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Plasmaspheric hiss waves generate a reversed energy spectrum of radiation belt electrons


Highly energetic electrons are trapped in the magnetic field of Earth’s radiation belts. The physical mechanisms driving the dynamics of the Van Allen belts can be understood from the electron’s energy spectrum, which is believed to be steeply falling with increasing energy. This view has been prevalent for the past 60 years since the energy spectra were first measured. Here, we report the observation of a reversed energy spectrum with abundant high-energy and fewer low-energy electrons spanning from hundreds of keV to around two MeV in electron energy in data collected with NASA’s Van Allen Probes. We find that this spectrum dominates inside the plasmasphere—a dense cold plasma region co-rotating with the Earth. Using two-dimensional Fokker–Planck diffusion simulations with a time-dependent, data-driven model of hiss waves in the plasmasphere, we demonstrate that the formation of the reversed spectrum is explained by the scattering of hiss waves. The results have important implications for understanding the distributions of charged particles and wave–particle interactions in magnetized plasmas throughout the solar system and beyond.

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Fig. 1: Radiation belt electron fluxes and energy spectra during the 17 March 2015 storm.
Fig. 2: Statistics of bump-on-tail (BOT) electron energy spectrum during 2015.
Fig. 3: Properties of plasmaspheric hiss waves during the 17 March 2015 storm.
Fig. 4: Comparison of Fokker–Planck simulation results with observations.

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Data availability

The particle data analysed during the current study are available from the ECT Science Operations and Data Center ( The field data are available from the EMFISIS Data Center ( Solar wind data and geomagnetic indices are available from OMNIWeb (


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This work was supported by RBSP-ECT funding through JHU/APL contract 967399 (under prime NASA contract NAS5-01072), by the NSFC grants 41674163, 41474141, 41574160 and 41204120, by the Chinese Thousand Youth Talents Program, and by the Hubei Province Natural Science Excellent Youth Foundation (2016CFA044). We thank the Van Allen Probes REPT, MagEIS, HOPE and EMFISIS Science Teams for providing the particle and wave data. We also thank the NSSDC OMNIWeb for the use of solar wind and geomagnetic index data.

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Authors and Affiliations



H.Z. led the study, performed the data analysis of the bump-on-tail energy spectrum and wrote the manuscript. B.N. initialized the concept of hiss wave scattering, led the simulations and their quantitative comparisons with observations, and contributed to writing of the manuscript through reviews and edits. X.L. and D.N.B. supervised the study and contributed to writing of the manuscript through reviews and edits. W.R.J. initialized the concept of bump-on-tail energy spectrum, helped with data analysis, and contributed to writing of the manuscript through reviews and edits. W.Z. conducted the Fokker–Planck simulation runs to investigate the hiss-induced electron dynamics and produced the majority of Figs. 3 and 4. Z.X. provided the wave information to establish the data-driven, time-dependent hiss wave model and helped produce Fig. 3. X.G. helped analyse the simulation results and compare them with observations. A.N.J., S.G.K., J.B.B., S.G.C., M.A.T., H.O.F., G.D.R. and A.J.B. contributed to writing of the manuscript through reviews and edits.

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Correspondence to H. Zhao or B. Ni.

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Zhao, H., Ni, B., Li, X. et al. Plasmaspheric hiss waves generate a reversed energy spectrum of radiation belt electrons. Nat. Phys. 15, 367–372 (2019).

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