Letter | Published:

Electron acceleration from contracting magnetic islands during reconnection

Nature volume 443, pages 553556 (05 October 2006) | Download Citation



A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields ‘reconnect’ and release energy. In the Earth's magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1–3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects4. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons5,6. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting ‘magnetic islands’ that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls—the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    & Simultaneous observations of relativistic electron bursts and neutral-line signatures in the magnetotail. Planet. Space Sci. 24, 855–856 (1976)

  2. 2.

    & Energetic electron anisotropies in the magnetotail: identification of open and closed field lines. Geophys. Res. Lett. 3, 557–560 (1976)

  3. 3.

    , , & Spatial distribution of energetic particles in the distant magnetotail. J. Geophys. Res. 86, 5682–5700 (1981)

  4. 4.

    , , , & Evidence for electron acceleration up to 300 keV in the magnetic reconnection diffusion region in the earth's magnetotail. Phys. Rev. Lett. 89, 195001 (2002)

  5. 5.

    & 10–100 keV electron acceleration and emission from solar flares. Sol. Phys. 17, 412–435 (1971)

  6. 6.

    et al. RHESSI observations of particle acceleration and energy release in an intense solar gamma-ray line flare. Astrophys. J. 595, L69–L76 (2003)

  7. 7.

    , , , & Formation of secondary islands during magnetic reconnection. Geophys. Res. Lett. 33, L13105, doi:10.1029/2006GL025957 (2006)

  8. 8.

    & Three-dimensional collisionless magnetic reconnection in the presence of a guide field. J. Geophys. Res. 109, A01220, doi:10.1029/2003JA009999 (2004)

  9. 9.

    , , & Production of energetic electrons during magnetic reconnection. Phys. Rev. Lett. 94, 095001 (2005)

  10. 10.

    & Regular and chaotic particle motion in sheared magnetic field reversals. Adv. Space Res. 11, 177–182 (1991)

  11. 11.

    , & Electron acceleration in the dynamic magnetotail: Test particle orbits in three-dimensional magnetohydrodynamic simulation fields. Phys. Plasmas 11, 1825–1833 (2004)

  12. 12.

    , & Particle acceleration by turbulent magnetohydrodynamic reconnection. Phys. Rev. Lett. 53, 1449–1452 (1984)

  13. 13.

    Particle orbits, trapping and acceleration in a filamentary current sheet model. Astrophys. J. 90, 719–727 (1994)

  14. 14.

    , & Magnetopause stability threshold for patchy reconnection. Space Sci. Rev. 44, 1–41 (1986)

  15. 15.

    & Plasmoid-induced-reconnection and fractal reconnection. Earth Planets Space 53, 473–482 (2001)

  16. 16.

    & Stochastic aspects of magnetic field lines of force with application to cosmic-ray propagation. Astrophys. J. 155, 777–798 (1969)

  17. 17.

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

  18. 18.

    , & in Frontiers in Magnetospheric Plasma Physics: Celebrating 10 Years of Geotail Operation (eds Hoshino, M., Omura, Y. & Lanzerotti, L. J.) 34–39 (Cospar Colloquia Series Vol.16, Elsevier, Oxford, 2005)

  19. 19.

    Energetic electrons in solar flares as viewed in x-rays. Adv. Space Res. 35, 1669–1674 (2005)

  20. 20.

    et al. Critical issues for understanding particle acceleration in impulsive solar flares. J. Geophys. Res. 102, 14631–14659 (1997)

  21. 21.

    et al. Direct observations of the magnetic reconnection site of an eruption on 2003 November 18. Astrophys. J 622, 1251–1264 (2005)

  22. 22.

    et al. Three-dimensional particle simulations of collisionless magnetic reconnection. J. Geophys. Res. 107, 1230, doi:10.1029/2001JA000287 (2002)

Download references


This work was supported by the NSF/DOE programme in plasma science, by NASA through the Supporting Research and Technology and the Sun-Earth Connections Theory programmes, through CMPD, a DOE FSC, and through CISM, an NSF STC. Computations were carried out in part at the National Energy Research Scientific Computing Center. Author Contributions J.F.D., M.S. and M.A.S. identified the Fermi mechanism; J.F.D. carried out the particle simulations of reconnection, obtained the solutions of the transport equation and wrote the paper; and M.S. and H.C. carried out the bubble and test particle simulations, respectively. All of the authors discussed the results and commented on the paper.

Author information


  1. University of Maryland, College Park, Maryland 20742, USA

    • J. F. Drake
    •  & H. Che
  2. Plasma Physics Division, Naval Research Laboratory, Washington DC 20375, USA

    • M. Swisdak
  3. University of Delaware, Newark, Delaware 19716, USA

    • M. A. Shay


  1. Search for J. F. Drake in:

  2. Search for M. Swisdak in:

  3. Search for H. Che in:

  4. Search for M. A. Shay in:

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Corresponding author

Correspondence to J. F. Drake.

Supplementary information

PDF files

  1. 1.

    Supplementary Notes

    Derivation of the powerlaw spectrum. The notes outline the derivation the solution of the particle transport equation in the limit in which the back-pressure from energetic particles can be neglected. The resulting solution in Eq. (4) of the paper takes the form of a power-law at high energy.

About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.