X-ray free-electron lasers can generate intense and coherent radiation at wavelengths down to the sub-ångström region1,2,3,4,5, and have become indispensable tools for applications in structural biology and chemistry, among other disciplines6. Several X-ray free-electron laser facilities are in operation2,3,4,5; however, their requirement for large, high-cost, state-of-the-art radio-frequency accelerators has led to great interest in the development of compact and economical accelerators. Laser wakefield accelerators can sustain accelerating gradients more than three orders of magnitude higher than those of radio-frequency accelerators7,8,9,10, and are regarded as an attractive option for driving compact X-ray free-electron lasers11. However, the realization of such devices remains a challenge owing to the relatively poor quality of electron beams that are based on a laser wakefield accelerator. Here we present an experimental demonstration of undulator radiation amplification in the exponential-gain regime by using electron beams based on a laser wakefield accelerator. The amplified undulator radiation, which is typically centred at 27 nanometres and has a maximum photon number of around 1010 per shot, yields a maximum radiation energy of about 150 nanojoules. In the third of three undulators in the device, the maximum gain of the radiation power is approximately 100-fold, confirming a successful operation in the exponential-gain regime. Our results constitute a proof-of-principle demonstration of free-electron lasing using a laser wakefield accelerator, and pave the way towards the development of compact X-ray free-electron lasers based on this technology with broad applications.
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All data are available upon reasonable request from the corresponding authors. Source data are provided with this paper.
All codes written for use in this study are available upon reasonable request from the corresponding authors.
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We thank D. Wang and B. Liu for discussions and assistance. This work was supported by the Strategic Priority Research Program (B) (grant no. XDB16) and Center for Excellence in Ultra-intense Laser Science of Chinese Academy of Sciences (CAS), the National Natural Science Foundation of China (grant nos. 11127901, 11875065 and 11991072), the Natural Science Foundation of Shanghai (nos 18JC1414800 and 18ZR1444500) and the State Key Laboratory Program of the Chinese Ministry of Science and Technology and CAS Youth Innovation Promotion Association (Y201952).
The authors declare no competing interests.
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Extended data figures and tables
Energy spectra of the accelerated electron beams for 50 shots measured in spectrometer 1 located 2.3-m downstream of the gas target. Electron beams with an average peak energy of about 490 MeV, r.m.s. energy spread of 0.2–1.2%, r.m.s. divergence of 0.1–0.4 mrad and charges of 10–50 pC were experimentally obtained. The associated fluctuations of the electron beam peak energy were estimated to be less than 3%.
a, b, Measured fringe pattern for plasma density diagnosis and the corresponding density profile along the optical axis. c–e, Longitudinal phase space of the trapped electrons and the corresponding accelerating electric field at different positions. f, Longitudinal phase space of the accelerated electrons at the exit of the plasma and the corresponding energy spectrum shown in red. s is the longitudinal position of the electron in an electron beam in the co-moving coordinate. The simulated electron beam had a peak energy of 495 MeV, charge of 25.4 pC, global energy spread of 0.67% in r.m.s. (93% of the total electrons), and normalized projected emittance of 0.23 mm mrad and 0.73 mm mrad in the horizontal and vertical directions, respectively.
a, Coordinate space distribution of accelerated electrons, with various colours representing the various energies. b, Beam current (blue) and slice energy spread (red) within the beam. RES, relative energy spread. c, Normalized slice emittance of the beam in the horizontal (enx, red) and vertical (eny, blue) directions. Each slice has a length of 31.25 nm, which was set as the grid size in the particle-in-cell simulation.
a, b, Start-to-end simulation for horizontal and vertical envelopes of the electron beam along the beamline with a beam energy of 475 MeV (blue), 490 MeV (red) and 505 MeV (black). c–e, Measured transverse profiles of the electron beam at the entrance of the undulator located 4-m downstream from the gas target without (c) and with (d) focusing and at the exit of the undulator located 9.5-m downstream from the gas target (e). With the quadrupoles installed, the measured r.m.s. size of the electron beam was reduced from approximately 0.8 mm to a minimum value of less than 0.1 mm in the horizontal and vertical directions. f–h, Shot-to-shot pointing distribution over 50 shots (f), and beam size statistics in the horizontal (g) and vertical (h) directions. The relative positions of the quadrupoles (green) and undulators (cyan) are shown in a and b.
Extended Data Fig. 5 Properties of an electron beam with a reference energy of 490 MeV along the beamline.
a–c, Simulated beam envelopes (a), normalized projected emittance (b) and Twiss parameters β (c) of the electron beam in the horizontal (red) and vertical (blue) directions. The beam used for tracking was directly derived from the FBPIC code.
a, Beam current (blue) and slice energy spread (red) within the beam. b, Normalized slice emittance of the beam in the horizontal (red) and the vertical (blue) directions. Despite the slice emittance in the bunch tail increasing substantially (b) and causing an increase in projected emittance (Extended Data Fig. 5b), most of the electrons in the beam still showed a small slice emittance.
Energy spectra of electron beams for 200 consecutive shots detected with spectrometer 2. The average energy of the electron beam was estimated to be 485 MeV with energy fluctuations of 3.3% and a reproducibility of approximately 100%.
a, b, Spectra of the undulator radiation with a groove density of the grating of 3,000 lines per mm (a) and 500 lines per mm (b). The radiation wavelength was typically centred at 27 nm with a corresponding electron beam energy of 492 MeV, which is reasonably consistent with the measured values shown in Extended Data Fig. 7. The minimum bandwidth was measured to be 2%, which indicated a reasonable agreement with the simulated values in the exponential-gain regime. The measured spectra of broadband spontaneous emission are also depicted with a bandwidth of approximately 7%.
Extended Data Fig. 9 Measured radiation energy at the exit of the undulator for various electron beam charges and relative energy spreads.
The black diamonds represent cases with energy spreads larger than 2% (exponential gain is typically not available under such conditions), and the corresponding linear fitting curve (black dashed line) indicates the spontaneous emission. The radiation emitted by a low-energy-spread electron beam (<1%) typically has energy one to two orders higher than that in spontaneous cases, thus indicating the operation in the exponential-gain regime in the present scheme. The exponential gain of the radiation is illustrated with the orbit kick method in the main text.
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Wang, W., Feng, K., Ke, L. et al. Free-electron lasing at 27 nanometres based on a laser wakefield accelerator. Nature 595, 516–520 (2021). https://doi.org/10.1038/s41586-021-03678-x