On August 10, 2015, BARREL balloon payload 3 A observed bremsstrahlung x-rays (∼5–150 keV) attributed to precipitation of energetic electrons with energies < 200 keV. The balloon was located over Kiruna, Sweden, and magnetically conjugate to the Van Allen Probes (RBSP) spacecraft as they entered a region of high plasma density. The high density region was spatially confined and persisted for multiple orbits indicating that it is a plasmaspheric plume or detached plasma region. Strong whistler-mode hiss waves were observed by both spacecraft in the high density region.

Plasmaspheric hiss is a major driver of radiation belt loss inside the plasmasphere, contributing to the creation of the slot region between the inner and outer radiation belts (Lyons and Thorne, 1973). These low-frequency (∼50 Hz-2 kHz) electromagnetic whistler-mode waves are broadband and incoherent. Their power is also proportional to the density, with more power in dense regions (Malaspina et al., 2016; Malaspina et al., 2018). Recent RBSP observations and simulations demonstrate the importance of hiss waves; these waves generate major loss up to L = 5.5 from pitch angle diffusion when the plasmasphere is widely extended during quiet times (Ripoll et al., 2016; Ripoll et al., 2017; Ripoll et al., 2019). More information about hiss waves and the dynamics of the radiation belts can be found in the review of Ripoll et al. (2020a).

Outside the plasmasphere, at higher L-values, energetic electron precipitation has been primarily attributed to whistler mode chorus waves or electromagnetic ion cyclotron (EMIC) waves [e.g., Millan and Thorne (2007); Thorne (2010)]. Recent work suggests that hiss may also be active at higher L-values in dense plasmaspheric plumes and detached plasma regions. A plasmaspheric plume (also called a “tail” in the literature) is a narrow region of dense cold plasma that extends out from the main plasmasphere at Earth. The EUV instrument on the IMAGE spacecraft provided the first global observations of plasmaspheric plumes, their formation and evolution (Sandel et al., 2001; Goldstein, 2004). Plume evolution is driven by changes in the dawn-dusk convection electric field due to changes in the solar wind (Grebowsky, 1970; Lemaire, 2000). A sudden increase in the convection electric field causes the plasmapause boundary to move inward leaving behind plasma that E × B drifts towards the dayside, forming a dayside plume that is wide in magnetic local time (MLT). With a subsequent decrease in the convection electric field, the plume wraps around Earth and the MLT extent narrows. Spacecraft passing through a plume observe a localized increase in cold plasma density over a narrow range in MLT. In the absence of global imaging, the twin Van Allen Probes spacecraft, moving in similar orbits - one following the other, provide an opportunity to distinguish between temporal and spatial variations, helping to identify spatial density structures like plumes.

Properties of hiss waves in plumes have been statistically characterized in Shi et al. (2019). The occurrence rate of hiss in plumes has a clear dependence on MLT and geomagnetic activity, peaking near the dusk sector during active times. These waves are more powerful in plumes than inside the plasmasphere, particularly during active times, and have low wave normal angles compared to the wide wave distribution function in the plasmasphere. Plume whistler-mode waves were frequently observed by Van Allen Probes and may be an efficient loss mechanism for radiation belt seed electrons (Zhang et al., 2019). Zhang et al. (2018) calculated loss rates due to observed hiss emissions in a nightside plume and found that such emissions may result in fast (few hours) loss of 10–100 keV electrons at L in [4.5, 5.5] and a slower decay of higher energy particles. Li et al. (2019) examined a particular event and found that plume whistler mode waves are an effective pitch-angle scattering mechanism, particularly for electrons with energies from tens to hundreds of keV.

In this paper, we investigate plume whistler-mode hiss waves as the primary cause of the energetic electron precipitation observed by BARREL balloon 3 A on 10 August, 2015. The observations are described in Section 2.1. Data from Van Allen Probes are used to precisely determine the properties of observed waves, trapped electrons, and cold plasma density. An event-driven quasi-linear diffusion model is then used (Section 2.2) to investigate wave-particle interactions between the plume whistler-mode waves and the trapped electrons, seeking to identify the theoretical energy of the precipitating electrons. We further investigate the time evolution of the electron phase space density.

Figure 5 shows the bounce averaged diffusion coefficients calculated using the input parameters described above. At large L-shell (e.g., in the outer belt or in plasmaspheric plumes, L ∼ 6), hiss waves will predominantly act on low energy electrons. Here, the diffusion coefficient for small pitch angle particles is largest between ∼10–150 keV, consistent with the energy of x-rays observed by BARREL. As mentioned previously, the diffusion coefficient is not drift-averaged and is representative of the wave particle interactions only within the plume. The waves were observed only within the plume region, extending ∼1 h of MLT, thus drift-bounce-averaged diffusion coefficients would be a factor 1/24 lower in amplitude. Here, due to the intense wave amplitude and the absence of MLT-averaging, diffusion coefficients reach very high rates with D _αα ∼10^{−2 s−1}. Since BARREL was located in the northern hemisphere, it observed predominantly local precipitation. This local bounce loss comes from the immediate and intense (low pitch angle) precipitation within the plume (thus proportional to the local wave amplitude squared) and is not the result of wave particle interactions all along the drift path (that would be proportional to the MLT-averaged squared amplitude, a factor 1/24 lower in this case).

Figure 6 shows the evolution of the phase space density for electrons as a function of energy, E, and equatorial pitch angle, α, from t = 0 to t = 100 min of interaction with hiss waves in the high-density region. The initial condition (top left panel) is f(t = 0, E) =  sin ^b(E)(α) −   sin ^b(E)(α _lc ). Sudden loss of 10–30 keV electrons occurs almost immediately, within the first 5 min, in the vicinity of the loss cone (Figure 6, top middle). Loss of 100 keV electrons by one order of magnitude takes 25 min of interaction. After 100 min (Figure 6, bottom right), the phase space density has vanished by ∼2 (resp. 1) orders of magnitude for all pitch angles below 70° for E in [20, 70] keV (resp [70, 200] keV). Note that electrons, particularly of higher energy, may interact with the plume multiple times as they gradient-curvature drift around Earth in order to reach a total of 100 min of interaction. 10 keV electrons with small pitch angle take ∼40 min to drift across the plume, thus the rapid loss of low energy electrons within the first 5 min occurs upon their first encounter with the plume. The predicted range of energies of the main loss are also in agreement with the range of energy found by Shi et al. (2019). Some loss of high energy electrons up to 1 MeV within the vicinity of the loss cone are also computed.

We also study the influence of the initial conditions on the loss and on the dynamics at early times, when pitch angle diffusion has not yet reached an equilibrium state. Figure 7 shows the evolution of the PSD in the vicinity of the loss cone (at α = 7.95°, rounded to 7° in the figure’s label) during the first 100 min of interaction with hiss waves. Comparing the top and bottom rows of Figure 7 illustrates the important role of the loss cone regularization. Comparing lines within each figure allows to see the influence of the b(E) power index, with two limits bounding the variations. The low limit b(E) → 0 (i.e. b = 0.01) is equivalent to the widely used and standard f(t = 0, α) = 1 initial condition, either dropping abruptly from one for α ≠ α _lc to 0 for α = α _lc if there is no regularization (top row) or going continuously from one to 0 if regularized (bottom row). The second limit of b(E) → 1 is a PSD approaching sin(α) and with significant gradient at intermediate pitch angle. Figure 7 provides interesting new insight into the dynamics and how they are modeled. First, as expected, the larger the gradient at the loss cone, the more intense will be the loss in the vicinity of the loss cone and at the earliest times (generally below 1 min for our case, depending on energy). The regularization, which can be seen as a continuous process to fill out the loss cone, limits the gradient and thus the intensity of the earliest loss. In turn, large b(E) power index leads to intermediate pitch angle diffusion that will make the overall loss-gain budget at fixed pitch angle to lean in favor of a temporary growth of the PSD level during the earliest times. This is better seen in the presence of the regularization (since loss is even milder). On the contrary, without regularization the loss can dominate for certain low energy and b(E), and temporary growth can no longer exist. Most past parameter studies in the literature have been done with f(t = 0, α) = 1 and f(t = 0, α _lc ) = 0 (e.g., Shprits et al. (2008)) so that PSD growth could not be seen. This is because the infinite gradient at the loss cone creates intense sudden loss, and the absence of other gradients with respect to pitch angle make the appearance of temporary PSD growth impossible. This explains why this particular behavior has not been discussed in the past (to the authors’ knowledge).

The temporary growth of the PSD can be best analyzed and understood looking at Figure 8 in which we see a temporary growth happening for times below 5 min at 135 keV for equatorial pitch angle between ∼12 and ∼40°. The growth is due to the diffusion coefficient whose maximum (first cyclotron resonance) is located above 40° for 135 keV (cf. Figure 5). That diffusion turns out to be faster than the diffusion of the lower pitch angles below 40°and outside the loss cone vicinity region. High pitch angle electrons (40°–75°) thus diffuse faster and fill out lower pitch angles (∼12°–40°) causing the flux at low pitch angles to rise progressively during the first 3–5 min. That type of diffusion explains the various growths of PSD we see happening in time in Figure 7. Comparison of Figure 8 with Figure 7 also shows that the growth cannot happen at ∼7° for this energy and initial condition for which the absence of regularization in this example increases the gradient at the loss cone and favors the loss.

Figure 9 shows the evolution of the PSD using the specific energy-dependent b(E) observed by RBSP-B. In addition, we plot in Figure 10 the respective instantaneous growth (τ > 0) and loss rates (τ < 0), previously discussed. We define these rates as 1/τ = |Δf(t)/Δt| in units of hours. The considerable variation of τ with time (including a change of sign) shows that steady state, which defines the general electron lifetime (Lyons et al., 1972), is not reached within the first 100 min for most of the energies below 200 keV. At 74 keV, we see, for instance, a fast loss rate of ∼12 min persisting during ∼30 min, which signifies that the flux decreases by a factor e ¹ every 12 min during 30 min, i.e. a factor of e ^(30/12) = 12 after 30 min. The constant loss rate during that time is controlled by the largest gradients, which flatten as diffusion occurs. After 30 min, the loss rate of 74 keV starts to increase and reaches a plateau value at ∼80 min, which is the steady state value. This is in agreement with the theoretical lifetime from direct steady state computation for 74 keV electron that is 90 min for this problem. Therefore, during the first 30 min that followed the growth phase, the loss is 7.5 times faster than the lifetime would predict. After 100 min, the 49 and 74 keV electron flux are reduced by two orders of magnitude and the 100–200 keV electron flux is reduced by ∼1 order of magnitude. The initial electron energy distribution observed by RBSP is exponential and also strongly weighted towards lower energies (Figure 4), thus the precipitation observed by BARREL was also dominated by these energies.

An event-based study was conducted to investigate wave-particle interactions in the radiation belts. A fortuitous magnetic conjunction between the RBSP spacecraft and BARREL balloon payload 3 A provided a rare opportunity to study pitch-angle scattering by plume whistler-mode hiss waves. A quasi-linear pitch angle diffusion model was developed using wave and plasma parameters observed by RBSP as they passed through a stable region of dense cold plasma (n ∼80 cm⁻³) near L = 6. The model results show that interaction with the plume hiss waves leads to rapid loss of electrons over the same energy range observed by BARREL. Moreover, a significant decrease in the trapped electron flux can occur within 2 h for electrons of pitch angle up to 70° for E in [50, 100] keV.

We also examined the effects of the initial pitch-angle distribution that is assumed when evolving the phase space density. Many previous studies assume a completely empty initial loss cone distribution which leads to an artificially rapid loss rate due to the very steep gradient at the loss cone. Regularization of the loss cone distribution reduces this effect and also reveals how diffusion from larger pitch angles can actually cause an initial increase in flux near the loss cone. This effect is very sensitive to the initial pitch angle distribution assumed for a given energy. These results illustrate the importance of modeling the dynamic evolution of the PSD; the assumption of steady-state loss lifetimes is not accurate for event-based studies such as this one, since the event duration is comparable to the time to reach a steady state. We incorporated the observed pitch angle distribution into the dynamic model of PSD. The present study did not include the effects of the energy-dependent drift time for electrons, rather examined the evolution of the PSD as a function of total interaction time with the waves. The lowest energy (∼10 keV) electrons spend ∼ 40 min within the wave region (the plume) while higher energy (∼100 keV) electrons drift across the plume more quickly and may encounter the plume several times as they drift around Earth. In order to more accurately model the energy spectrum observed by BARREL, these effects must be included. The development of the model presented here will allow for such future work.

Recent work from the Van Allen Probes mission has revealed the prevalence of whistler-mode hiss waves in plasmaspheric plumes, and several studies have suggested that plume hiss waves could lead to strong loss of electrons. The event examined here occurred during a substorm injection of electrons into the radiation belts as observed by the RBSP MagEIS instruments. Thus it was not possible to separate the effects of acceleration and loss in order to quantify the overall impact of this plume on the radiation belts. However, the loss rate indicated by this study suggests that scattering by plume whistler-mode hiss waves, which is currently not included in radiation belt models, could be an important loss mechanism, particularly for radiation belt seed electrons. In particular, the plume investigated in this study was stable and persisted for several RBSP orbits. Electrons gradient-curvature drift around the earth many times per day and thus experience multiple encounters with such high-density plumes and the hiss waves they support. Future work should investigate the overall impact of plumes as a loss mechanism for radiation belt electrons and the seed particles that generate them.