Tens to hundreds of keV electron precipitation driven by kinetic Alfven waves during an electron injection

Yangyang Shen
Earth, Planetary, and Space Sciences, UCLA, Los Angeles


Magnetospheric plasma sheet electron earthward injections feature abrupt and intense flux increases of electrons with energies of tens to hundreds of keV on the nightside magnetotail-inner magnetosphere interface, which are an inherent phenomenon associated with magnetospheric substorms. These energetic electron injections provide a seed population for the radiation belts and generate significant magnetospheric electron precipitation to the ionosphere. The energetic precipitation is typically ascribed to wave-particle interactions, which are responsible for both electron scattering and acceleration. However, what wave modes contribute to this energetic precipitation from the nightside transient region has not been well understood. One potential candidate is kinetic Alfven waves (KAWs). KAWs have perpendicular wavelengths (λ_⊥) comparable to the ion thermal gyroradius (ρ_i), and the finite Larmor radius effect produces charge separation and coupling to electrostatic (ion-acoustic) mode, so that a significant parallel-to-B electric field develops to maintain charge neutrality and counteracts the electron thermal pressure (Lysak and Lotko, 1996). KAWs parallel electric fields allow electron Landau resonance but typically require the electron velocity to approach the Alfven speed v_∥≈ω/k_∥~v_A, limiting the resonant energies to below a few keV. Thus, KAWs are conventionally not expected to resonate with injection energetic electrons directly. However, when observed by electrons drifting across the curved magnetic field with velocity v_drift, KAW plasma frame ω can be significantly increased due to Doppler shift and the resonant energy can be shifted to a higher value v_∥ ~ (ω-k_⊥ v_drift)/k_∥, potentially moving energetic electrons into Landau resonance with KAWs. Will KAWs drive energetic electron precipitation associated with the plasma sheet injection via this Doppler-shifted Landau resonance? Testing of this hypothesis can be obtained via conjugate ground-based magnetometers, ionospheric and magnetospheric in-situ observations of energetic electrons, such as those provided by ELFIN, THEMIS, and MMS spacecraft. Here we present ELFIN-MMS observations to show evidence of tens to hundreds of keV electron precipitation driven by KAWs during a magnetotail electron injection. Test particle simulation results support the proposed mechanism with such observations.


Figure 1. ELFIN-MMS conjunction event on 29 September 2020. (a) Panels from top to bottom: MMS Bx in Geocentric Solar Magnetospheric (GSM); MMS By and Bz; MMS ion flows; fast-mode wave electric field spectrogram; DC-coupled perpendicular electric field wavelet spectrogram (E2); DC-coupled perpendicular magnetic field (B1) wavelet spectrogram; high-energy electron energy flux spectra; low-energyelectron energy flux spectra; the time stamps of the twin ELFIN passes and the ground-inferred current maps (at 100 km altitude) are also shown. (b) ELA trapped and precipitating electron energy fluxes, along with the spectrogram and line plots (63, 138, and 183 keV) of the loss cone filling ratios. (c) ELB observations during the injection, in the same format as (b). (d) Three snapshots of equivalent ionospheric horizontal currents (EICs) and spherical elementary current amplitudes (SECAs, vertical currents) inferred from magnetometer arrays in geographic coordinates (Weygand et al., 2011). In d3, MMS (magenta triangle) and ELB (green line) footprints (TS04 mapping) are shown in the context of the substorm current wedge. ELB plasma sheet precipitation is indicated as a thickened green line.

Figure 1a demonstrates MMS observations of enduring broadband waves from sub-Hz up to ∼1 kHz associated with the sustaining injected electrons during 06:35--07:20 UT at L ∼ 9R_E in the midnight magnetotail. These broadband waves are electromagnetic below a few Hz and become increasingly electrostatic above a few Hz, which are potentially comprised of KAWs and nonlinear time-domain structures (TDSs). Before the injection took place, ELA crossed the ionospheric footprint of MMS in the southern hemisphere during 06:24–06:30 UT around magnetic midnight. Figure 1b presents ELA-measured trapped and precipitating electron energy fluxes in the outer radiation belt. Figure 1c shows that ELB traversed the magnetically conjugate region to MMS in the northern hemisphere during the injection period of 06:56–07:02 UT. The identified intense plasma sheet precipitation during the injection by ELB is in sharp contrast to scant precipitation observed by ELA before the injection occurred (Figure 1b). The precipitation driven by wave-particle interactions can be distinguished from current sheet scattering or field-line curvature-driven scattering (which produces more efficient higher-energy precipitation) (Sergeev et al., 1993), via comparing precipitating-to-trapped flux ratios measured at adjacent energy channels of ELFIN (last panel of Figure 1c). The linkage of ELB precipitation to MMS is established through the corresponding ground-based current observations of EICs and SECAs of the injection and compressional wave observations that are related to KAWs in the magnetosphere (Figure 1d3).

Figure 2. (a–f) MMS-measured magnetic field and electric field in the field-aligned coordinates (B3 is in the B direction), spanning the period from 06:00 UT to 07:20 UT. (g) Mean E2/B1 spectra (red) in comparison with the prediction by kinetic Alfven wave dispersion relation using different observed values of ion flows (black lines). The black dots represent the measured E2/B1 spectra at different frequenices, each calculated using a window size of 16 s. The local Alfvén speed is shown as the red dashed line. (h) Least squares power law fitting of the mean KAW E2 spectra.

Figure 2 presents the nature of KAWs associated with the injection observed by MMS during the period of 06:00–07:20 UT. The electric field measurements demonstrate small-scale quasi-electrostatic fluctuations and intermittent spikes, consistent with the quasi-electrostatic property of KAWs with k_⊥≫k_∥. We have transformed the measured fields into the field-aligned coordinates. We compare the measured perpendicular fields E2/B1 spectra with the theoretical prediction of KAW dispersion relation, assuming the measured spacecraft frame spectra are largely due to Doppler shifts of KAW perpendicular wave structures due to ion flows: |E_2/B_1 |=v_A (1+k_⊥^2 ρ_i^2 ) [1+k_⊥^2 (ρ_i^2+ρ_s^2 )]^(-1/2) (Lysak and Lotko, 1996). Based on these KAW observations and background magnetic fields of dipolarization, we perform test particle simulations to study energetic electron pitch-angle scattering by KAWs at the magnetic field gradients of dipolarized fields.

Figure 3. (a) Three test electron trajectories and pitch angle variations as a function of time and position in x direction, in which the magnetic field Bz gradients are present. (b) Normalized magnetic moment variations of the three test electrons with an arbitrary unit. (c) Test particle simulation of electron loss rates (rloss, red stars) driven by kinetic Alfven waves (KAWs) and magnetic field gradients. The black triangles are interpolated loss rates at energy channels of MMS FEEPS. The two gray-dashed lines indicate the obtained loss rates when we double and halve the KAWs electric field amplitudes. (d) Comparison of precipitating electron energy fluxes measured by the three MMS spacecraft (1–3) in the magnetosphere and by ELFIN-B in the ionosphere when only wave-driven precipitation intervals are used (Figure 1c).

Figure 3 presents the preliminary test particle simulation results and comparison with data. Figure 1a and 1b show the evolution of the trajectories (in x direction) and magnetic moments of three test particles with an initial pitch angle of 5° and an energy of 100 keV. Electrons can be driven into the loss cone by the combination of the large-scale adiabatic transport and small-scale perpendicular momentum kicks due to varying E × B and ∇B drifts. Here we did not include bounce motion (field-aligned motion) of electrons; a revisit from Shen et al. [2022b] includes electron bounce motion and finds that energetic electron pitch-angle decreases are, to a larger extent, due to KAW parallel electric field acceleration. Figure 3c presents the simulated electron loss rates for the observed energy range of the injection and precipitation. Applying the loss rates in Figure 3c to estimating precipitating electron energy fluxes from MMS in the magnetosphere, we compare the expected precipitation fluxes with those observed by ELFIN in Figure 3d. The resultant average precipitating energy fluxes measured by ELFIN-B (black line) and MMS (red line) are consistent at energies below ∼300 keV within spectral variations.


In this study, we consider KAWs with k_⊥ ρ_i >1 interacting with plasma sheet injection electrons via Doppler-shifted Landau resonances in the energy range of 10–500 keV, which is the main population of injected electrons from the magnetotail. This range of resonant energies with KAWs has so far not been explored but can be significant if we include electron perpendicular guiding-center drifts in the magnetic field gradients associated with injections and dipolarizations, where KAWs have been found to be pervasive. Using conjugate ELFIN and MMS spacecraft observations and interpreting these observations through test particle simulations, we find that dipolarized magnetic field gradients and the associated perpendicular guiding-center drifts allow Doppler-shifted Landau resonant interaction between injected electrons and KAWs, producing scattering and precipitation of injection electrons.


Shen, Y., Artemyev, A. V., Zhang, X.-J., Angelopoulos, V., Vasko, I., Turner, D., et al. (2022a). Tens to hundreds of keV electron precipitation driven by kinetic Alfvén waves during an electron injection. Journal of Geophysical Research: Space Physics, 127, e2022JA030360. https://doi. org/10.1029/2022JA030360.

Shen, Y., Artemyev, Vasko, I. Y., Zhang, X.-J., Angelopoulos, V., An, X., and Runov, A. (2022b). Energetic electron scattering by kinetic Alfvén waves at strong magnetic field gradients of dipolarization front. Physics of Plasmas, 29, 082901. https://doi.org/10.1063/5.0096338.

Lysak, R. L., and Lotko, W. (1996). On the kinetic dispersion relation for shear Alfvén waves. Journal of Geophysical Research: Space Physics, 101(A3), 5085–5094. https://doi.org/10.1029/95JA03712.

Sergeev, V. A., Malkov, M., and Mursula, K. (1993). Testing the isotropic boundary algorithm method to evaluate the magnetic field configuration in the tail. Journal of Geophysical Research: Space Physics, 98(A5), 7609–7620. https://doi.org/10.1029/92JA02587.

Biographical Note

Yangyang Shen is an Assistant Researcher in the Department of Earth, Planetary, and Space Sciences at UCLA. His research interest is wave-particle interactions and the associated particle acceleration and precipitation in the magnetosphere and ionosphere using spacecraft observations and numerical simulations.

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Emmanuel Masongsong / emasongsong @ igpp.ucla.edu