Role of Subauroral Polarization Streams in Deep Injections of Energetic Electrons Into the Inner Magnetosphere

The electric fields of subauroral polarization streams (SAPS) have been suggested to affect energetic charged particles' dynamics in the inner magnetosphere, though their role on radiation belt electrons has never been properly quantified. A moderate geomagnetic storm on 2015‐09‐07 caused the deep injection of 10–100s of keV electrons in Earth's inner magnetosphere to low L* (L* < 4). Using a 2‐D test particle tracer, we present the effects of electric fields given by the Volland‐Stern model, a SAPS (Goldstein et al., 2005, https://doi.org/10.1029/2005ja011135) model, and a modified SAPS model on the energetic electron deep injections. The modified SAPS model reflects the SAPS electric field observations by the Van Allen Probes and is supported by Defense Meteorological Satellite Program observations. Simulations suggest that the SAPS electric field pushes 10–20 MeV/G electrons Earthward to L* ∼ 2.7 in 2.5 hr, much deeper compared to the Volland‐Stern electric field.


Introduction
Earth's radiation belts are zones with large fluxes of energetic charged particles and consisting of outer and inner belts, with the in-between slot region having much lower fluxes (e.g., Lyons & Thorne, 1973;Millan & Baker, 2012).The particles within the radiation belts represent one of the most widespread and enduring hazards encompassed by what we collectively name as space weather (Baker & Lanzerotti, 2016).Understanding these highly dynamic zones has been opened up as a new challenge with the launch of the Van Allen Probes (Kessel et al., 2013;Mauk et al., 2012).Observations have shown that the energetic charged particles are frequently pushed to very deep regions of Earth's inner magnetosphere during geomagnetic active times (Califf et al., 2022;Reeves et al., 2016;Zhao et al., 2017Zhao et al., , 2023)).Different mechanisms such as interplanetary shock induced electric fields, radial diffusion, substorm-related injections, and enhanced convection electric fields have been proposed as driving causes for such deep injections.The interplanetary shock induced electric fields energize the charged particles, but high intensity shocks capable of causing such energization at low L-shells rarely occur (e.g., Kanekal et al., 2016;Li et al., 1993).Fast transport into L* < 4 by substorms also does not occur frequently (e.g., Turner et al., 2015).Research has suggested that short-lived increases in the convection electric field can account for enhancements of electrons in the 100 s of keV range at lower L-shells (Califf et al., 2017;Su et al., 2016).Zhao et al. (2017) suggested a localized DC electric field as a potential mechanism to explain the observed MLT distributions of electrons and differential deep injections between protons and electrons, where electrons systematically reach lower L* than protons with similar energies.Based on Defense Meteorological Satellite Program (DMSP) and Van Allen Probes observations, Lejosne et al. (2018) have shown the strong correlation between deep injections of energetic electrons and the Subauroral Polarization Streams (SAPS) and attributed it to SAPS's significant electric potential drop of several tens of kilovolts in the pre-midnight sector.Supporting Information may be found in the online version of this article.Foster and Burke (2002) introduced the term "SAPS" for a mechanism with large latitudinal extents (Yeh et al., 1991), long durations polarization jets (Galperin et al., 1974) and subauroral ion drifts (Spiro et al., 1979).SAPS typically manifest at storm onset, flowing westward, and exhibits strong correlations with geomagnetic indices, as noted in previous works by Foster (1993) and Foster and Vo (2002).Based on Combined Release and Radiation Effects Satellite (CRRES) data, Rowland and Wygant (1998) discovered an unexpected increase in the duskward electric field within L = 3.5-5.5 in the evening sector during active periods (Kp > 3).This behavior contradicted the predictions made by empirical models such as Volland-Stern (VS) model (Stern, 1975;Volland, 1973).This enhancement was later linked to SAPS electric fields, underscoring their importance in shaping the overall electric field dynamics in the inner magnetosphere.Furthermore, Califf et al. (2014), based on 4 years of Time History of Events and Macroscale Interactions during Substorms (THEMIS) data, provided a complete picture of dawn-dusk electric field with a full MLT coverage in the inner magnetosphere.Their results strongly agree with the CRRES results from Rowland and Wygant (1998) on the duskside.
In the present study, we demonstrate the role of SAPS electric fields on deep injections of energetic electrons during the 2015-09-07 geomagnetic storm using test particle simulations.Our study uses an Hp-driven version of the VS model, combined with an Hp-driven model for SAPS derived from statical averages of ground-based radar data (Goldstein et al., 2005).A quantitative modification to the SAPS model fitted to event-specific electric field observations from the Van Allen Probes is also conducted.The results under different electric field models are compared, and the role of SAPS electric fields on energetic electron deep injections is revealed quantitatively for the first time.

Observations
A moderate geomagnetic storm on 2015-09-07 with Kp index reaching 6+ and Dst (Disturbance Storm Time) index attaining a minimum of 72 nT disturbed Earth's radiation belt particle fluxes.Figures 1a-1c show the electron phase space density (PSD) variations as a function of L* on this day, for populations with different first These primarily correspond to 10s-100s of keV electrons at L* ∼ 2-5.The PSD is calculated using Magnetic Electron Ion Spectrometer (MagEIS) observations (Blake et al., 2013;Claudepierre et al., 2021) under the T89D (Tsyganenko, 1989) external magnetic field model using the method described by Chen et al. (2005).Figure 1d shows the Kp & Hp30 (a Kp-like index with a time resolution of half an hour; Yamazaki et al., 2022) indexes and Figure 1e shows the Dst index for 2015-09-07.Figures 1f-1h show the Van Allen Probes' trajectories in Geocentric Solar Ecliptic coordinates.The Van Allen Probes' apogees were in the pre-dusk sector, and the probes were located near noon during outbound passes and near dusk during inbound passes.During the consecutive outbound passes between 14 and 18 UT (shown as the rectangular box), Van Allen Probes observed the electron PSD enhanced by over an order of magnitude at L* ∼ 3-4 within 3 hr, which is more apparent for lower energy electrons, showing fast, deep injections of 10s-100s of keV electrons.The deep injection of electrons is defined as the daily-averaged PSD increasing by at least a factor of two within a day over ΔL* ≥ 0.5 at L* < 4 (Zhao et al., 2023).Such deep injections cause flux enhancement at very low radial locations (e.g., Hua et al., 2019).During the inbound pass shortly after these observations, Probe-A observed an enhanced radial electric field (outward from the Earth, perpendicular to the ambient magnetic field) using two pairs of spherical double probe sensors (Wygant et al., 2013) at L* ∼ 3-4, (Figure 2a black curve).These observed electric fields during this event, along with observations of 1-50 keV electron and proton fluxes and plasma density, have been reported by Califf et al. (2022) and identified as SAPS electric fields.These enhanced SAPS electric fields below L* ∼ 4 spatially coincided with the deep injections of energetic electrons shown in Figure 1.
The deep injection event that occurred between ∼14:00 UT and 17:00 UT was observed by the Van Allen Probes during outbound passes.However, the SAPS features were observed by the Probes later during their inbound passes near dusk.Due to the limited spatiotemporal coverage of the Van Allen Probes, it is not immediately clear whether SAPS were present at the dusk sector during electron injections, which motivated us to make use of Low-Earth-orbit (LEO) DMSP observations.Figure 2b shows the horizontal ion drift velocities measured by the DMSP, which indicates westward SAPS flow velocity (Foster & Vo, 2002), during 20:20-20:30 UT, around the time of observations of SAPS by Probe-A.L* is calculated by mapping DMSP's location to the magnetic equator using the T89D magnetic field model.The DMSP observations show elevated horizontal ion drift velocities at L* ∼ 3-4, showing the presence of SAPS at these spatial locations.This is consistent with Van Allen Probes observations of SAPS near the magnetic equator.Leveraging the higher spatiotemporal resolution of LEO observations, the DMSP observations in the dusk sector during the electron injections were also studied.Figure 2c shows one example: during 16:45-17:02 UT, around the time of deep injections of energetic electrons, enhanced horizontal ion drifts at low L* were also observed by DMSP.These observations indicate that SAPS were present during the fast, deep injections of energetic electrons.

Electric Field Models
We use a 2D particle tracer combined with the SAPS electric field model to study the effect of SAPS electric fields on electron populations of different energies.We use Goldstein et al. (2005) model for the SAPS electric field; for the convection electric field, we use the VS model.The VS model represents a symmetrical convection electric field through the electric potential U(r,ϕ) = a r br γ sin ϕ.Here, r denotes the equatorial distance from the Earth's center, and ϕ represents the azimuthal angle at the magnetic equatorial plane (where ϕ = 0 aligns with noon), with the empirical shielding exponent γ = 2 as suggested by previous studies (e.g., Maynard and Chen (1975) and Korth et al. (1999)), a = 92.4kV R E and b = 0.045 Chen, 1975).Based on the SAPS statistical properties measured by ground-based radar (Foster & Vo, 2002), the magnetospheric SAPS potential model of Goldstein et al. (2005) is given by Φ S (r, ϕ, t) = F(r, ϕ)G(ϕ)V S (t), where Φ S describes a potential drop with a time-dependent magnitude V S (t) = (0.75 kV) K 2 p .The radial width and radial location of the potential drop are controlled by F(r,ϕ)   2005)'s SAPS model (hereafter referred to as G05 model; green curve) along the Probe -A trajectory during 18:15 UT to 21:15 UT.The VS model does not capture the enhanced radial electric field observations.The G05 model does present an enhanced radial electric field but at a higher L* than the observed electric field enhancement and with a lower amplitude.To better capture the observed SAPS electric field, a modification to the G05 model is made, shown as a combined VS and modified SAPS model (hereafter referred to as mG05; red curve) in Figure 2a.
The quantitative modifications to the G05 model have been done minimally by keeping the peak potential drop, temporal dependence V S (t) and azimuthal variation G(ϕ) the same, while including an inward shift of the radial location of SAPS (R 0 ) and narrowing the radial width of SAPS (α).The modified forms of the equations can thus be written as: (2) By using the above modified equations in G05 model, we see an enhancement in the modeled radial electric field (red curve in Figure 2a) that quantitatively captures the observed radial electric field enhancement.
Figure 3 shows the contour plots representing the equatorial magnetospheric electrostatic potential variations using VS, SAPS, and modified SAPS models for extreme geomagnetic conditions (Hp = 7).The black circle shows L* = 4 and the red circle presents the geosynchronous orbit (L* = 6.6). Figure 3a shows the VS potential representing composite convection and corotation potentials which presents some flow stagnations around the dusk region.Figure 3b shows the equipotential lines using the SAPS model, which presents the most significant potential drop around dusk. Figure 3c shows the modified SAPS model.As a result of the modifications (Equations 1 and 2), the closely spaced equipotential lines (corresponding to strong electric fields), which occur inside L* = 4 at dusk in the original model (Figure 3b), now appear closer to Earth (L* ∼ 2) in the dusk-midnight region.The maximum potential drop to around 35 kV, which occurs at L* >4 in the original model, occurs as close to Earth as L* ∼ 3.2 with the modified model.Figure 3d illustrates that incorporating the SAPS potential into the VS model notably amplifies the sunward flow component on the duskside while modifying the flow streamlines around noon to post-midnight. Figure 3e shows that, as expected, the mG05 model pushes this pattern radially inward in comparison to the G05 model (Figure 3d).
Figure 4 shows the global maps of the SAPS radial electric fields during deep injections from 14:00 UT to 17:00 UT.The top panel in Figure 4 shows the electric fields calculated using the original SAPS model, and the bottom panel shows the same using the modified SAPS model.As the original model depicts, evolving from moderate (Figure 4a) to extreme geomagnetic storm conditions(Figure 4d), the SAPS radial electric field gets stronger and closer to Earth, with the maximum electric field being ∼11 mV/m.This maximum occurs around the dawn sector at 16:00 UT with Hp = 7 at L* ∼ 3.5 (Figure 4c).Another local maximum of lower amplitude ∼5 mV/m also appears close to dusk in Figure 4c.On the other hand, the radial electric field using modified SAPS not only shifts to smaller radial locations, but the radial width of the SAPS flow channel is also scaled down.The modified SAPS model also depicts a larger magnitude of radial electric field (up to ∼ 20 mV/m) spread over a larger MLT region around dusk (Figure 4g).The peak radial electric field inherited from the original SAPS model also appears in Figure 4g around post-midnight.The corresponding temporal variations of the azimuthal electric field have also been shown in the supporting information.

Test-Particle Tracing Simulation
In this study, we use a test particle-tracing model to simulate the electron PSD variations.An equatorial 2-D guiding-center code is used to trace 10 4 electrons of a specific μ value.The total velocity of the particle guiding center is given by here B is the dipole magnetic field of Earth and E is the electric field given by different models, and q is the charge of the electron.
We have used the VS, G05, and mG05 models to simulate their effects on electrons.For the energy range 10s-100s keV, we consider μ = 10 MeV/G, 20 MeV/G, 30 MeV/G electrons.The initial PSDs are taken from Van Allen Probe -A measurements right before the deep injection.The simulation time is set to 2.5 hr based on the approximate time difference between the consecutive outbound passes by Probes A and B. The initial location of an electron is randomly chosen by the code between L* = 2 and L* = 5, the trajectory of each electron is calculated, and the PSD is conserved along the trajectory assuming no source or loss process.The results present the simulated PSDs as a function of L* calculated at spacecraft locations (averaged over a 0.1 L* and 0.4 MLT bin).In terms of the PSD enhancements, the VS model produces minimal PSD enhancements.The G05 model produces some PSD enhancements, which are more significant for 10 MeV/G electrons at L* ∼ 2.9-3.6 (panel (a)).

Results
The electric field generated using the mG05 model causes up to five times larger PSD enhancements of 10 MeV/G electrons at L* ∼ 3-3.3 and significant PSD enhancements of 20 MeV/G electrons (panel (b)) at L* ∼ 2.9-3.5, which even completely captures the PSD enhancements of 20 MeV/G electrons at L* ∼ 2.85-2.95.
Overall, including SAPS electric fields causes more realistic injections, especially at lower energies (10 MeV/G), and fitting the SAPS model to observations causes the model to better match the particle observations.These results suggest that SAPS play a major role in the deep injections of 10s-100s keV electrons, and the modified SAPS model inspired by SAPS observations produces larger electron PSD enhancements at low L* than the original SAPS model.

Discussion
While the main indicator of SAPS in the equatorial magnetosphere is a robust radial electric field, there are concurrent azimuthal electric fields on the eastern and western sides of the SAPS region.These azimuthal electric fields lead to inward particle transport on the dawn side and outward transport on the dusk side.In addition, the effect of SAPS electric fields is drift-phase dependent, which may result in a PSD enhancement at one MLT location and a PSD decrease at the other.So, we also calculated the averaged PSD across all MLTs in the simulation.The results, shown in the supplementary information, still show overall PSD enhancements at low L*, indicating that the net effect of SAPS electric fields is to push electrons inwards into lower L*.This is likely due to the steep positive radial gradient in electron PSD, as shown in Figure 5.
Although the modified model produces more significant injections compared to the original models, it does not fully reproduce the observed PSD enhancements during the deep injection event.Also, it is inferred that SAPS does not appear to be an important mechanism to transport 30 MeV/G electrons across L*.One possible reason is that the actual electric field strength which caused this deep penetration was stronger, since the Volland-Stern model may underestimate the convection electric field magnitude (the results with a modified Volland-Stern model together with the modified SAPS model are presented in the supplementary information, and the deep injections of 10 and 20 MeV/G electrons are largely reproduced), and/or the temporal electric field variation may be more dynamic than that described by Hp30 index.Another potential reason is that we did not consider the source process in the present study.During geomagnetic disturbances, such as substorms triggered by interactions between the solar wind and the Earth's magnetic field, plasma sheet electrons are injected into the inner magnetosphere.Such injections may significantly increase the PSD of low-energy electrons in the intermediate L*, such as those shown in Figure 5a for 10 MeV/G electrons at L* ∼ 3.2 and above.Our future studies will include the plasma sheet source and we will also consider modifying the VS model to further improve the composite model qualitatively as well as quantitatively.
injected energetic charged particles into Earth's lower L* (≤4) • The electric fields generated by subauroral polarization streams (SAPS) are a potential cause behind these deep injections • The quantitative fitting of the SAPS model to Van Allen Probes observations highly affects the simulated lower energy electron fluxes Supporting Information:

Figure 1 .
Figure 1.phase space density (PSD) variations as a function of L* and time on 2015-09-07 for μ = (a) 10 MeV/G, (b) 20 MeV/G, (c) 30 MeV/G, K = 0.1 G 1/2 R E electrons.Panel (d) shows the Kp and Hp indices and panel (e) shows the Dst index.The dotted black box highlights the two probes' passes during which the PSD enhancements are observed at L* ∼ 3-4.Panels (f-h) present the spacecraft trajectories in Geocentric Solar Ecliptic coordinate system on 2015-09-07.

κ
determines SAPS radial location; β = 0.97, κ = 0.14; R 0 /R E = 4.4-0.6(Kp 5), R E is the radius of the Earth; α = 0.15 + (2.55 0.27K p ) [1 + cos φ 7π 12 )] governs the SAPS radial width.G(ϕ) governs the variation of potential drop across local time.Both the VS and SAPS models are originally driven by the Kp index; however, we used the Hp index instead of Kp in this study since Hp has a half-hour time cadence while Kp only varies every 3 hr.During storm time, especially in the case of fast injections, it is important to Geophysical Research Letters 10.1029/2024GL108863 account for faster variations than the 3-hour time cadence given by Kp index.Hence, Hp index is more useful in the present case.

Figure
Figure 2a also shows the variations of radial electric fields calculated using the VS model (blue curve) and a combined VS and Goldstein et al. (2005)'s SAPS model (hereafter referred to as G05 model; green curve) along the Probe -A trajectory during 18:15 UT to 21:15 UT.The VS model does not capture the enhanced radial electric field observations.The G05 model does present an enhanced radial electric field but at a higher L* than the observed electric field enhancement and with a lower amplitude.To better capture the observed SAPS electric field, a modification to the G05 model is made, shown as a combined VS and modified SAPS model (hereafter referred to as mG05; red curve) in Figure 2a.

Figure 4 .
Figure 4.The temporal variation of the global map of radial electric field due to SAPS model (a-d) and modified SAPS model (e-h) during 14:00-17:00 UT on 2015-09-07.

Figure 5
Figure5shows the observed PSD (averaged in L* bins of size 0.1 L*) before (dotted-dashed red lines) and after (dotted-dashed black lines) the deep injection event for each electron population with a specific μ.The solid colored lines present the simulation results at spacecraft locations calculated using different electric field models.The VS model (blue curves) causes minimum inward transport of electrons of different μ's.The 10 MeV/G electrons (panel (a)) are pushed to L* as low as ∼2.8 using G05 model (green curves), but the electric field generated using mG05 model (red curves) causes 10 MeV/G electrons to move more inward to L* ∼ 2.7, closer to the observed innermost enhancement (L* ∼ 2.6).At L*> ∼ 3.2, the mG05 model produces similar results to the G05 model.The G05 model transports the 20 MeV/G electrons (panel (b)) to L* ∼ 2.9.These 20 MeV/G electrons are pushed to L* ∼ 2.8 by the mG05 electric field.At 30 MeV/G, none of the models have much impact on radial transport (panel (c)).

Figure 5 .
Figure 5.The radial profiles of simulated phase space density as a function of L* using three different electric field models for electrons with (a) μ = 10 MeV/G, (b) μ = 20 MeV/G, (c) μ = 30 MeV/G at the spacecraft locations.The observational PSDs before and after the deep injection event are shown by dashed-dotted lines in each panel.