Electron acceleration in laboratory-produced turbulent collisionless shocks


Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the interstellar medium, supernova remnant shocks are observed to amplify magnetic fields1 and accelerate electrons and protons to highly relativistic speeds2,3,4. In the well-established model of diffusive shock acceleration5, relativistic particles are accelerated by repeated shock crossings. However, this requires a separate mechanism that pre-accelerates particles to enable shock crossing. This is known as the ‘injection problem’, which is particularly relevant for electrons, and remains one of the most important puzzles in shock acceleration6. In most astrophysical shocks, the details of the shock structure cannot be directly resolved, making it challenging to identify the injection mechanism. Here we report results from laser-driven plasma flow experiments, and related simulations, that probe the formation of turbulent collisionless shocks in conditions relevant to young supernova remnants. We show that electrons can be effectively accelerated in a first-order Fermi process by small-scale turbulence produced within the shock transition to relativistic non-thermal energies, helping overcome the injection problem. Our observations provide new insight into electron injection at shocks and open the way for controlled laboratory studies of the physics underlying cosmic accelerators.

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Fig. 1: Laser-driven collisionless shock experiments.
Fig. 2: Thomson scattering measurements indicating shock formation.
Fig. 3: Two-dimensional PIC simulation of the shock structure.
Fig. 4: Non-thermal electron acceleration.

Data availability

The data represented in Fig. 2, Fig. 3c,d and Fig. 4 are provided with the paper as source data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The PIC code OSIRIS36,37 used in this study can be obtained from the OSIRIS Consortium, consisting of UCLA and IST (Portugal).


  1. 1.

    Völk, H. J., Berezhko, E. G. & Ksenofontov, L. T. Magnetic field amplification in tycho and other shell-type supernova remnants. Astron. Astrophys. 433, 229–240 (2005).

    ADS  Article  Google Scholar 

  2. 2.

    Koyama, K. et al. Evidence for shock acceleration of high-energy electrons in the supernova remnant SN1006. Nature 378, 255–258 (1995).

    ADS  Article  Google Scholar 

  3. 3.

    Aharonian, F. A. et al. High-energy particle acceleration in the shell of a supernova remnant. Nature 432, 75–77 (2004).

    ADS  Article  Google Scholar 

  4. 4.

    Ackermann, M. et al. Detection of the characteristic pion-decay signature in supernova remnants. Science 339, 807–811 (2013).

    ADS  Article  Google Scholar 

  5. 5.

    Blandford, R. & Eichler, D. Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys. Rep. 154, 1–75 (1987).

    ADS  Article  Google Scholar 

  6. 6.

    Treumann, R. A. Fundamentals of collisionless shocks for astrophysical application, 1. non-relativistic shocks. Astron. Astrophys. Rev. 17, 409–535 (2009).

    ADS  Article  Google Scholar 

  7. 7.

    Sagdeev, R. Z. Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23–91 (1966).

    ADS  Google Scholar 

  8. 8.

    Oka, M. et al. Electron scattering by high-frequency whistler waves at Earth’s bow shock. Astrophys. J. 842, L11 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Hoshino, M. & Shimada, N. Nonthermal electrons at high mach number shocks: electron shock surfing acceleration. Astrophys. J. 572, 880–887 (2002).

    ADS  Article  Google Scholar 

  10. 10.

    Spitkovsky, A. Particle acceleration in relativistic collisionless shocks: Fermi process at last? Astrophys. J. 682, L5–L8 (2008).

    ADS  Article  Google Scholar 

  11. 11.

    Kato, T. N. & Takabe, H. Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas. Astrophys. J. 681, L93–L96 (2008).

    ADS  Article  Google Scholar 

  12. 12.

    Matsumoto, Y., Amano, T., Kato, T. N. & Hoshino, M. Stochastic electron acceleration during spontaneous turbulent reconnection in a strong shock wave. Science 347, 974–978 (2015).

    ADS  Article  Google Scholar 

  13. 13.

    Kugland, N. L. et al. Self-organized electromagnetic field structures in laser-produced counter-streaming plasmas. Nat. Phys. 8, 809–812 (2012).

    Article  Google Scholar 

  14. 14.

    Ross, J. S. et al. Characterizing counter-streaming interpenetrating plasmas relevant to astrophysical collisionless shocks. Phys. Plasmas 19, 056501 (2012).

    ADS  Article  Google Scholar 

  15. 15.

    Fox, W. et al. Filamentation instability of counterstreaming laser-driven plasmas. Phys. Rev. Lett. 111, 225002 (2013).

    ADS  Article  Google Scholar 

  16. 16.

    Huntington, C. M. et al. Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows. Nat. Phys. 11, 173–176 (2015).

    Article  Google Scholar 

  17. 17.

    Ross, J. S. et al. Transition from collisional to collisionless regimes in interpenetrating plasma flows on the national ignition facility. Phys. Rev. Lett. 118, 185003 (2017).

    ADS  Article  Google Scholar 

  18. 18.

    Schaeffer, D. B. et al. Generation and evolution of high-mach-number laser-driven magnetized collisionless shocks in the laboratory. Phys. Rev. Lett. 119, 025001 (2017).

    ADS  Article  Google Scholar 

  19. 19.

    Li, C. K. et al. Collisionless shocks driven by supersonic plasma flows with self-generated magnetic fields. Phys. Rev. Lett. 123, 055002 (2019).

    ADS  Article  Google Scholar 

  20. 20.

    Rigby, A. et al. Electron acceleration by wave turbulence in a magnetized plasma. Nat. Phys. 14, 1745–2481 (2018).

    Article  Google Scholar 

  21. 21.

    Ryutov, D. D. et al. Basic scalings for collisionless-shock experiments in a plasma without pre-imposed magnetic field. Plasma Phys. Control. Fusion 54, 105021 (2012).

    ADS  Article  Google Scholar 

  22. 22.

    Takabe, H. et al. High-mach number collisionless shock and photo-ionized non-LTE plasma for laboratory astrophysics with intense lasers. Plasma Phys. Control. Fusion 50, 124057 (2008).

    ADS  Article  Google Scholar 

  23. 23.

    Tidman, D. A. & Krall, N. A. Shock Waves in Collisionless Plasmas (Wiley-Interscience, 1971).

  24. 24.

    Gurevich, A. V. et al. Self-similar motion of rarefied plasma. Sov. Phys. J. Exp. Theor. Phys. 22, 449–454 (1966).

    ADS  Google Scholar 

  25. 25.

    Trubnikov, B. A. Particle interactions in a fully ionized plasma. Rev. Plasma Phys. 1, 105 (1965).

    ADS  Google Scholar 

  26. 26.

    Weibel, E. S. Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83–84 (1959).

    ADS  Article  Google Scholar 

  27. 27.

    Fried, B. D. Mechanism for instability of transverse plasma waves. Phys. Fluids 2, 337–337 (1959).

    ADS  Article  Google Scholar 

  28. 28.

    Medvedev, M. V., Fiore, M., Fonseca, R. A., Silva, L. O. & Mori, W. B. Long-time evolution of magnetic fields in relativistic gamma-ray burst shocks. Astrophys. J. 618, L75–L78 (2004).

    ADS  Article  Google Scholar 

  29. 29.

    Ruyer, C. & Fiuza, F. Disruption of current filaments and isotropization of the magnetic field in counterstreaming plasmas. Phys. Rev. Lett. 120, 245002 (2018).

    ADS  Article  Google Scholar 

  30. 30.

    Hillas, A. M. The origin of ultra-high-energy cosmic rays. Annu. Rev. Astron. Astrophys. 22, 425–444 (1984).

    ADS  Article  Google Scholar 

  31. 31.

    Froula, D. H., Glenzer, S. H., Luhmann, N. C. & Sheffield, J. (eds) Plasma Scattering of Electromagnetic Radiation 2nd edn (Academic Press, 2011).

  32. 32.

    Mariscal, D. et al. Calibration of proton dispersion for the NIF electron positron proton spectrometer (NEPPS) for short-pulse laser experiments on the NIF ARC. Rev. Sci. Instrum. 89, 10I145 (2018).

    Article  Google Scholar 

  33. 33.

    Bonnet, T. et al. Response functions of imaging plates to photons, electrons and 4He particles. Rev. Sci. Instrum. 84, 103510 (2013).

    ADS  Article  Google Scholar 

  34. 34.

    Halverson, W. Bremsstrahlung photon emission rate from Maxwellian plasmas. Plasma Phys. 14, 601–604 (1972).

    ADS  Article  Google Scholar 

  35. 35.

    Marinak, M. M. et al. Three-dimensional hydra simulations of National Ignition Facility targets. Phys. Plasmas 8, 2275–2280 (2001).

    ADS  Article  Google Scholar 

  36. 36.

    Fonseca, R. A et al. OSIRIS: A Three-Dimensional, Fully Relativistic Particle in Cell Code for Modeling Plasma Based Accelerators (Springer, 2002).

  37. 37.

    Fonseca, R. A. et al. One-to-one direct modeling of experiments and astrophysical scenarios: pushing the envelope on kinetic plasma simulations. Plasma Phys. Control. Fusion 50, 124034 (2008).

    ADS  Article  Google Scholar 

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We thank M. Hohenberger and G. Fiksel for their assistance in the analysis of FFLEX and NEPPS data, respectively. This work was supported by the US Department of Energy SLAC contract no. DE-AC02-76SF00515 and Lawrence Livermore National Laboratory contract no. DE-AC52-07NA27344, the US DOE Early Career Research Program under FWP 100331, the US DOE Office of Science, Fusion Energy Sciences under FWP 100182, the LLNL Laboratory Directed Research and Development Program grant 15-ERD-065, and the Engineering and Physical Sciences Research Council of the United Kingdom (grant nos. EP/M022331/1 and EP/N014472/1). We also acknowledge the OSIRIS Consortium, consisting of UCLA and IST (Portugal) for the use of the OSIRIS 4.0 framework and the visXD framework. Simulations were run on Mira and Theta (ALCF) through ALCC awards and on Vulcan and Quartz (LLNL) through grand challenge awards.

Author information




F.F. and H.-S.P. conceived and led this project. The experiments were designed and carried out by G.F.S., H.G.R., H.-S.P. and F.F. The data were analysed by G.F.S., H.G.R., C.B., B.B.P. and F.F. Numerical simulations were performed by A.G., F.F., D.P.H. and S.W. Additional theoretical support was provided by D.D.R., W.R., A.S. and G.G. The paper was written by F.F. with contributions from all the authors.

Corresponding author

Correspondence to F. Fiuza.

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Extended data

Extended Data Fig. 1 X-ray self emission from the plasma.

Lineouts of the X-ray signal along the mid-plane between the two targets for a) single flow and b) double flow experiments at 15 ns from the laser irradiation. The gated X-ray detector uses Vanadium (V, left) and Nickel (Ni, right) filters. The measured signal ratio between double flow and single flow experiments is ~100−200, consistent with predictions based on the plasma density and temperature from Thomson scattering measurements.

Supplementary information

Supplementary Information

Supplementary Figs. 1–4, discussion, and Tables 1 and 2.

Source data

Source Data Fig. 2

Numerical data used to generate the graphs in Fig. 2.

Source Data Fig. 3

Numerical data used to generate the graphs in Fig. 3c,d.

Source Data Fig. 4

Numerical data used to generate the graphs in the Fig. 4a,b,c(inset),4d.

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Fiuza, F., Swadling, G.F., Grassi, A. et al. Electron acceleration in laboratory-produced turbulent collisionless shocks. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-0919-4

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