Intense Energetic Electron Precipitation Caused by the Self‐Limiting of Space Radiation

Understanding intense electron precipitation is crucial for characterizing radiation belt loss and assessing related impacts on the atmosphere. We investigate the evolution of electron flux during an ensemble of 70 geomagnetic storms, focusing on equatorial and low‐Earth orbit observations of trapped and precipitating ∼30–100 keV energy electrons. We reveal that the most intense electron precipitation is associated with equatorial flux capping through self‐limiting processes, for example, as described theoretically by Kennel and Petschek (1966, https://doi.org/10.1029/jz071i001p00001). Our results indicate that the most intense electron precipitation is caused by electron injections associated with self‐limiting processes. Dawn side injections are observed to have fluxes that exceed the Kennel‐Petschek limit, consistent with the excitation of strong chorus waves and resulting in intense precipitation and return of the trapped flux to the Kennel‐Petschek limit. Our results clearly demonstrate the important role of self‐limiting processes in affecting the dynamics of newly injected electrons and driving intense electron precipitation.


Introduction
Since the discovery of the hazardous trapped electron population in the Van Allen radiation belts of our planet more than 60 years ago (Van Allen & Frank, 1959), significant effort has been dedicated to specifying what physical processes are responsible for their creation and dynamics.This research has become increasingly important with the growing number of satellites around the Earth that may be susceptible to the impacts of such "satellite killer" electron radiation (Eastwood et al., 2017;Welling, 2010).Determining the worst-case scenario radiation levels that may be formed in the Earth's inner magnetosphere is especially important (Baker et al., 1994;Meredith et al., 2023).Recent studies by Olifer et al. (2021Olifer et al. ( , 2022) ) have shown that the electron flux across a wide range of energies (from 10 s of keV to a few MeV) can reach a maximum limit, consistent with the Kennel-Petschek process (Kennel & Petschek, 1966).According to the original Kennel-Petschek (K-P) theory, derived on the basis of quasilinear wave-particle interactions, once the electron fluxes reach a certain threshold, the particle losses arising from scattering into the atmosphere due to interactions with self-generated chorus waves shall limit further flux increase, capping the trapped flux at a maximum.Under strong forcing, this capping process would be expected to drive a strong pitch angle diffusion and result in intense electron precipitation.By using data from the Polar Operational Environmental Satellites (POES; Peck et al., 2015) in low Earth orbit (LEO) and comparing measurements of trapped and precipitating particles in different magnetic local time (MLT) Abstract Understanding intense electron precipitation is crucial for characterizing radiation belt loss and assessing related impacts on the atmosphere.We investigate the evolution of electron flux during an ensemble of 70 geomagnetic storms, focusing on equatorial and low-Earth orbit observations of trapped and precipitating ∼30-100 keV energy electrons.We reveal that the most intense electron precipitation is associated with equatorial flux capping through self-limiting processes, for example, as described theoretically by Kennel and Petschek (1966, https://doi.org/10.1029/jz071i001p00001).Our results indicate that the most intense electron precipitation is caused by electron injections associated with self-limiting processes.Dawn side injections are observed to have fluxes that exceed the Kennel-Petschek limit, consistent with the excitation of strong chorus waves and resulting in intense precipitation and return of the trapped flux to the Kennel-Petschek limit.Our results clearly demonstrate the important role of self-limiting processes in affecting the dynamics of newly injected electrons and driving intense electron precipitation.

Plain Language Summary
In this study, we investigate the behavior of electrons in Earth's magnetosphere and how they impact the upper atmosphere during geomagnetic storms.We focus on electron precipitation events with energies that are often associated with pulsating aurora.Our findings show that during the most intense periods of electron precipitation, the electron flux in the equatorial region is associated with a natural process that caps it at an upper limit.We also reveal that electron injections occurring on the dawn side of the magnetosphere trigger these processes, leading to the most significant electron precipitation events occurring in this region.Our results highlight the importance of these natural self-limiting processes in shaping the behavior of the radiation belts, and the potential impact of the related precipitation of these particles into the upper atmosphere.Understanding these processes is crucial for studying space weather and its potential effects on our planet's atmosphere and climate.regions, we show that the electron injections into the magnetosphere can often briefly increase the electron flux levels above the Kennel-Petschek limit in the equatorial plane (see also Olifer et al., 2022).These periods are also associated with an enhanced flux of precipitating particles as measured by POES.This also must be associated with very strong chorus wave growth in order for the flux of equatorial electrons to be quickly reduced to the K-P limit (see also, e.g., the discussion in Mauk & Fox, 2010;Chakraborty et al., 2022).We show that the K-P limit is characterized by an asymptotic PAD which has the same shape and intensity in all storms that were investigated in this study.We also reveal that the electron flux only exceeds the K-P limit on the dawn side of the Earth.Meanwhile, the dusk side electron fluxes are always capped at or just below the K-P levels.This study showcases for the first time how the self-limiting Kennel-Petschek processes define the magnitude of the electron flux and the shape of the entire pitch angle distribution from the equator to the loss cone and cause intense energetic electron precipitation events.Importantly, while the original Kennel and Petschek (1966) paper used a quasilinear description of wave-particle interactions, in this letter we do not limit our interpretations to only this type of interaction.Instead, by referring to "self-limiting Kennel-Petschek processes" we assume any quasilinear or nonlinear chorus wave-particle interaction that ultimately results in the generation of the natural asymptotic limit to the electron flux.

Low Earth Orbit Observations of the Upper Limit to Electron Radiation
Figure 1 shows a superposed epoch analysis of 54 keV electron differential flux measured during 70 isolated geomagnetic storms of at least moderate intensity (Dst ≤ −50 nT) from 2012 to 2019 identified in Olifer et al. (2021).Epoch time zero represents the minimum Dst in each storm.Panels (a-c) (Figure 1) show 90° differential flux measured by the Van Allen Probes (Mauk et al., 2012) in the dawn (3-9 MLT) and dusk (15-21 MLT) local time sectors.Panels (d-i) show estimates of the trapped and precipitating differential electron flux obtained from POES integral flux measurements (Peck et al., 2015) in LEO assuming an E −2 spectral shape for the same Top row of Figure 1 shows that the trapped near equatorial electron fluxes at 54 keV are enhanced almost immediately at the start of the geomagnetic storm (∼0.5 days before zero epoch), increasing the median flux by two orders of magnitude.However, there is a clear difference in how the variability of the fluxes change from one storm to the next between the dawn and dusk regions.While both MLT regions are characterized by large error bars during the pre-storm, the dawn side region retains a relatively high variability of the fluxes when the median flux is at its highest, with the median and upper quartiles exceeding the K-P limit by approximately a factor of five (Figure 1b).This variability drops substantially to the factor of two at most once the median fluxes are lowered below the limit.On the other hand, the flux variability on the dusk side immediately collapses to only a factor of two when the fluxes are at their highest.Note that the small flux variability present in the Van Allen Probe data near the equator (Figure 1b) at superposed epoch time zero is caused by the fluxes reaching the saturation limit for the MagEIS instrument, that is ∼10 6 cm −2 s −1 sr −1 keV −1 (Blake et al., 2013).
An important aspect of the observed flux dynamics at the Van Allen Probes and POES is the change in the flux variability once the flux approaches a certain limit, from above in the case of dawn, and from below in the case of dusk.We argue here that both can be explained by the flux-limiting processes consistent with those proposed by Kennel and Petschek (1966).Significantly, panels (e and f) show that POES 90° detector demonstrated an almost identical flux morphology to that of the Van Allen Probes at both dawn and dusk (cf., panels (b) and (c), respectively).This provides strong evidence that the K-P process is associated with the same asymptotic pitch angle distribution in every storm.Whilst the form of such an asymptotic K-P limited PAD is determined by the rate of the processes acting to generate the K-P limit, and such are not well-known (see e.g., the discussion in Summers et al., 2009;Summers & Shi, 2014), Figure 1 demonstrates that the K-P processes affect all pitch angles from 90° to close to the very boundary of the loss cone.In particular, chorus waves, generated by the near-equatorial electrons at or above the K-P limit (e.g., Chakraborty et al., 2022), can drive fast pitch angle transport that results in increased flux at low pitch angles.Moreover, the transport of this population would be expected to produce intense precipitation into the loss cone at such times, as observed by the POES 0° detector in panels h and i of Figure 1.However, when such strong driving stops, the rate of transport rapidly drops, such that trapped electron fluxes on LEO remarkably reach the same flux level in all of the storms, similar to the dynamics observed for the near-equatorial fluxes.In this study, we refer to such an electron flux level in the POES 90° detector as the "asymptotic" flux level, as it characterizes the electron flux value reached in all storms from above on the dawn side and from below on the dusk side.In our view, the existence of this asymptotic flux level at LEO altitude is a direct consequence of the K-P processes acting to self-limit the equatorial population that affects the entirety of the PAD.In Figure 1, this asymptotic level is estimated as the upper quartile of superposed epoch fluxes at the time when the median fluxes transition from rising to falling in the dusk region.For L = 4.5, this level is estimated to be ∼5 • 10 3 cm −2 s −1 sr −1 keV −1 .
The bottom row of Figure 1 shows details of the observed precipitation from the superposed epoch analysis of POES 0° detector data.It further reveals a strong asymmetry in the precipitation intensity in the dawn and dusk MLT sectors, with the dawn-side precipitation being more than an order of magnitude more intense.Moreover, the highest intensity of the precipitation is observed during periods when the near-equatorial flux is above the K-P limit (Figure 1b) and the trapped flux near the loss cone (Figure 1e) is above its asymptotic level.This is consistent with the generation of strong chorus wave pitch angle diffusion caused by the electrons near the magnetic equator exceeding the K-P limit as discussed above.

Pitch Angle Distribution of the Limited Electron Fluxes
Figure 2 shows superposed epoch equatorial PADs, normalized to the equatorial flux, as well as the sin 0.6 α eq PAD model assumed by Mauk and Fox (2010) for the K-P limit calculation, during four characteristic storm times.At superposed epoch time zero (Figure 2b), the pitch angle distribution measured by the Van Allen Probes develops into a more anisotropic shape with the fluxes at ∼20-70° lying below the sin 0.6 α eq line.As discussed above, this period is also associated with fast flux enhancement and exceeding the K-P limit by the near-equatorial particles (cf., Figure 1b).The rapid decrease of the median near-equatorial flux in its absolute value from panel 2b to panel 2c is also associated with the isotropization of the pitch angle distributions and collapse of the flux variability by the end of one day after superposed epoch zero (Figure 2c).Significantly, during this time the median precipitating flux decreases by a factor of ∼300.Interestingly, the median electron fluxes measured by Van Allen Probes in panel 2c are well characterized by the sin 0.6 α eq shape.By the end of the recovery phase (Figure 2d), the variability of the electron flux is increased; however, the median fluxes retain a close correspondence to the asymptotic pitch angle distribution.The relative electron flux inside the loss cone is also highly variable with the storm phase.Indeed, the times when the PAD is revealed to be the most anisotropic (Figure 2b), and when the equatorial 90° flux exceeds the K-P limit, are also associated with periods of very fast transport into the loss cone and the highest median flux of precipitating electrons.
Importantly, the POES 90° detector measurements close to the loss cone clearly reveal that the loss cone can have a substantial influence on the shape of the asymptotic PAD even at ∼5° equatorial pitch angle, and cannot be described with a single simple sin n α eq shape.Olifer et al. (2022) previously reported an example of short-lived (∼2 − 4 hr) enchantment of the lower energy ∼100 keV populations that can exceed the K-P limit.They speculated that these enhancements above the limit are caused by electron injections that can increase electron flux levels on timescales shorter than the K-P processes can act to limit particle flux.This idea is consistent with the higher anisotropy of the pitch angle distributions evident in Figure 2b and the fact that the K-P limit is exceeded only on the dawn side consistent with drift trajectories of typical electron injections.

Magnetic Local Time Variation of the Limited Electron Flux
It is interesting to investigate the detailed magnetic local time (MLT) and drift phase dependence of the electron flux dynamics in the context of the action of the K-P limiting processes during storm-time electron injection.Figure 3 shows superposed epoch trapped 90° detector 54 keV differential electron flux as measured by POES in eight different MLT sectors.The MLT diagram in the center shows the maximum superposed epoch electron flux in a corresponding MLT region with a colormap (higher flux is represented by brighter colors).Similar to Figure 1, Figure 3 reveals that the electron fluxes in the dawn sector (between approximately 0 and 15 MLT) are enhanced to the levels above the estimated LEO asymptotic flux level.Meanwhile, the dusk side fluxes are limited under the limit and approach it from below.The superposed epoch time series in Figure 3 shows a highlighted blue region that designates the group of particles connected with the measurements of the highest electron flux in the 0-3 hr MLT sector.This blue-shaded region is shifted in the positive time direction in all other MLT regions with the azimuthal drift velocity of 54 keV energy electrons, thus highlighting the expected trajectory of the same group of particles.High variability and high flux intensity are retained within the blue regions through approximately half of a drift orbit until the electrons reach the postnoon sector.On the dawn side, the maximum superposed epoch fluxes decrease by almost an order of magnitude with increasing MLT toward noon.Once on the dusk side, the fluxes do not appear to exceed the asymptotic flux but approach the same value of the asserted LEO limit from below, before slowly decreasing with low variability.
Figure 4 shows a characterization of the superposed epoch precipitating electron flux in the same format as Figure 3.It reveals that the electron precipitation is also the strongest during times when the fluxes are above the estimated asymptotic flux.In the MLT sectors from 0 to 15 MLT, the peak precipitation also follows the blue electron trajectories.The magnitude of the precipitating electron flux on the dusk side (when the POES 90° electron fluxes are at the asymptotic limit and the near-equatorial electron fluxes are below the K-P limit) is almost an order of magnitude lower than the maximum precipitation in those MLT sectors observed a few hours earlier in the storm, and almost two orders of magnitude lower than the maximum precipitation levels on the dawn side along the same drift trajectory.This level remains almost unchanged in the 15-24 hr MLT sectors.Figure S2 in Supporting Information S1 also shows the ratio between POES 0° and POES 90° electron fluxes.In some studies, this ratio has been related to the amplitude of chorus waves, with higher wave intensities tending to be observed as the ratio gets closer to one (Li et al., 2013).Figure S2 in Supporting Information S1 shows that this ratio is also highest in the nightside-dawn MLT sector during the periods when the K-P limit is reached or exceeded.This suggests the generation of high amplitude chorus waves in that region, consistent with the K-P mechanism.Interestingly, substantial precipitating flux, as well as the flux ratio being close to one, is measured in the pre-and post-midnight sectors during the early stages of the storm main phase, seemingly unconnected to the fluxes reaching the K-P limit.This paper does not focus on investigating the causes of the earlier precipitation in the 15-24 MLT sectors; however, losses associated with the nightside dipolarizations or with chorus or hiss are possible candidates.
The observed behavior along the injected electron drift trajectory can be associated with an active loss process which is directly related to the amount of electron flux present in the radiation belts through the action of the K-P The central MLT diagram shows a colormap of the median electron flux in the blue-shaded regions, with the radial width of each MLT bin representing the interquartile separation.The schematic electron injection trajectories are obtained by integrating equations for the guiding-center motion (see e.g., Northrop, 1963) in a dipole field with a Kp-dependent electric field potential (Stern, 1975;Volland, 1973).
process.The increase of near-equatorial electron flux in the dawn sector above the K-P limit is associated with the trapped POES fluxes being elevated above their estimated asymptotic levels (see Section 2 for more detail) and the highest intensity precipitation is also observed at that time.Notably, and according to Figure 3, the median fluxes in the 3 to 9 MLT sectors exceed their asymptotic level by the largest margin.In the other MLT sectors, this feature is less prevalent but continues to ∼15 MLT.The 3 to 9 MLT dawn sector is also expected to be associated with the highest intensity of newly injected electrons that drift eastward and follow the drift trajectories schematically shown in Figure 3.This MLT region is also associated with the highest intensity of chorus waves (e.g., Chen et al., 2014;Meredith et al., 2014;Shprits et al., 2023), and was related to fast chorus wave transport in simulations by Tao et al. (2011).Therefore, the results presented in Figures 3 and 4 point toward a scenario where electron injections drive fast pitch angle transport and intense electron precipitation along their drift trajectories.Once injected into the nightside magnetosphere, the electrons would drift eastward, increasing the electron flux in the radiation belts in that MLT sector, thus driving intense chorus waves.A key issue is the extent to which the K-P flux capping process plays a key role in driving the most intense precipitation.
In our view, because electron injections represent a very fast process for increasing the electron flux during the main phase of the storm, they may increase electron fluxes above the K-P limit, thus resulting in a generation of a distinct population of very intense chorus waves associated with the K-P process (cf., Chakraborty et al., 2022).This drives fast pitch angle transport and intense precipitation, increasing both trapped and precipitating fluxes at LEO, which are measured by the POES 90° and 0° detectors respectively (Figures 3  and 4).The very strong precipitation and active pitch angle transport are present until the fluxes are lowered below the K-P limit.Figures 3 and 4 clearly show that by the time electrons drift into the post-noon and dusk regions, the precipitation has subsided dramatically and the trapped fluxes at POES 90° detector only reach their asymptotic levels from below.This is also related to the electron flux at the Van Allen Probes reaching the K-P limit from below in the dusk sector (Figure 1c).This explanation is consistent with the data presented in Figure 3 as it clearly shows that the injected flux above the limit is gradually lowered over the course of 90 min along half of a drift orbit, while it remains close to the limit thereafter for days after the end of the main phase and only decays very slowly.

Discussion and Conclusions
Overall, this paper presents strong evidence for the key role of the flux capping associated with a Kennel-Petscheklike process in producing the most intense electron precipitation during magnetic storms.In particular, we show that: 1.The electron precipitation into the atmosphere is the highest during periods when the near-equatorial electron flux exceeds the (Kennel & Petschek, 1966) limit.When compared to the precipitation fluxes during the pre-storm or recovery phases, the K-P-related precipitation is more than 100 times more intense.Chakraborty et al. (2022) also showed that the K-P limiting processes are associated with the generation of a separate population of very intense chorus waves.2. During the storm main phase, electron injections are responsible for increasing the electron flux above the K-P limit, resulting in fast pitch angle transport and intense precipitation into the loss cone.These K-P-related processes act to lower the source electron population below K-P the limit along half of an electron drift orbit in the heart of the radiation belt (∼1.5 hr), resulting in the highest trapped and precipitating fluxes to be measured on the dawn side of the magnetosphere.3. The electron fluxes exceed the K-P limit predominantly on the dawn side.The dawn MLT region is also associated with the highest intensity precipitation reported here, as well as with the highest chorus wave activity as reported in many earlier studies (e.g., Aryan et al., 2022;Chakraborty et al., 2022;Chen et al., 2014).
An important future consideration is the nature of the wave-particle interactions which lead to natural self-limiting of the electron flux, especially in light of recent studies showing the potential importance of the nonlinear chorus wave-particle interaction.For example, studies by Zhang et al. (2022Zhang et al. ( , 2023) ) show how a nonlinear interaction between high amplitude chorus waves and electrons can cause "superfast" precipitation on much shorter timescales than predicted by quasilinear theory.Meanwhile, the studies by Allanson et al. (2021), Artemyev et al. (2022), andTsai et al. (2022) further reveal the importance of this type of interaction for fast pitch angle transport.Moreover, nonlinear interactions have also been shown to be associated with microburst precipitation (Mozer et al., 2018;Shumko et al., 2018) Regardless of the nature of the wave-particle interactions associated with flux capping, the K-P theory (Mauk & Fox, 2010) appears to provide a flux limit in close agreement with observations (e.g., Olifer et al., 2021).The exact role of the nonlinear processes acting during periods when the K-P limit is exceeded remains an open question.
Finally, we can assess the role of the K-P-related processes in driving energy input into the atmosphere from particle precipitation.Figures 1 and 4 clearly show that the precipitation observed by the POES 0° detector during the one-day periods when the K-P flux limit is exceeded by near-equatorial electrons is almost 50 times higher than at any other time.The average frequency of geomagnetic storms of at least moderate intensity has also been investigated in a number of studies, with one storm every ∼20 days being a conservative estimate (e.g., Reyes et al., 2021).This results in substantial energy input into the atmosphere during these one-day periods of storm main phase K-P-related activity which is on average at least 2 times larger than the integrated energy input from precipitation from all other times between the occurrence of moderate storms.While these simple statistical estimates require a more detailed evaluation, for example, through the use of more accurate models that incorporate electron effects on the upper layers of the atmosphere (e.g., Fang et al., 2008;Seppälä et al., 2014), the results presented in this paper clearly reveal the importance and indeed potential dominance of Kennel-Petschek self-limiting processes for magnetosphere-atmosphere-climate coupling.

Figure 1 .
Figure 1.Superposed epoch 54 keV electron differential flux measured by the Van Allen Probes (here labeled as the Radiation Belt Storm Probes, RBSP) and POES in the dawn (3-9 MLT) and dusk (15-21 MLT) sectors during geomagnetic storms with Dst ≤ −50 nT.Left column, median flux in the dawn MLT sector as a function of L shell and superposed epoch time.Center and right columns, median flux (scatter points) with upper and lower quartiles (error bars) in dawn and dusk MLT regions, respectively, at fixed L of 4.5 as a function of superposed epoch.a, 90° pitch angle electron flux from the Magnetic Electron-Ion Spectrometer (MagEIS) (Blake et al., 2013) instrument on board of the Van Allen Probes.(d, g) Trapped and precipitating differential electron flux derived from integral flux measurements in two energy channels of the Medium Energy Proton and Electron Detectors (MEPED) on board POES in the dawn MLT sector.(b, c) 90° pitch angle electron flux from the Van Allen Probes measurements plotted with the superposed epoch Kennel-Petschek (K-P) limit in red with the K-P model uncertainty in blue.(e, f) Trapped electron flux in the 90°-detector of POES (center on ∼6.5° equatorial pitch angle).The red line shows an estimated asymptotic flux level at the POES altitudes (see text for details).(g, h) Precipitating electron flux in the 0°-detector of POES (center on ∼2.2° equatorial pitch angle).

Figure 2 .
Figure 2. Equatorial pitch angle distributions of the 54 keV energy electron flux normalized to the 90° pitch angle during selected geomagnetic storms in the dawn-side MLT sector at L of 4.5.All panels show superposed epoch median electron flux from the Van Allen Probes (circular symbols) and POES (square symbols) with the corresponding upper and lower quartiles represented by error bars.The red dashed line shows a sin 0.6 α eq pitch angle distribution used for the Kennel-Petschek limit calculation(Mauk & Fox, 2010) and the gray shaded bands show the regions of the local bounce loss cone.Each panel also labels the absolute value of the median electron flux for the 90° pitch angle electrons from the Van Allen Probes and for the precipitating electrons from POES.Panels (a) through (d) show different characteristic times during the geomagnetic storms.

Figure 3 .
Figure 3. 54 keV energy superposed epoch trapped electron differential flux from the POES 90° detector in different MLT sectors at L = 4.5.Eight panels on the periphery of the figure show the temporal evolution of the 90°-detector median electron flux, and its quartiles, plotted together with the estimated asymptotic flux limit in the same format as Figures 1e and 1f.The blue-shaded region represents and asserted MLT trajectory of the same group of electrons that are injected into the radiation belt around zero epoch and drift around the Earth over the course of a single drift obit (drift time of a 54 keV electron in the dipole field at L = 4.5 is ∼4.5 hr).The central MLT diagram shows a colormap of the median electron flux in the blue-shaded regions, with the radial width of each MLT bin representing the interquartile separation.The schematic electron injection trajectories are obtained by integrating equations for the guiding-center motion (see e.g.,Northrop, 1963) in a dipole field with a Kp-dependent electric field potential(Stern, 1975;Volland, 1973).

Figure 4 .
Figure 4. 54 keV energy superposed epoch precipitating electron differential flux from the POES 0° detector in different MLT sectors at L = 4.5.Same format as Figure 3.