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Trapped radiation belt electrons undergo three characteristic types of motion: gyro-motion around magnetic field lines due to any velocity component perpendicular to the field, bounce-motion along field lines between magnetic mirror points due to any velocity component parallel to the field, and drift-motion around the Earth resulting from magnetic gradient and curvature drifts. Associated with each of these oscillatory motions are adiabatic invariants, which are conserved so long as electric and/or magnetic fields do not change on scales similar to those of the associated motions. The first invariant conserves the magnetic moment of the particle and is proportional to the perpendicular momentum squared divided by the local magnetic field strength; the second and third invariants conserve the integral of parallel momentum over one full bounce period and the magnetic flux through a particle’s drift orbit, respectively. Magnetospheric changes on timescales much longer than electron drift periods are considered fully adiabatic, that is, they are fully reversible. Initially, it was thought that the observed flux dropouts were fully adiabatic changes in the system. Essentially, electrons moved radially outward (inward) during a storm’s main (recovery) phase to conserve their third invariant as Earth’s magnetic field was altered by the field produced by an enhanced (weakening) ring current7,8, which is a magnetospheric current system resulting from charge-dependent particle drift. As electrons moved radially outward (inward) in the field, their fluxes decreased (increased) for fixed energy as the first adiabatic invariant was also conserved. It was later shown that although this ‘Dst effect’ (after the disturbance storm time (Dst) geomagnetic index (Kp) used to indicate storm activity) does play a role in the flux dynamics, many flux dropouts do not return to the pre-storm flux level on field recovery. These dropouts therefore result in true particle loss due to irreversible (non-adiabatic) processes9,10,11. Such losses ultimately occur to either the atmosphere or the magnetosphere’s outer boundary, the magnetopause12. Mechanisms resulting in atmospheric loss include pitch-angle scattering through wave particle interactions with magnetospheric plasma waves13 and violation of the first adiabatic invariant due to highly stretched magnetotail fields (that is, those in which the field line curvature becomes comparable to the particle’s gyro-radius14). Several recent statistical studies have concluded that losses to the atmosphere are probably responsible for main phase5,11 and recovery phase15,16 electron loss during certain types of geomagnetic storms. However, the main-phase dropout results were inferred in those studies, with no clear observations showing that the primary loss was to the atmosphere.

Losses to the magnetopause can occur through magnetopause ‘shadowing’17 and outward radial transport17,18,19. Magnetopause shadowing describes the scenario in which the magnetopause moves inward in response to increased solar wind dynamic pressure and results in the loss of electrons on open drift paths that were closed before the boundary motion. Test-particle simulations have revealed that both enhanced dawn–dusk electric fields19 and diamagnetic effects from a partial ring current17 during the storm’s main phase can result in violation of the third invariant and rapid outward radial transport, resulting in losses to the magnetopause in only a few hours. Radial diffusion can also result in outward transport if the third adiabatic invariant is not conserved and the radial gradient of the electron phase space density (PSD) is negative with respect to increasing radial distance (diffusion always acts to transport particles in the opposite direction to the PSD gradient). Recent studies of PSD radial gradients in the outer belt have shown that most often the gradient is negative for relativistic electrons beyond geosynchronous orbit20,21. Also, ultralow-frequency (ULF) waves, a regularly occurring phenomenon, can violate the third invariant condition and allow for electron radial diffusion22. Modelling efforts have revealed a scenario combining magnetopause shadowing and outward diffusion as a possible explanation for storm-time outer belt flux dropouts18. Most recently, this loss scenario was also proposed to explain observations of an electron dropout event23; no evidence discounting loss to the atmosphere was provided, however. Other studies24,25 argued that losses could be explained by a combination of magnetopause shadowing and subsequent outward transport at high L-shells (L>5–6, with L being the radial distance in RE (Earth radii) of electron drift orbits in the magnetic equatorial plane) and loss to the atmosphere by interactions with various plasma waves at lower L-shells. Ultimately, the long-standing, fundamental question as to what mechanism is primarily responsible for non-adiabatic electron losses during dropout events is still debated.

On 06 January 2011, a co-rotating interaction region (CIR) impacted Earth’s magnetosphere, resulting in a small geomagnetic storm, as indicated by the Dst index (minimum>−50 nT; Fig. 1). Associated with the main phase of this storm, several spacecraft from vantage points throughout the outer radiation belt observed a dropout of relativistic electrons (Figs 1d and 2e,g). The dropout of radiation belt fluxes occurred over a broad range of energies (>300 keV from the National Oceanic and Atmospheric Administration Polar Orbiting Environmental Satellites (NOAA–POES) to >800 keV from Geostationary Operational Environmental Satellite (GOES)), and fluxes decreased over a range of L-shells encompassing almost the entirety of the outer belt. The dropout was clearly non-adiabatic and propagated generally from higher to lower L-shells based on the GOES observations (Supplementary Figs S1, S15–S17). Furthermore, the dropout did not result from a change in pitch-angle distribution because it was observed over the same range in L by the NOAA–POES spacecraft in Sun-synchronous, low-Earth orbits (measuring low equatorial pitch angles over the full range of the outer belt) and the three THEMIS spacecraft (TH-A, TH-D, and TH-E) in the noon local time sector near the equatorial plane (measuring high equatorial pitch angles throughout the outer belt), as seen in the red lines of Fig. 2b and in Supplementary Fig. S2. Interestingly, based on the NOAA–POES data, the fluxes of >30 keV and >100 keV electrons (Fig. 2) did not experience the same dropout. We infer that at those energies the electron losses due to the inward magnetopause motion were more than balanced by substorm injections and enhanced convection from a source in the plasma sheet; this occurred nearly instantaneously for the >30 keV electrons and within half a day for the >100 keV electrons. These injections resulted in an overall enhancement of electrons with these energies throughout the outer belt and increased precipitation of these electrons to the atmosphere. However, the radiation belt electrons with energy >300 keV exhibited a markedly different behaviour (Fig. 2); their dropout persisted for over 6 h at L∼5 and even longer at higher L-shells. At the time of the dropout, the >300 keV-precipitating electron fluxes were not enhanced. Such precipitation took place only about a day later, well after the main-phase dropout, when the >300 keV-trapped fluxes increased to levels much higher than before the storm. This is clear evidence that most of the true losses from the system during the main-phase dropout were to the magnetopause. For this to have been the case, outward radial transport must have played a role, as the magnetopause only moved in to ∼7RE during the pressure enhancement associated with the CIR.

Figure 1: Overview of solar wind, geomagnetic indices, electron flux and ULF wave activity during the 06 January 2011 storm and dropout event.
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a, Solar wind dynamic pressure PDyn and speed from the OMNI dataset. b, Interplanetary magnetic field (IMF) total field strength BTot and Z-component in Geocentric Solar Magnetospheric coordinates BZ. These exhibit the clear features of the CIR, with the initial compressed slow solar wind, the compressed fast wind segment associated with a strong southward IMF component, and the fast solar wind stream following behind them. The period of negative BZ results in enhanced substorm activity. c, The Dst and Kp indices, both calculated using arrays of ground magnetometers. Dst shows a small storm, which is typical for CIRs, with a minimum value of greater than −50 nT, while Kp of 5.7 during the storm’s main phase implies very active geomagnetic conditions. d, GOES-13>800 keV electron fluxes (#cm−2s−1sr−1) measured from geosynchronous orbit showing the main phase flux dropout and subsequent recovery phase enhancement. e, McGrath ground station (MCGR) magnetometer data, D-component (∼east), with the d.c. field removed (No-d.c.). Enhanced ULF wave activity is evident during the entirety of the storm. The blue shaded periods marked by dashed lines indicate the overlap with the periods shown in f and g. f,g, The TH-A power spectral densities for the magnetic field magnitude (d.c. field removed) exhibiting ULF waves at frequencies comparable to outer belt electron drift frequencies. f, The TH-A inbound pass on 05–06 January during the quiet time before the storm. g, The following inbound pass during the main phase and flux dropout.

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Figure 2: Electron flux observations from low-Earth orbit and near the magnetic equator during the event.
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a–f, NOAA–POES Medium Energy Proton/Electron Detector (MEPED) fluxes (#cm−2s−1sr−1) corrected for proton contamination30 and binned by L-shell (0.1 RE resolution) and time (30-min resolution). a, c and e show the trapped population, while b, d and f show precipitating electrons. The rows show the different electron energy channels as labelled and data gaps are indicated in black. The green line is the plasmapause location31, and the grey line is the magnetopause location32. White traces show the TH-A orbit tracks, which are very similar to TH-D and TH-E during this period. The dropout at >300 keV is clearly evident and extends to L∼5, which is significantly lower than the minimum magnetopause distance of 7 RE. Also, the fluxes around L∼4 are enhanced during the dropout in both the trapped and precipitating populations. This precipitation is observed in the dusk sector in both the Northern and Southern hemispheres. g, TH-A energy fluxes (eV cm−2s−1sr−1eV−1) from the first Solid State Telescope (SST) coincidence channel, representing electrons with an equivalent energy of ∼400 keV. This channel is relatively unaffected by proton contamination. The passes shown here correspond to the first six inbound and outbound shown in a-f, and they are colour-coded as indicated in the legend. Note that there is generally good agreement between THEMIS and NOAA observations before, during, and after the dropout.

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Enhanced ULF wave activity, observed both on the ground and in space, occurred during the main phase of the storm, as seen in Fig. 1e–g. These ULF waves exhibited globally intensified power (Supplementary Figs S18 and S19), when compared with the quiet time before the storm, over a broad band of frequencies comparable to drift rates of >300 keV electrons and at L-shells exhibiting the flux dropout (L>4). ULF waves at these frequencies violated the third adiabatic invariants of the energetic electrons and allowed radial diffusion. The rate of diffusion: (1) increases with ULF wave power26, (2) increases with increasing L, and (3) is dependent on the PSD gradient. Thus, losses due to magnetopause shadowing are compounded by further loss to the outer boundary through rapid outward radial diffusion, which is driven by the sharp negative gradients in PSD from the initial loss and enhanced ULF wave activity, as explained in Fig. 3. Further rapid outward radial transport may also occur during the storm’s main phase owing to enhanced electric fields and/or a partial ring current. Furthermore, any outward radial transport results in a flux decrease at lower L-shells throughout the belt because electrons are simultaneously decelerated owing to decreased magnetic field strengths and diverging mirror points as they move outward while conserving their first and second adiabatic invariants. Simulations of these scenarios using test-particles in realistic fields17,19 or one-dimensional radial diffusion models (ref. 18; Supplementary Fig. S3) confirm that these mechanisms can indeed deplete the outer radiation belt above L∼4RE rapidly (in only a few hours).

Figure 3: Schematic depicting distributions of electron PSD in L* (similar to L, but inversely proportional to the third adiabatic invariant and thus also an invariant quantity) for the scenario in which magnetopause shadowing followed by outward radial diffusion results in a dropout of energetic electrons throughout most of the outer belt.
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a, Before the CIR impacts the magnetosphere, initial distributions for both a positive PSD distribution (blue) and a peaked distribution (red) are shown. b, The high-pressure solar wind at the start of the CIR moves the magnetopause (MP) inward, resulting in magnetopause shadowing. c,d, The magnetopause moves back out, responding to the lower pressure as the main phase of the storm begins. The loss above ∼7RE results in a very sharp PSD gradient and subsequent enhanced diffusion, as indicated by the black arrows. Outward radial transport results in further losses to the magnetopause and irreversible flux reductions throughout much of the rest of the belt, because electrons lose energy as they move outward. Diffusion coefficients calculated using the global ULF waves observed during the 06 January 2011 event (see Supplementary Information) reveal that rapid outward radial diffusion would have occurred when the combined effects of the enhanced diffusion coefficient and the sharp radial gradient are accounted for. Rapid outward radial transport resulting in flux loss can also occur during the storm’s main phase through enhanced electric fields19 and/or diamagnetic effects from a partial ring current17.

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The results presented here clearly show that the majority of non-adiabatic loss of outer radiation belt electrons with energies above 300 keV during the main phase of a small, CIR-driven geomagnetic storm was not to the atmosphere but to Earth’s magnetopause through magnetopause shadowing and subsequent rapid outward radial transport, which further enhanced the total flux loss throughout much of the rest of the belt. This is a viable loss mechanism for outer belt flux dropouts during not only storms but also any event initiated by a period of high solar wind dynamic pressure that results in the magnetopause moving into the outer range of the radiation belt. Interestingly, coronal-mass-injection- and CIR-driven storms often meet this condition, including ones examined in previous studies4,11,23, which also reveal that there is insufficient loss to the atmosphere to explain the dropouts(Supplementary Figs S4, S5 and S6). This loss mechanism is also consistent with recent statistical studies that showed many electron dropouts are associated with solar wind dynamic pressure enhancements27 and there is no evidence for enhanced electron precipitation during main-phase dropouts in CIR-driven storms28. Some important questions remain, however, including: (1) Comparatively, how much do a partial ring current17, enhanced outward diffusion18, and enhanced electric fields19 contribute to the outward radial transport of electrons? (2) What causes loss during dropouts that do not correspond to magnetopause shadowing events?

Non-adiabatic losses during the storm-time main phase have broader implications concerning the extreme dynamics of the outer radiation belt. After flux dropouts such as the ones discussed here, the relativistic electron population is almost entirely depleted and subsequently replenished by a fresh population of electrons from an active source during storm recovery. This is analogous to the outer radiation belt being ‘reset’ at every storm associated with an onset of high dynamic pressure in the solar wind. Armed with this new understanding, more accurate system models of storm main phases can be developed to better study and understand competition between sources, losses and transport during the recovery phases29 and better predict overall storm-time flux variation. This improved understanding of outer radiation belt dynamics will be complemented by the upcoming NASA Radiation Belt Storm Probes (RBSP) mission in conjunction with continuing missions such as GOES, POES and THEMIS.