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Autogenous and efficient acceleration of energetic ions upstream of Earth’s bow shock


Earth and its magnetosphere are immersed in the supersonic flow of the solar-wind plasma that fills interplanetary space. As the solar wind slows and deflects to flow around Earth, or any other obstacle, a ‘bow shock’ forms within the flow. Under almost all solar-wind conditions, planetary bow shocks such as Earth’s are collisionless, supercritical shocks, meaning that they reflect and accelerate a fraction of the incident solar-wind ions as an energy dissipation mechanism1,2, which results in the formation of a region called the ion foreshock3. In the foreshock, large-scale, transient phenomena can develop, such as ‘hot flow anomalies’4,5,6,7,8,9, which are concentrations of shock-reflected, suprathermal ions that are channelled and accumulated along certain structures in the upstream magnetic field. Hot flow anomalies evolve explosively, often resulting in the formation of new shocks along their upstream edges5,10, and potentially contribute to particle acceleration11,12,13, but there have hitherto been no observations to constrain this acceleration or to confirm the underlying mechanism. Here we report observations of a hot flow anomaly accelerating solar-wind ions from roughly 1–10 kiloelectronvolts up to almost 1,000 kiloelectronvolts. The acceleration mechanism depends on the mass and charge state of the ions and is consistent with first-order Fermi acceleration14,15. The acceleration that we observe results from only the interaction of Earth’s bow shock with the solar wind, but produces a much, much larger number of energetic particles compared to what would typically be produced in the foreshock from acceleration at the bow shock. Such autogenous and efficient acceleration at quasi-parallel bow shocks (the normal direction of which are within about 45 degrees of the interplanetary magnetic field direction) provides a potential solution to Fermi’s ‘injection problem’, which requires an as-yet-unexplained seed population of energetic particles, and implies that foreshock transients may be important in the generation of cosmic rays at astrophysical shocks throughout the cosmos.

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Fig. 1: Overview of the MMS burst data during the HFA.
Fig. 2: MMS observations of energetic ions and context data during and after the encounter with the HFA.
Fig. 3: Conceptual scenario for the HFA observed by MMS on 28 December 2015.
Fig. 4: Comparing observations and theory.

Data availability

All MMS data used for this study are publicly available via the MMS Science Data Center at


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This work was supported by NASA contract NNG04EB99C at Southwest Research Institute, a NASA grant (NNX16AQ50G) and research supported by the International Space Science Institute’s (ISSI) International Teams programme. We thank all of the MMS team and the SPEDAS software developers for their publicly available data and software products. D.L.T. thanks T. Phan, S.-H. Lee and D. G. Sibeck for discussions and NASA’s From Earth to the Solar System collection.

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Nature thanks H. Zhang and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations



D.L.T. performed the data analysis, interpretation and manuscript preparation. L.B.W., T.Z.L., S.J.S. and A.O. contributed to data interpretation, multipoint analysis and development of the theory for comparison to the observations. J.F.F., J.H.C., J.B.B., A.N.J., T.L. and D.N.B. contributed to the development, operation and data processing of the FEEPS energetic particle telescopes, data quality assurance and interpretation of those data. I.J.C., J.W. and B.H.M. contributed to the development, operation and data processing of the EIS instruments, data quality assurance and interpretation of those data. R.J.S. and C.T.R. contributed to the development, operation and data processing of the fluxgate magnetometers and related data quality assurance. D.J.G., L.A. and B.L.G. contributed to the development, operation and data processing of the fast plasma instruments and related data quality assurance. R.B.T. contributed to the development, operation and data processing of the FIELDS instrument suite and related data quality assurance. J.B., R.G.G. and S.A.F. contributed to the development operation and data processing of the HPCA instruments, data quality assurance and interpretation of those data. J.L.B. is the PI of MMS science and contributed with quality assurance and interpretation of the data.

Corresponding author

Correspondence to D. L. Turner.

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Extended data figures and tables

Extended Data Fig. 1 Solar-wind ion species observed by MMS HPCA.

a, Magnetic-field vector and strength from MMS-2. bf, FEEPS total energetic ion (b) and HPCA ion (cf) composition flux energy spectra (omni-directional) combined from all four spacecraft (MMS-X). HPCA observed many fewer He+ ion than He2+ ions (α particles) and no O+ ions (all zero counts despite energy channels up to about 38 keV) at E > 10 keV during the observation of the energetic ions between the HFA and the magnetosheath. The absence of low-charge-state oxygen in HPCA data (O+, O2+) indicates that the energetic CNO ions observed by EIS were at a high charge state. This confirms that the accelerated ions were high-charge-state ions (q/m ≥ 2) and thus of solar-wind origin. Like FEEPS, HPCA also shows that the most energetic beam of α particles and protons is streaming away from the HFA.

Extended Data Fig. 2 Conceptual model of the Fermi acceleration trap created by an HFA evolving along Earth’s bow shock.

At the top of this schematic is the solar wind, which is the ‘upstream’ direction to which some ions within the trap might escape. The region at the bottom of the schematic is the magnetosheath plasma, which is the ‘downstream’ direction to which some ions might also escape. The HFA sheath and shock region, with some finite thickness d, lies between the two horizontal black lines. The HFA core region lies between the HFA sheath/shock and magnetosheath regions. The HFA core has a characteristic length scale L and is perpetually converging on the magnetosheath such that dL/dt < 0 at any point along the core. Critical to the model (and as observed and simulated in HFAs), the magnetic-field strength within the HFA core (less than 1 nT) is much, much weaker than that in the HFA sheath or shock and in Earth’s bow shock or magnetosheath (more than 10 nT); this geometry ensures that some subset of ions within the HFA core can remain trapped between the two regions of higher field strength, owing to differences in the ion gyroradii (rc) in the different regions. We note that the orientations of the magnetic fields are sketched arbitrarily here. Three example ion trajectories are sketched: (i) escaping to the solar wind; (ii) escaping to the magnetosheath; and (iii) remaining trapped within the HFA core.

Extended Data Fig. 3 Simplified model of the HFA.

This model includes a finite thickness of the HFA sheath (that is, shocked plasma) and shock d, which is used to determine the energy spectra of ions accelerated within the trap considering losses through the boundary. In this picture, the HFA sheath and shock fall between the two horizontal black lines, with the HFA core being a larger region below this and the solar wind being the region above this. Only ions at particular energies, pitch angles and gyrophase can remain trapped in the Fermi acceleration trap between Earth’s bow shock or magnetosheath and the HFA shock. For example, the two ion trajectories shown are at the same energy but different gyrophase when they enter the HFA sheath with enhanced magnetic field strength: the rightmost ion is reflected and can continue to be accelerated, whereas the leftmost ion escapes the trap and is lost to the solar wind.

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Turner, D.L., Wilson, L.B., Liu, T.Z. et al. Autogenous and efficient acceleration of energetic ions upstream of Earth’s bow shock. Nature 561, 206–210 (2018).

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  • Energetic Ions
  • Hot Flow Anomalies (HFA)
  • Foreshock
  • Injection Problem
  • Solar Wind

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