Experimental demonstration of a single-spike hard-X-ray free-electron laser starting from noise

X-ray free-electron lasers (XFELs) are the brightest X-ray sources currently available, with a peak brightness that is several orders of magnitude higher than conventional synchrotron light sources. The Linac Coherent Light Source (LCLS) can generate pulses with a peak power up to 100 GW and pulse duration as short as 4 fs.¹ XFELs have enabled the time-resolved study of dynamical processes either with optical pump/X-ray probe methods or with X-ray pump/X-ray probe schemes. Such processes include phase-transitions,² structural dynamics in molecules,^3,4 lattice dynamics in solids,^5,6 or the formation and evolution of high-energy density states in materials.⁷ 

While much success has been obtained with experiments at the tens of fs level, sub-fs pulses would enable the study of electron dynamics in molecules at time scales so far not accessible with XFELs. The femtosecond is an important threshold in X-ray science, since it is the typical relaxation time of core-excited states. Sub-fs pulses can generate core-excited states and interact with them before they decay. Therefore, attosecond pulses are the natural tool to study coherent electronic processes in molecules.

The shortest pulse achievable with a conventional self-amplified spontaneous emission (SASE) free-electron laser (FEL) is given by the cooperation length

where λ_r and λ_w are the radiation wavelength and the undulator period, respectively, while L_g is the FEL field gain-length. l_c represents the path-length difference (slippage) between the radiation and the electrons accrued in a gain-length. If the electron bunch is significantly longer than l_c, the pulse will have many spikes with no mutual coherence, while a bunch duration comparable to l_c results in the emission of a single coherent spike. We note that typically, in the single-spike regime, the power level is reduced with respect to the multi-spike regime. This is mostly because in the single-spike regime, post-saturation tapering is not employed to avoid lengthening the spike length. Based on the well-known 1-D model of FELs,⁸ the shortest pulse duration achievable scales proportionally to the square root of the photon energy $Eph1/2$⁠. Assuming the baseline parameters of LCLS and based on these scaling laws, the single-spike length at hard-X-rays (E_ph > 1 keV) is typically below 1 fs.

Selective spoiling of the beam quality is a well established method to control the pulse duration of a SASE FEL.^1,9–11 The FEL instability is extremely sensitive to the electron beam brightness;¹² by increasing the emittance or energy spread of the electron beam but leaving a short fraction of the beam unspoiled, one can reduce the pulse duration. In the case of an emittance spoiler, the spoiling mechanism is scattering of the electron beam through a slotted metal foil in a dispersive region. If the electron beam is strongly chirped, one can establish a correlation between energy and the horizontal position; by introducing a slotted metal foil, one can spoil most of the electron beam leaving the electrons that go through the foil untouched.

Here, we report the generation of single-spike hard X-ray pulses using an emittance spoiler and tailoring the beam optics to improve the time-resolution. Figure 1 shows an illustration of the scheme used. The electron beam is generated by a photo-injector and accelerated and compressed in the LCLS linac. An emittance spoiler is inserted in the middle of the second bunch compressor. Matching quadrupoles are used to minimize the beta function at the foil location, achieving a minimum value of 8 m. To further reduce the electron beam size, we use the 20 pC working point of LCLS,¹³ which results in a normalized projected emittance of ϵ_n = 0.2 μm. The length of the unspoiled fraction of the electron bunch is given by⁹ 

where Δx is the size of the slot, σ_d,x is the RMS transverse size of the dispersed electron beam, and σ_t is the total duration of the bunch. The value of Δx is limited by the undispersed size of the electron bunch $Δx<6σβ,x=6ϵnβx/γ$⁠, where β_x is the Twiss beta function at the slotted foil location and γ is the electron beam Lorentz factor. With the machine configuration considered in this paper, we have σ_t ∼ 5 fs, σ_d,x ∼1 mm, and σ_β,x ∼15 μm, with a resulting minimum bunch duration of Δt ∼ 1 fs.

The SASE spectra generated in the LCLS undulator were measured by means of a bent crystal spectrometer.¹⁴ The average photon energy was 5.5 keV. Figure 2 shows single-shot and average spectra for different slot widths, as well as histograms of the number of shots as a function of the number of spectral SASE spikes. For the unspoiled electron beam, the number of spikes peaks around 5. Selectively spoiling the electron beam results in shorter pulses and lower number of spikes. For a slot width of 220 μm, roughly 45% or the shots exhibit single-spike spectra. The number of single-spike shots is optimized for a slot width of Δx = 130 μm, with 65% of the shots being single spike. The average pulse energy in the single-spike configuration is E_pulse ∼5 μJ with peaks up to 30 μJ and 30% of the shots being above 10 μJ. The intensity fluctuation level is σ_E/E_pulse = 76%.

Figure 3 shows 10 consecutive spectra in the optimized single-spike configuration [corresponding to the parameters in Figs. 2(c) and 2(f)]. The average full-width at half-maximum (FWHM) bandwidth of the single-shot spectra is ΔE = 4.5 eV. The pulse duration could not be directly measured with our experimental setup, but it can be estimated with a simple argument based on the electron beam chirp. The short current spike generated by the emittance spoiler has a small energy-chirp due to the longitudinal space-charge field (see, e.g., Ref. 15). The energy chirp can be compensated by tapering the undulator¹⁶ and ensuring that the resonant frequency matches the radiation frequency as it propagates across the beam

where K₀ and γ₀ are the average undulator parameter and beam Lorentz factor, respectively, z is the position along the undulator, and ζ is the position along the electron bunch. Under these conditions, the chirp in the radiation pulse matches the chirp in the electron bunch consistently with the FEL resonant condition

The performance was optimized for a taper value of $dK/K0dz=1.75×10−5 m−1$⁠. The LCLS gain-length for the beam parameters considered here is roughly 4 m, which means that the variation of the K parameter over a gain-length is roughly 10⁻⁴, with a corresponding relative variation of the resonant frequency across the bunch of ∼2 × 10⁻⁴. This is much smaller than the relative bandwidth ΔE_p/E_p ∼8 × 10⁻⁴, which means that the correlated bandwidth induced by space-charge forces is negligible with respect to the natural bandwidth of the FEL. With a negligible chirp, it has been shown that single-spike FEL pulses are nearly Fourier transform limited,¹⁷ so the average pulse duration can be estimated as

This scheme was demonstrated at a photon energy of 5.6 keV, but the photon energy can be tunable in the LCLS photon energy range (500 eV to 12 keV). Typically at higher energy, the slippage length is shorter, which may result in more spikes in the temporal and spectral domain. In the soft-X-ray range, instead, the slippage length is longer which would result in a narrower bandwidth and longer pulses.

In conclusion, we have demonstrated the generation of single-spike SASE FEL in the hard X-ray regime with a slotted emittance spoiler. The average single-spike bandwidth is 4.5 eV, and the pulse duration is estimated to be close to the Fourier-transform limited value of 420. We note that similar results were obtained at LCLS using non-linear compression in the low-charge working point and are the subject of a separate paper.¹⁸ These results pave the way for attosecond science at FEL facilities in the hard-X-ray regime.

The authors would like to acknowledge E. Allaria, L. Giannessi, E. Roussel, C. Pellegrini, and E. Hemsing for useful discussions and suggestions. We also acknowledge the SLAC accelerator operations group as well as the LCLS operations group for their invaluable support during the experiment. This work was supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-76SF00515 and DOE-BES Field Work Proposal 100317.