Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Electron acceleration by wave turbulence in a magnetized plasma


Astrophysical shocks are commonly revealed by the non-thermal emission of energetic electrons accelerated in situ1,2,3. Strong shocks are expected to accelerate particles to very high energies4,5,6; however, they require a source of particles with velocities fast enough to permit multiple shock crossings. While the resulting diffusive shock acceleration4 process can account for observations, the kinetic physics regulating the continuous injection of non-thermal particles is not well understood. Indeed, this injection problem is particularly acute for electrons, which rely on high-frequency plasma fluctuations to raise them above the thermal pool7,8. Here we show, using laboratory laser-produced shock experiments, that, in the presence of a strong magnetic field, significant electron pre-heating is achieved. We demonstrate that the key mechanism in producing these energetic electrons is through the generation of lower-hybrid turbulence via shock-reflected ions. Our experimental results are analogous to many astrophysical systems, including the interaction of a comet with the solar wind9, a setting where electron acceleration via lower-hybrid waves is possible.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Illustration of a magnetized plasma–sphere interaction.
Fig. 2: Optical data and radiation-hydrodynamic simulations.
Fig. 3: X-ray data.
Fig. 4: OSIRIS PIC simulations.
Fig. 5: Atomic transition simulations.


  1. 1.

    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 

  2. 2.

    Masters, A. et al. Electron acceleration to relativistic energies at a strong quasi-parallel shock wave. Nat. Phys. 9, 164–167 (2013).

    Article  Google Scholar 

  3. 3.

    Helder, E. A. et al. Observational signatures of particle acceleration in supernova remnants. Space Sci. Rev. 173, 369–431 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    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 

  5. 5.

    Van Weeren, R. et al. Particle acceleration on megaparsec scales in a merging galaxy cluster. Science 330, 347–349 (2010).

    ADS  Article  Google Scholar 

  6. 6.

    Marcowith, A. et al. The microphysics of collisionless shock waves. Rep. Progress. Phys. 79, 046901 (2016).

    ADS  Article  Google Scholar 

  7. 7.

    Amano, T. & Hoshino, M. Electron injection at high Mach number quasi–perpendicular shocks: Surfing and drift acceleration. Astrophys. J. 661, 190–202 (2007).

    ADS  Article  Google Scholar 

  8. 8.

    Riquelme, M. & Spitkovsky, A. Electron injection by Whistler waves in non-relativistic shocks. Astrophys. J. 733, 63 (2011).

  9. 9.

    Bingham, R. et al. Generation of X-rays from Comet C/Hyakutake 1996 B2. Science 275, 49–51 (1997).

    ADS  Article  Google Scholar 

  10. 10.

    McClements, K. G. et al. Acceleration of cosmic ray electrons by ion-excited waves at quasiperpendicular shocks. Mon. Not. R. Astron. Soc. 291, 241–249 (1997).

    ADS  Article  Google Scholar 

  11. 11.

    Bingham, R. et al. X-ray emission from comets, cometary knots and supernova remnants. Astrophys. J. 127, 233–237 (2000).

    Article  Google Scholar 

  12. 12.

    Vink, J. & Laming, M. J. On the magnetic fields and particle acceleration in Cassiopeia A. Astrophys. J. 584, 758–769 (2003).

    ADS  Article  Google Scholar 

  13. 13.

    McBride, J. B. et al. Theory and simulation of turbulent heating by the modified two-stream instability. Phys. Fluids 15, 2367–2382 (1972).

    ADS  Article  Google Scholar 

  14. 14.

    Fisch, N. J. Theory of current drive in plasmas. Rev. Mod. Phys. 59, 175–234 (1987).

    ADS  Article  Google Scholar 

  15. 15.

    Porkolab, M. et al. High-power electron Landau-heating experiments in the lower hybrid frequency range in a tokamak plasma. Phys. Rev. Lett. 53, 1229–1232 (1984).

    ADS  Article  Google Scholar 

  16. 16.

    Cesario, R. et al. Current drive at plasma densities required for thermonuclear reactors. Nat. Commun. 1, 55 (2010).

    Article  Google Scholar 

  17. 17.

    Eilek, J. A. & Weatherall, J. C. in Diffuse Thermal and Relativistic Plasma in Galaxy Clusters (eds Böhringer, H., Feretti, L. & Schuecker, P.) 71–76 (Max-Planck-Institut fur Extraterrestrische Physik, Garching, 1999).

  18. 18.

    Cairns, I. H. & Zank, G. P. Turn-on of 2-3 kHz radiation beyond the heliopause. Geophys. Res. Lett. 29, 47-1–47-2 (2002).

    Article  Google Scholar 

  19. 19.

    Zakharov, Y. P. et al. Simulation of astrophysical plasma dynamics in the laser experiments. AIP Conf. Proc. 369, 357–362 (2008).

    ADS  Article  Google Scholar 

  20. 20.

    Beiersdorfer, P. et al. Laboratory simulation of charge exchange-produced X-ray emission from comets. Science 300, 1558–1559 (2003).

    ADS  Article  Google Scholar 

  21. 21.

    Bell, A. R. et al. Collisionless shock in a laser-produced ablating plasma. Phys. Rev. A. 38, 1363–1369 (1988).

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  Google Scholar 

  23. 23.

    Cruz, F. et al. Formation of collisionless shocks in magnetized plasma interaction with kinetic-scale obstacles. Phys. Plasmas 24, 022901 (2017).

    ADS  Article  Google Scholar 

  24. 24.

    Omelchenko, Y. et al. Numerical simulation of quasilinear relaxation of an ion ring and production of superthermal electrons. Sov. J. Plasma Phys 15, 427–431 (1989).

    Google Scholar 

  25. 25.

    Laming, M. J. Accelerated electrons in Cassiopeia A: thermal and electromagnetic effects. Astrophys. J. 563, 828–841 (2001).

    ADS  Article  Google Scholar 

  26. 26.

    Yamamoto, T. et al. Experimental observation of the rf-driven current by the lower-hybrid wave in a tokamak. Phys. Rev. Lett. 45, 716–719 (1980).

    ADS  Article  Google Scholar 

  27. 27.

    Stenzel, R. L. et al. Electrostatic waves near the lower hybrid frequency. Phys. Rev. A. 11, 2057–2060 (1975).

    ADS  Article  Google Scholar 

  28. 28.

    Boswell, R. W. et al. Very efficient plasma generation by whistler waves near the lower hybrid frequency. Plasma Phys. Control. Fusion 26, 1147 (1984).

    ADS  Article  Google Scholar 

  29. 29.

    Torney, al. Modelling X-ray line and continuum emission from comets. Physica Scr. 2002, T98 (2002)..

  30. 30.

    Cravens, T. E. et al. Comet Hyakutake X-ray source: Charge transfer of solar wind heavy ions. Geophys. Res. Lett. 24, 105–108 (1997).

    ADS  Article  Google Scholar 

Download references


We thank all the LULI technical staff at École Polytechnique for their support during the experiment. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreements no. 256973 and 247039, AWE plc, the Engineering and Physical Sciences Research Council (grant numbers EP/M022331/1, EP/N014472/1, EP/N013379/1 and EP/N002644/1) and the Science and Technology Facilities Council of the United Kingdom. F.C. and L.O.S. acknowledge support from the European Research Council (InPairs ERC-2015-AdG 695088), FCT Portugal (grant no. PD/BD/114307/2016) the Calouste Gulbenkian Foundation and PRACE for awarding access to resource MareNostrum, based in Spain at the Barcelona Supercomputing Center. The PIC simulations were performed at the IST cluster (Lisbon, Portugal), and MareNostrum (Spain). This work was supported in part at the University of Chicago by the US DOE NNSA ASC through the Argonne Institute for Computing in Science under FWP 57789 and the US DOE Office of Science through grant no. DE- SC0016566. The software used in this work was developed in part by the DOE NNSA ASC- and DOE Office of Science ASCR-supported Flash Center for Computational Science at the University of Chicago.

Author information




G.G., B.R. A.R.B., F.F., S.L., F.M., S.S. and R.Bi. conceived this project, which was designed by G.G., S.L. and M.K. The LULI experiment was carried out by A.R., B.A., J.E.C., Y.H., P.M.K., Y.K., J.R.M., T.M., M.O., Y.S. and M.K. The paper was written by A.R., F.C., B.R. and G.G. The data were analysed by A.R. Numerical simulations were performed by F.C. and P.T. Further experimental and theoretical support was provided by R.Ba., P.G., D.Q.L., C.S., R.T. and L.O.S.

Corresponding author

Correspondence to A. Rigby.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary figures 1,2, Supplementary Table 1, Supplementary notes and supplementary references

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rigby, A., Cruz, F., Albertazzi, B. et al. Electron acceleration by wave turbulence in a magnetized plasma. Nature Phys 14, 475–479 (2018).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing