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

Nature Physics volume 17, pages 639–645 (2021)Cite this article

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Abstract

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.

References

  1. Tajima, T. & Dawson, J. M. Laser electron accelerator. Phys. Rev. Lett. 43, 267–270 (1979).

    Article  ADS  Google Scholar 

  2. Barber, S. K. et al. Measured emittance dependence on the injection method in laser plasma accelerators. Phys. Rev. Lett. 119, 104801 (2017).

    Article  ADS  Google Scholar 

  3. Lundh, O. et al. Few femtosecond, few kiloampere electron bunch produced by a laser-plasma accelerator. Nat. Phys. 7, 219–222 (2011).

    Article  Google Scholar 

  4. Buck, A. et al. Real-time observation of laser-driven electron acceleration. Nat. Phys. 7, 543–548 (2011).

    Article  Google Scholar 

  5. Phuoc, K. T. et al. Imaging electron trajectories in a laser-wakefield cavity using betatron X-ray radiation. Phys. Rev. Lett. 97, 225002 (2006).

    Article  ADS  Google Scholar 

  6. Albert, F. et al. Betatron oscillations of electrons accelerated in laser wakefields characterized by spectral X-ray analysis. Phys. Rev. E 77, 056402 (2008).

    Article  ADS  Google Scholar 

  7. Kneip, S. et al. Bright spatially coherent synchrotron X-rays from a table-top source. Nat. Phys. 6, 980–983 (2010).

    Article  Google Scholar 

  8. Corde, S. et al. Femtosecond X-rays from laser-plasma accelerators. Rev. Mod. Phys. 85, 1–48 (2013).

    Article  ADS  Google Scholar 

  9. Migliorati, M. et al. Intrinsic normalized emittance growth in laser-driven electron accelerators. Phys. Rev. ST Accel. Beams 16, 011302 (2013).

    Article  ADS  Google Scholar 

  10. Floettmann, K. Adiabatic matching section for plasma accelerated beams. Phys. Rev. ST Accel. Beams 17, 054402 (2014).

    Article  ADS  Google Scholar 

  11. Xu, X. L. et al. Physics of phase space matching for staging plasma and traditional accelerator components using longitudinally tailored plasma profiles. Phys. Rev. Lett. 116, 124801 (2016).

    Article  ADS  Google Scholar 

  12. Ariniello, R., Doss, C. E., Hunt-Stone, K., Cary, J. R. & Litos, M. D. Transverse beam dynamics in a plasma density ramp. Phys. Rev. Accel. Beams 22, 041304 (2019).

    Article  ADS  Google Scholar 

  13. Zhao, Y. et al. Emittance preservation through density ramp matching sections in a plasma wakefield accelerator. Phys. Rev. Accel. Beams 23, 011302 (2020).

    Article  ADS  Google Scholar 

  14. van Tilborg, J. et al. Active plasma lensing for relativistic laser-plasma-accelerated electron beams. Phys. Rev. Lett. 115, 184802 (2015).

    Article  ADS  Google Scholar 

  15. Lindstrøm, C. A. et al. Emittance preservation in an aberration-free active plasma lens. Phys. Rev. Lett. 121, 194801 (2018).

    Article  ADS  Google Scholar 

  16. Lehe, R., Thaury, C., Guillaume, E., Lifschitz, A. & Malka, V. Laser-plasma lens for laser-wakefield accelerators. Phys. Rev. ST Accel. Beams 17, 121301 (2014).

    Article  ADS  Google Scholar 

  17. Thaury, C. et al. Demonstration of relativistic electron beam focusing by a laser-plasma lens. Nat. Commun. 6, 6860 (2015).

    Article  ADS  Google Scholar 

  18. Doss, C. E. et al. Laser-ionized, beam-driven, underdense, passive thin plasma lens. Phys. Rev. Accel. Beams 22, 111001 (2019).

    Article  ADS  Google Scholar 

  19. Šmíd, M. et al. Highly efficient angularly resolving X-ray spectrometer optimized for absorption measurements with collimated sources. Rev. Sci. Instrum. 88, 063102 (2017).

    Article  ADS  Google Scholar 

  20. Rykovanov, S. G., Schroeder, C. B., Esarey, E., Geddes, C. G. R. & Leemans, W. P. Plasma undulator based on laser excitation of wakefields in a plasma channel. Phys. Rev. Lett. 114, 145003 (2015).

    Article  ADS  Google Scholar 

  21. Xiao, H. et al. Control of transverse motion and X-ray emission of electrons accelerated in laser-driven wakefields by tuning laser spatial chirp. Plasma Phys. Control. Fusion 62, 024002 (2019).

    Article  ADS  Google Scholar 

  22. Lehe, R., Thaury, C., Lifschitz, A., Rax, J.-M. & Malka, V. Transverse dynamics of an intense electron bunch traveling through a pre-ionized plasma. Phys. Plasmas 21, 043104 (2014).

    Article  ADS  Google Scholar 

  23. Ferri, J. et al. High-brilliance betatron γ-ray source powered by laser-accelerated electrons. Phys. Rev. Lett. 120, 254802 (2018).

    Article  ADS  Google Scholar 

  24. Mahieu, B. et al. Probing warm dense matter using femtosecond X-ray absorption spectroscopy with a laser-produced betatron source. Nat. Commun. 9, 3276 (2018).

    Article  ADS  Google Scholar 

  25. Thick mirror reflectivity tool (Center for X-ray Optics, LBNL); https://henke.lbl.gov/optical_constants/

  26. Wenz, J. et al. Dual-energy electron beams from a compact laser-driven accelerator. Nat. Photon. 13, 263–269 (2019).

    Article  ADS  Google Scholar 

  27. Thaury, C. et al. Shock assisted ionization injection in laser-plasma accelerators. Sci. Rep. 5, 16310 (2015).

    Article  ADS  Google Scholar 

  28. Schmid, K. et al. Density-transition based electron injector for laser driven wakefield accelerators. Phys. Rev. ST Accel. Beams 13, 091301 (2010).

    Article  ADS  Google Scholar 

  29. Buck, A. et al. Shock-front injector for high-quality laser-plasma acceleration. Phys. Rev. Lett. 110, 185006 (2013).

    Article  ADS  Google Scholar 

  30. McGuffey, C. et al. Ionization induced trapping in a laser wakefield accelerator. Phys. Rev. Lett. 104, 025004 (2010).

    Article  ADS  Google Scholar 

  31. Chou, S. et al. Collective deceleration of laser-driven electron bunches. Phys. Rev. Lett. 117, 144801 (2016).

    Article  ADS  Google Scholar 

  32. Shaw, J. L. et al. Role of direct laser acceleration of electrons in a laser wakefield accelerator with ionization injection. Phys. Rev. Lett. 118, 064801 (2017).

    Article  ADS  Google Scholar 

  33. GallardoGonzález, I. et al. Effects of the dopant concentration in laser wakefield and direct laser acceleration of electrons. New J. Phys. 20, 053011 (2018).

    Article  Google Scholar 

  34. Fourment, C. et al. Broadband, high dynamics and high resolution charge coupled device-based spectrometer in dynamic mode for multi-keV repetitive X-ray sources. Rev. Sci. Instrum. 80, 083505 (2009).

    Article  ADS  Google Scholar 

  35. Lifschitz, A. F. et al. Particle-in-cell modelling of laser-plasma interaction using Fourier decomposition. J. Comput. Phys. 228, 1803–1814 (2009).

    Article  ADS  MATH  Google Scholar 

  36. Lee, S. Y. Accelerator Physics 3rd edn (World Scientific, 2011).

  37. Svendsen, K. et al. Optimization of soft X-ray phase-contrast tomography using a laser wakefield accelerator. Opt. Express 26, 33930–33941 (2018).

    Article  ADS  Google Scholar 

  38. Gallardo Gonzalez, I. Development and Applications of a Laser-Wakefield X-ray Source. PhD thesis, Lund Univ. (2019).

  39. Albert, F. & Thomas, A. G. R. Applications of laser wakefield accelerator-based light sources. Plasma Phys. Control. Fusion 58, 103001 (2016).

    Article  ADS  Google Scholar 

  40. Couperus, J. P. et al. Demonstration of a beam loaded nanocoulomb-class laser wakefield accelerator. Nat. Commun. 8, 487 (2017).

    Article  ADS  Google Scholar 

  41. Gilljohann, M. F. et al. Direct observation of plasma waves and dynamics induced by laser-accelerated electron beams. Phys. Rev. X 9, 011046 (2019).

    Google Scholar 

  42. Götzfried, J. et al. Physics of high-charge electron beams in laser-plasma wakefields. Phys. Rev. X 10, 041015 (2020).

    Google Scholar 

  43. Zhu, X.-L. et al. Extremely brilliant GeV γ-rays from a two-stage laser-plasma accelerator. Sci. Adv. 6, eaaz7240 (2020).

    Article  ADS  Google Scholar 

  44. Wang, X. et al. Role of thermal equilibrium dynamics in atomic motion during nonthermal laser-induced melting. Phys. Rev. Lett. 124, 105701 (2020).

    Article  ADS  Google Scholar 

  45. Hidding, B. et al. Monoenergetic energy doubling in a hybrid laser-plasma wakefield accelerator. Phys. Rev. Lett. 104, 195002 (2010).

    Article  ADS  Google Scholar 

  46. Yakimenko, V. et al. FACET-II facility for advanced accelerator experimental tests. Phys. Rev. Accel. Beams 22, 101301 (2019).

    Article  ADS  Google Scholar 

  47. Gonsalves, A. J. et al. Petawatt laser guiding and electron beam acceleration to 8 GeV in a laser-heated capillary discharge waveguide. Phys. Rev. Lett. 122, 084801 (2019).

    Article  ADS  Google Scholar 

  48. Schmid, K. & Veisz, L. Supersonic gas jets for laser-plasma experiments. Rev. Sci. Instrum. 83, 053304 (2012).

    Article  ADS  Google Scholar 

  49. Kurz, T. et al. Calibration and cross-laboratory implementation of scintillating screens for electron bunch charge determination. Rev. Sci. Instrum. 89, 093303 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  50. Smith, S. W. The Scientist & Engineer’s Guide to Digital Signal Processing 1st edn (Elsevier, 2002).

  51. Esarey, E., Shadwick, B. A., Catravas, P. & Leemans, W. P. Synchrotron radiation from electron beams in plasma-focusing channels. Phys. Rev. E 65, 056505 (2002).

    Article  ADS  Google Scholar 

  52. Lehe, R., Lifschitz, A., Thaury, C., Malka, V. & Davoine, X. Numerical growth of emittance in simulations of laser-wakefield acceleration. Phys. Rev. ST Accel. Beams 16, 021301 (2013).

    Article  ADS  Google Scholar 

  53. Nuter, R. et al. Field ionization model implemented in particle in cell code and applied to laser-accelerated carbon ions. Phys. Plasmas 18, 033107 (2011).

    Article  ADS  Google Scholar 

  54. Jackson, J. D. Classical Electrodynamics 3rd edn (Wiley, 1999).

  55. Lu, W. et al. A nonlinear theory for multidimensional relativistic plasma wave wakefields. Phys. Plasmas 13, 056709 (2006).

    Article  ADS  Google Scholar 

  56. Rosenzweig, J. B., Barov, N., Thompson, M. C. & Yoder, R. Energy loss of a high charge bunched electron beam in plasma: nonlinear plasma response and linear scaling. AIP Conf. Proc. 647, 577–591 (2002).

    Article  ADS  Google Scholar 

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Acknowledgements

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

  1. Department of Physics, Lund University, Lund, Sweden

    Jonas Björklund Svensson, Diego Guénot, Henrik Ekerfelt, Isabel Gallardo González, Anders Persson, Kristoffer Svendsen & Olle Lundh

  2. Department of Physics, Chalmers University of Technology, Gothenburg, Sweden

    Julien Ferri

  3. Department of Physics, University of Gothenburg, Gothenburg, Sweden

    Julien Ferri

  4. SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Henrik Ekerfelt

  5. Department of Physics, Umeå University, Umeå, Sweden

    László Veisz

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Contributions

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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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

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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). https://doi.org/10.1038/s41567-020-01158-z

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