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Low-divergence femtosecond X-ray pulses from a passive plasma lens


Electron and X-ray beams originating from compact laser-wakefield accelerators have very small source sizes that are typically on the micrometre scale. Therefore, the beam divergences are relatively high, which makes it difficult to preserve their high quality during transport to applications. To improve on this, tremendous efforts have been invested in controlling the divergence of the electron beams, but no mechanism for generating collimated X-ray beams has yet been demonstrated experimentally. Here we propose and realize a scheme where electron bunches undergoing focusing in a dense, passive plasma lens can emit X-ray pulses with divergences approaching the incoherent limit. Compared with conventional betatron emission, the divergence of this so-called plasma lens radiation is reduced by more than an order of magnitude in solid angle, while maintaining a similar number of emitted photons per electron. This X-ray source offers the possibility of producing brilliant and collimated few-femtosecond X-ray pulses for ultra-fast science, in particular for studies based on X-ray diffraction and absorption spectroscopy.

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Fig. 1: Experimental set-up and electron beam examples.
Fig. 2: Shock-bunch features.
Fig. 3: X-ray emission from jet 2.
Fig. 4: PIC simulation results.
Fig. 5: Results from the semi-analytical model.

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Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The codes that support the findings of this study are available from the corresponding authors upon reasonable request.


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We thank D. Cardenas for his help and support. We acknowledge support from the Swedish Research Council (VR 2015-03749, 2019-04784), the Knut and Alice Wallenberg Foundation (KAW 2014.0170, 2018.0450 and 2019.0318), the European Research Council (ERC-2014-CoG 647121), Laserlab-Europe (EU-H2020 871124) and ARIES (EU-H2020 730871). L.V. acknowledges support from the Swedish Research Council (VR 2016-05409 and 2019-02376). H.E. acknowledges support from the US Department of Energy (DE-AC02-76SF00515). J.F. acknowledges support from the Swedish Research Council (VR 2016-03329). Simulations were performed on resources at C3SE and LUNARC, provided by the Swedish National Infrastructure for Computing (SNIC).

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Authors and Affiliations



J.B.S., D.G., L.V. and O.L. devised the experiment. J.B.S. and D.G. built the experimental set-up and performed the measurements assisted by I.G.G., H.E., K.S. and A.P. J.B.S. analysed the electron data and constructed the semi-analytical model. D.G. and H.E. analysed the X-ray data. J.F. and H.E. performed and analysed the PIC simulations. O.L. supervised the work. J.B.S., D.G., J.F. and L.V. wrote the manuscript, with input and feedback from all authors.

Corresponding authors

Correspondence to Jonas Björklund Svensson or Olle Lundh.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Min Chen and Eduardo Oliva for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–4, Table 1, experimental set-up, additional electron data, semi-analytical modelling of the electron propagation, calculation of the X-ray emission from the second jet, conclusions and remarks on the model.

Source data

Source Data Fig. 1

Plot data for Fig. 1d.

Source Data Fig. 2

Plot data for Fig. 2d,h.

Source Data Fig. 3

Plot data for Fig. 3a–f.

Source Data Fig. 4

Plot data for Fig. 4a–d,f,h.

Source Data Fig. 5

Plot data for Fig. 5 a–d.

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Björklund Svensson, J., Guénot, D., Ferri, J. et al. Low-divergence femtosecond X-ray pulses from a passive plasma lens. Nat. Phys. 17, 639–645 (2021).

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