axis with |n| small. Optimized echo harmonics are given in general approximately by the h h ≈−nλ R(1) λ R(2) n − resonance of the U3 undulator was 117 nm at the u = 1 fundamental. Four intra- ratio 2 56 / 1 56 . In all of our experiments, the tuning was such that = 1. undulator retractable beam profile screens imaged by charge-coupled device (CCD) cameras allowed electron beam orbit and beta-matching correction with external Smearing of bunching. The beam betatron motion in U3 resulted in longitudinal steering magnets and upstream quadrupoles, respectively. smearing effects that reduced the bunching factor at high harmonic frequencies. Each four-dipole chicane was remotely adjustable but had a minimum This is due to the fact that particles with larger betatron amplitudes√ have longer path dispersion to allow the electron beam to pass cleanly by the laser injection/rejection lengths. The longitudinal smearing effect is estimated as Δz = 2ϵnL/γ〈β〉 ≈ 5nm mirror assembly, which was located between the second and third dipoles. This set which is comparable to λ/2π, where L = 2 m is the length of undulator U3, R ∼ μ the geometric minimum 56 to 500 m to avoid beam scraping, but there is a ϵn ≈ 0.5 mm mrad is the (assumed) electron beam slice transverse emittance, known uncertainty of 100 μm in the recorded dispersion at these small values. Each ⟨β⟩ = 65 cm is the average beta function in U3 and λ is the wavelength of the chicane also had two magnetic quadrupoles for horizontal dispersion correction: harmonic radiation. The beta function in the undulator is fixed by the permanent one positioned halfway between the first and second dipole, and one halfway magnetic focusing at the 190 MeV beam energy, so the beta function of the beam between the third and fourth dipole. cannot be increased to mitigate this effect without mismatching the beam. In the absence of this smearing effect, simulations indicate a bunching factor of several Laser and electron beam overlap. Effective interaction between the lasers and percent, depending on the harmonic tune. Given that the effective bunching due to b ∼ N ∼ −4 N electron beam was achieved when the electron and laser beam overlapped both noise is SN 1/ s 4×10 (where s is the number of electrons in a slippage Lλ λ spatially and temporally in the modulators. Spatial overlap between the 800 nm laser length r/ u), this would result in an increase of the coherent emission by about and the electron beam was achieved by steering the laser to the same position as the four orders of magnitude above the incoherent background. Similarly, for optimized beam on the screens upstream and downstream of the undulators. Temporal overlap FELs operating in the water window, the few percent echo bunching factor is also was achieved with two steps. First, an optical transition radiation screen downstream about two orders of magnitude higher than shot noise bunching, which enables the of each undulator was used to reflect out the laser and undulator radiation, which production of fully coherent radiation. was detected by a fast photodiode. By referencing the signals to an external trigger, the laser and electron beam could be synchronized to within ∼30 ps. More precise timing was then carried out by using a scanning delay stage and measuring the References coherent transition radiation from the electron beam downstream of C1. The second 25. Carr, R. et al. Visible-infrared self-amplified spontaneous emission amplifier free laser at 2,400 nm was made to overlap with the beam in U2 in a similar way. electron laser undulator. Phys. Rev. ST Accel. Beams 4, 122402 (2001). Unattenuated, the 2,400 nm idler pulse profile could be seen with the CCD beam 26. Garcia, B., Dunning, M. P., Hast, C., Hemsing, E. & Raubenheimer, T. O. Facility profile cameras for transverse overlap with the electrons. A bandpass filter centred at upgrades for the high harmonic echo program at SLAC’s NLCTA. In Proc. 37th 2,400 nm was used in the experiment to ensure that the beam was only modulated by Int. Free Electron Laser Conf. (FEL 2015) (eds Kang, H.-S. et al.) 422–426 the 2,400 nm laser in U2 and not the 1,200 nm signal pulse from the OPA. (JACoW, 2015).

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