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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).


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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.

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Authors and Affiliations



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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The authors declare no competing interests.

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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. 16, 916–920 (2020).

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