Relativistic electron flux decay and recovery

Key Points

1. Multi-satellite observations of EMIC and chorus waves and injections are used to investigate their relative importance in electron dynamics.
2. We show that chorus-driven acceleration during plasma sheet injections can overcome EMIC-driven losses.
3. We develop an analytical model of relativistic electron flux variations subject to acceleration and losses.

Introduction

There are six important physical processes that affect the dynamics of relativistic (\(>0.3\) MeV) electrons trapped in the Earth’s outer radiation belt: (a) electron losses due to pitch angle scattering toward the loss cone via resonant interactions with electromagnetic ion cyclotron (EMIC) waves , (b) electron losses due to pitch angle scattering toward the loss cone via resonant interactions with whistler-mode waves , (c) electron flux increases due to chorus wave-driven acceleration of \(\approx100-300\) keV “seed” electrons provided by recurrent strong injections , (d) electron losses due to magnetopause shadowing and outward radial diffusion , (e) electron flux increase due to inward radial diffusion by ULF waves , and (f) electron flux increase due to direct injections of \(\sim0.5-1.5\) MeV electrons in the outer belt .

EMIC wave-driven electron precipitation is considered a key contributor to electron losses at energies exceeding the minimum energy for cyclotron resonance with such waves, \(E_{\min}\sim 0.5-1\) MeV , because EMIC wave-driven electron pitch angle scattering rates near the loss cone at such energies are much larger than chorus wave-driven ones \cite<e.g.,>{Glauert&Horne05,Summers07:rates,Ni15}. And indeed, numerical simulations of the dynamics of the outer radiation belt and data-model comparisons have demonstrated that EMIC waves can efficiently scatter relativistic electrons and rapidly deplete their fluxes in the outer radiation belt.

But for energies below ultra-relativistic energies (below several MeV) and for typical plasma characteristics, EMIC wave-driven electron scattering mostly affects low pitch angle electrons \cite< equatorial \(\alpha_{eq}<30^\circ\), see>{Ni15, Kersten14}. It has been suggested that additional high pitch angle(\(\alpha_{eq}>30^\circ\)) electron scattering by whistler-mode waves can assist EMIC waves in the precipitation of the near-equatorial (trapped) electron population . Indeed, it has been shown that a combination of electron scattering by EMIC and whistler-mode waves at the same \(L\)-shell (even if at different longitudes) can result in a very effective electron flux depletion .

In addition, there is a competition between electron acceleration by chorus waves \cite<produced by anisotropic electrons that are directly adiabatically heated during injections, see, e.g.>{Sorathia18} and electron precipitation by EMIC and chorus waves, and this dynamic competition ultimately results in the observed radiation belt electron flux time-series, and also its energy spectrum, in response to multiple injections. In particular, recent work has shown that in the presence of sustained injections and both energy diffusion by chorus waves and pitch angle diffusion by chorus and/or EMIC waves, the normalized electron flux energy spectrum \(J(E)\) at \(\sim 0.1-2\) MeV should dynamically tend toward a steady-state normalized energy spectrum \(J_{UL}(E)\), which represents an attractor for the system dynamics and corresponds to a balance, at each energy, between electron flux increase and electron flux loss, fine-tuned by the electron phase space density (PSD) energy gradient . This suggests that a net flux decrease (increase) should occur when \(J(E)\) decreases with energy less (more) rapidly than the steady-state attractor energy spectrum \(J_{UL}(E)\), corresponding to a sufficiently mild (steep) PSD decrease with energy .

Although injections of anisotropic \(\sim 1-100\) keV “source” ions and electrons from the plasma sheet can simultaneously drive EMIC and chorus waves , these particle injections do not fully determine the associated wave power (which also depends on Landau damping and cold plasma density as well as the spatio-temporal extent and intensity of injections), nor do they directly control the impact of these waves on electrons (since this impact also depends on cold plasma density, wave power, and Landau damping during wave propagation, with/without wave ducting). Accordingly, EMIC and chorus wave-driven electron scattering can be examined separately from injections, traditionally on the basis of event-based or statistical wave measurements.

However, one cannot prove that more injections preferentially cause a flux increase at relativistic energies (through an increase of \(\sim 100-300\) keV seed electron flux accompanied by chorus wave-driven electron acceleration to higher energies) as opposed to a flux decrease (through more precipitation by EMIC and/or whistler-mode waves generated by injections). In this paper, we will show qualitatively that there is an association of higher injection rate with higher rate of chorus wave-driven electron energy diffusion and flux increase that helps overcome the rate of EMIC wave-driven pitch angle scattering and flux decrease. This event is illustrative, and more cases like that (or a statistical analysis) may help prove or refute this conjecture in the future.

In this study, we investigate a fortuitous conjunction between equatorial and low-altitude satellites, which enables direct observations of electron loss due to scattering by EMIC and whistler-mode waves, electron acceleration by whistler-mode waves, and plasma sheet injections. This allows us to examine the first three mechanisms listed above near \(L \sim 5\) in the outer radiation belt. During the investigated period, direct injections of \(0.5-1.5\) MeV electrons at \(L \sim 5-5.5\) are assumed to be absent based on the rarity of \(>600\) keV injections at \(L\leq5.5\) in statistical observations from the Van Allen probes , and no significant dropout should have occurred due to weakly negative IMF \(B_z\) and low solar wind dynamic pressure \(Pdyn\) (see details below). Combining spacecraft observations during this event with theoretical estimates of electron scattering rates, we show that even long-lasting (\(\sim 4\) hours) electron losses driven by EMIC waves cannot deplete \(\sim 0.1-1.5\) MeV electron fluxes in the outer radiation belt if plasma sheet electron injections are sufficiently strong. Resupply of relativistic electron fluxes can occur due to chorus wave-driven acceleration of freshly injected \(\sim 100-300\) keV seed electrons.

The structure of this paper includes Sect.~\(\ref{sec:data}\) with the general description of spacecraft instruments and the event overview, Sect.~\(\ref{sec:injections}\) describing near-equatorial observations of plasma sheet injections during the event, Sect.~\(\ref{sec:emic}\) describing low-altitude observations of EMIC wave-driven electron precipitation, Sect.~\(\ref{sec:emic&whistlers}\) assessing the relative importance of chorus waves in compensating for the EMIC wave-driven electron precipitation losses, and Sect.~\(\ref{sec:conclusions}\) summarizing the obtained results.

Spacecrafts and Dataset

• At \(\sim\) 01:15 UT ERG observed strong electron injections likely supporting whistler-mode wave generation (the onset of whistler-mode chorus waves coincides with this injection)
• At 01:30-02:30 UT GOES16&17 observed strong ion injections that arrived at ELFIN’s MLT (\(\sim16.5\)) around 02:30-03:00 UT (based on ion azimuthal drift estimates) and should have driven EMIC wave generation
• At 02:40-06:00 UT ELFIN observed continuous precipitation of relativistic electrons at MLT\(\sim 16\); NOAA/POES observations suggest precipitations are located right at the inner edge of the ion plasma sheet; to support such precipitations by EMIC waves, whistler-mode waves recorded by ERG (at MLT \(\sim 20\)) should continuously scatter relativistic electrons from higher equatorial pitch-angles into the pitch-angle range resonating with EMIC waves
• At 07:10-07:30 UT ERG and GOES16&17 observed a strong electron injection: dispersionless on ERG (MLT \(\sim 20\)) and dispersive on GOES 17 (MLT \(\sim4\)); This injection appears to restore electron fluxes and to largely compensate losses from EMIC wave-driven scattering, at least at \(E\leq1.5\) MeV

Figure 1: (top) An overview of the mission orbits recorded on April 17, 2021, from 00:00 to 12:00 UTC. The orbits of the distinct missions are projected onto the MLT and \(L\)-shell plane, designated with different colors; star markers denote the orbit start, squares indicate their termination, and time annotations are provided near the periods of interest. ELFIN-B’s trajectory is displayed during three time intervals: 02:42-02:46, 04:14-04:18, and 05:47-05:51 UT. NOAA-19’s trajectory is plotted for 01:47-01:52 and 03:30-03:36 UT, while NOAA-15’s is displayed at 01:15-01:20 and 02:58-03:03 UT. The trajectories of GOES, MMS, and Arase span the entire 12-hour interval from 00:00 to 12:00 UT. (bottom) \(Sym-H\) and SME indices during this event.

Figure 2: GOES-R electron and proton flux observations (70 keV to \(\sim\) 1 MeV) from two geostationary operational satellites. Ion injections are seen from 2 UT (right when ELFIN starts observing EMIC wave-driven precipitation) to 8 UT. Series of strong electron injections are observed around 07:10-07:30 UT at MLT\(\sim6-8\) after drifting from midnight.

Figure 3: MMS electron and proton flux observations (\(\sim 50\) keV to \(\sim 500\) keV). A localized decrease of electron fluxes is notable around the time of ELFIN observations of EMIC wave-driven electron precipitations (around 04:30 UT, at MLT \(\sim 16\)).

Figure 4: ERG(Arase) electron and proton flux observations (\(\sim\) 10 keV to \(\sim\) 120 keV). Strong electron injections are visible at the beginning of EMIC wave-driven electron precipitation and at the end of the time interval.

Figure 5: Two ELFIN CubeSats observations of EMIC wave-driven electron precipitation, where the precipitating flux reaches the trapped flux in high-energy channels, over an interval exceeding three hours, from 02:42 to 05:53 UT. The locations are projected to the equatorial L-Shell and MLT, using the magnetic field model. Panels (a), (b), and (d) show data from ELFIN-B, while panel (c) features observations from ELFIN-A.

Figure 6: Panel (a) Diffusion rates \(D_{\alpha\alpha}\) of electrons near the loss-cone inferred, using Equation 2, from ELFIN measurements of precipitating and trapped electron fluxes in the dusk sector near 16 MLT, at \(L=5\) (solid red) and \(L=6\) (solid black) as a function of electron energy \(E\). Diffusion rates \(D_{\alpha\alpha}\) near the loss-cone evaluated based on analytical estimates for H-band EMIC waves with typical wave and plasma parameters at \(L=5\) (red) and \(L=6\) (black) in a noon-dusk plasmaspheric plume, as a function of energy \(E\) are shown for a typical ratio \(f_{pe}/f_{ce}=20\), a peak wave amplitude of \(B_w=0.5\) nT at \(\omega_{\text{EMIC}}/\Omega_{cp}\sim 0.4\), and a (minimum) frequency \(\omega_{\text{EMIC}}/\Omega_{cp}\sim 0.45\) for cyclotron resonance with \(\sim2\) MeV electrons (dashed lines). (b) Same as (a) with analytical estimates of \(D_{\alpha\alpha}\) shown for H-band EMIC waves with a peak wave amplitude of \(B_w=0.5\) nT at \(\omega_{\text{EMIC}}/\Omega_{cp}\sim 0.4\) and a (minimum) frequency \(\omega_{\text{EMIC}}/\Omega_{cp}\sim 0.7\) for cyclotron resonance with \(\sim0.75\) MeV electrons (dashed lines).

Figure 7: Chorus wave-driven electron quasi-linear pitch-angle and energy diffusion rates \(D_{\alpha\alpha}(CH)\) and \(D_{EE}(CH)/E^2\) as a function of energy at \(L=5-6\), MLT-averaged based on ERG chorus wave data during this event (assuming a typical MLT distribution of chorus power, see {Agapitov18:jgr}), adopting an empirical plasma density model outside the plasmasphere. Here, chorus wave power is assumed constant at latitudes \(\sim0^\circ-30^\circ\) to first order.

Figure 8: Panel (a) Trapped electron flux energy spectra \(J(\alpha_0=90^\circ, E)\) (black to magenta curves) measured by ERG near the magnetic equator at different times on April 17, 2021, and projected to the equator by assuming a typical shape \(J(\alpha_0=90^\circ)/J(\alpha_0)\approx 1/\sin\alpha_0\), with \(\sin\alpha_0\approx (B(\lambda=0^\circ)/B(\lambda))^{1/2}\) and \(B(\lambda)\) the geomagnetic field strength at the latitude of measurement. The approximate steady-state spectrum shape \(J_{UL}(E)\) expected to be reached asymptotically in time in the presence of both EMIC and chorus wave-driven pitch-angle and energy diffusion is also shown (blue curve), normalized at the measured flux level at 100 keV and 10:30 UT. (b) Same as (a) but showing trapped electron flux energy spectra \(J(\alpha_0=90^\circ, E)\) (black to magenta curves) measured by ELFIN at low altitude at different times and projected to the equator. Two curves from panel (a) are reproduced for the sake comparison: \(J(\alpha_0=90^\circ,E)\) inferred from ERG data at 10:30 UT (dashed blue) and \(J_{UL}(E)\) normalized to ERG flux at 100 keV and 10:30 UT (solid blue).

Discussion and Conclusions

In this paper, we have investigated a particular event on 17 April 2021 characterized by series of strong electron and ion injections from the plasma sheet, significant electron precipitation by EMIC and whistler-mode chorus waves, and electron acceleration by chorus waves. During this event, GOES, Van Allen Probes, ERG (ARASE) and MMS spacecraft have measured waves and trapped particle fluxes at high altitude near the magnetic equator, while ELFIN and POES spacecraft have recorded trapped and precipitating particle fluxes at low altitude, providing sufficient data to enable a thorough analysis of the involved physical phenomena.

Although ELFIN and POES measurements have shown that EMIC and chorus waves did efficiently precipitate \(\sim0.1-1.5\) MeV electrons in the outer radiation belt during this event, trapped electron fluxes actually increased at nearly all energies. Combining theoretical estimates of electron quasi-linear pitch-angle and energy diffusion by chorus and EMIC waves with statistics of their wave power distribution, we have shown that long-lasting electron losses driven by EMIC waves may not deplete \(\sim0.1-1.5\) MeV electron fluxes in the outer radiation belt over the long run (\(>8\) hours) in the case of a sufficiently negative derivative \(\partial f/\partial E<0\) of the electron PSD \(f(E)\), because this negative PSD gradient can lead to a strong transport of low-energy injected electrons toward higher energy through efficient chorus wave-driven electron acceleration, more than compensating relativistic electron losses due to EMIC and chorus wave-driven precipitation into the atmosphere – although a brief initial net loss at high energy can cause an early decrease of \(\gtrsim 1\) MeV electron flux . In addition, electron injections from the plasma sheet, measured near \(L\approx 7\) by GOES, may have been sufficiently strong after 7 UT to compensate electron losses due to wave-driven electron precipitation below \(\sim1.5\) MeV at \(L=5-6.5\), leading together with chorus wave-driven acceleration to a net increase of relativistic elec tron fluxes. This case study therefore underlines the fact that strong EMIC and chorus wave-driven electron losses do not necessarily correspond to a simultaneous decrease of trapped electron fluxes. Both local electron energy PSD gradients and radial PSD gradients and injections can balance such wave-driven losses. Therefore, they should be included in global codes to accurately calculate the dynamical evolution of trapped fluxes.