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Whistler‐mode hiss waves are crucial to the dynamics of Earth's radiation belts, particularly in the scattering and loss of energetic electrons and forming the slot region between the inner and outer belts. The generation of hiss waves involves multiple potential mechanisms, which are under active research. Understanding the role of hiss waves in radiation belt dynamics and their generation mechanisms requires analyzing their temporal and spatial evolutions, especially for strong hiss waves. Therefore, we developed an Imbalanced Regressive Neural Network (IR‐NN) model for predicting hiss amplitudes. This model addresses the challenge posed by the data imbalance of the hiss data set, which consists of predominantly quiet‐time background samples and fewer but significant active‐time intense hiss samples. Notably, the IR‐NN hiss model excels in predicting strong hiss waves (>100 pT). We investigate the temporal and spatial evolution of hiss wave during a geomagnetic storm on 24–27 October 2017. We show that hiss waves occur within the nominal plasmapause, and follow its dynamically evolving shape. They exhibit intensifications with 1 and 2 hr timescale similar to substorms but with a noticeable time delay. The intensifications begin near dawn and progress toward noon and afternoon. During the storm recovery phase, hiss intensifications may occur in the plume. Additionally, we observe no significant latitudinal dependence of the hiss waves within |MLAT| < 20°. In addition to describing the spatiotemporal evolution of hiss waves, this study highlights the importance of imbalanced regressive methods, given the prevalence of imbalanced data sets in space physics and other real‐world applications. Plain Language Summary: Whistler‐mode hiss waves play a crucial role in understanding the dynamics of Earth's radiation belts, particularly scattering and loss of energetic electrons and the formation of the slot region. The underlying generation mechanisms of hiss wave sources remain an active area of research, which needs to quantify the global evolution of these waves, especially powerful ones. We developed an Imbalanced Regressive Neural Network (IR‐NN) model, which excels at accurately predicting strong hiss wave activity, that is of particular interest in radiation belt studies. We analyzed the evolution of hiss waves during a geomagnetically active period in October 2017. We found that these waves predominantly occur within the plasmapause boundary and exhibit dynamics that follow the plasmapause's changes. These waves strengthen on timescales similar to those of magnetospheric substorms, with a slight delay, and move to different local times during different phases of the storm. These waves maintain uniform intensity across low to mid‐latitudes. This study underlines the importance of imbalanced regressive methods in handling imbalanced data sets, a common challenge in space physics and related physical science fields. This approach is not only significant for advancing our understanding of space weather phenomena but also has broader implications in other areas. Key Points: An imbalanced regressive neural network model of hiss amplitude developed that predicts quiet‐time background and active‐time intense wavesHiss waves are well organized inside the plasmapause and follow its dynamic shape, evolving from dawn toward later local time during a stormModeled hiss evolution correlates with chorus, supporting the hypothesis that hiss is generated by evolving chorus waves [ABSTRACT FROM AUTHOR]

Whistler mode waves in the plasmasphere and plumes drive significant losses of energetic electrons from the Earth's radiation belts into the upper atmosphere. In this study, we conducted a survey of amplitude‐dependent whistler wave properties and analyzed their associated background plasma conditions and electron fluxes in the plasmasphere and plumes. Our findings indicate that extremely large amplitude (>400 pT) whistler waves (a) tend to occur at L > 4 over the midnight‐dawn‐noon sectors and have small wave normal angles; (b) are more likely to occur during active geomagnetic conditions associated with higher fluxes of anisotropic electrons at 10 s keV energies; and (c) tend to occur at higher latitudes up to 20° with increasing amplitude. These results suggest that extremely large amplitude whistler waves in the plasmasphere and plumes could be generated locally by injected electrons during substorms and further amplified when propagating to higher latitudes. Plain Language Summary: Whistler mode waves are known as one of the primary drivers of precipitating energetic electrons from the Earth's radiation belts into the upper atmosphere. We utilize plasma wave observations from the Van Allen Probes mission and conduct a survey of whistler mode waves inside the plasmasphere and plumes, which are plasma regions surrounding the Earth and filled with high‐density cold electrons. Statistical results indicate that extremely large amplitude whistler waves are more likely to occur at large L shells (L shell is defined as the distance from magnetic field lines to the center of the Earth at the magnetic equator) in the post‐midnight sectors during active geomagnetic conditions associated with high fluxes of tens of keV electrons exhibiting anisotropic pitch angle distributions (with a flux peak in the direction that is perpendicular to the background magnetic field). These waves tend to occur at higher latitudes with increasing amplitude. Results suggest that these waves could be generated locally by injected electrons during substorm activity and may be further amplified when propagating to higher latitudes. Key Points: Van Allen Probes wave measurements are used to statistically analyze the whistler waves in the plasmasphere or plume regionsExtremely large amplitude (>400 pT) whistler waves tend to occur at L shells >4 over 0–18 hr MLT with small wave normal angles (<10°)Larger amplitude whistler waves are observed during more active substorm activities and higher magnetic latitudes [ABSTRACT FROM AUTHOR]

Whistler‐mode chorus waves play an essential role in the acceleration and loss of energetic electrons in the Earth's inner magnetosphere, with the more intense waves producing the most dramatic effects. However, it is challenging to predict the amplitude of strong chorus waves due to the imbalanced nature of the data set, that is, there are many more non‐chorus data points than strong chorus waves. Thus, traditional models usually underestimate chorus wave amplitudes significantly during active times. Using an imbalanced regressive (IR) method, we develop a neural network model of lower‐band (LB) chorus waves using 7‐year observations from the EMFISIS instrument onboard Van Allen Probes. The feature selection process suggests that the auroral electrojet index alone captures most of the variations of chorus waves. The large amplitude of strong chorus waves can be predicted for the first time. Furthermore, our model shows that the equatorial LB chorus's spatiotemporal evolution is similar to the drift path of substorm‐injected electrons. We also show that the chorus waves have a peak amplitude at the equator in the source MLT near midnight, but toward noon, there is a local minimum in amplitude at the equator with two off‐equator amplitude peaks in both hemispheres, likely caused by the bifurcated drift paths of substorm injections on the dayside. The IR‐based chorus model will improve radiation belt prediction by providing chorus wave distributions, especially storm‐time strong chorus. Since data imbalance is ubiquitous and inherent in space physics and other physical systems, imbalanced regressive methods deserve more attention in space physics. Plain Language Summary: Whistler‐mode chorus waves are essential in accelerating radiation belt electrons. However, predicting the amplitude of strong chorus waves is difficult because of their imbalanced nature. In other words, there are many more observations of no‐chorus waves than strong chorus waves. A consequence is that these no‐chorus wave data dominate traditional models, so these models usually predict values that are too small for strong waves. Using an imbalanced regressive method, we developed a machine learning (ML) model of lower‐band chorus wave amplitude. For the first time, the ML‐chorus model can predict the amplitude of strong chorus waves. The ML‐chorus model shows the evolution of the chorus wave at the equator, similar to the drift path of injected electrons, which brings electron anisotropy that generates chorus waves. The ML‐chorus model shows that the chorus waves are stronger at the equator near midnight, the source region of plasma injection. Away from midnight, the chorus waves have an equatorial minimum instead. Our chorus model will improve the forecast of the radiation belt environment by providing chorus wave distributions, especially large‐amplitude strong chorus during geomagnetic storms. Because data imbalance is commonly seen in space physics and other physical systems, imbalanced regressive methods require more attention. Key Points: A neural network model of lower‐band chorus wave amplitude is developed using imbalanced regressionFor the first time, a chorus model can predict the large amplitude of strong chorus wavesChorus' evolution is consistent with electron injection drift paths, peak equatorial amplitude near midnight, and off‐equator peaks at noon [ABSTRACT FROM AUTHOR]

A mechanism recently proposed for magnetospheric electron loss into the atmosphere is the precipitation directly driven by ultralow‐frequency (ULF) waves. In this study, we quantitatively analyze the properties of ULF wave‐induced precipitation by simulating the electron bounce and drift motion in poloidal‐mode waves excited in a dipole magnetic field. Our results reveal that precipitation occurs only when electrons encounter a westward‐directed wave electric field in the magnetosphere, which leads to cross‐field energy enhancements and reduces their mirror heights. The simulations also demonstrate longer duration electron precipitation at the drift‐resonance energy. We calculate the temporal variations of the energy spectrum for precipitating electrons and the total precipitating energy fluxes. These results improve our understanding of ULF wave‐induced electron precipitation as well as provide a point of comparison for observations from balloons or ground‐based instruments. Plain Language Summary: Electron precipitation into the atmosphere is a major mechanism for electron loss in the radiation belts. A critical driver for the precipitation is the pitch‐angle scattering induced by various plasma waves in the frequency range between several hertz and tens of kilohertz. On the other hand, ultralow‐frequency (ULF) waves on the order of several millihertz are usually believed to play an indirect role, by modulating other types of waves. Here, we investigate a recently proposed mechanism of electron precipitation directly driven by ULF waves, by simulating electron motion within a poloidal‐mode wave field. The simulations, which cover electron bounce and drift time scales, reveal the important role of the azimuthal wave electric field in the induced electron precipitation. The precipitation occurs when the electrons encounter a westward‐directed electric field, which accelerates the electrons and reduces their mirror heights. The induced precipitation also shows an energy dependence; electrons at the drift‐resonance energy, which encounter a sustained westward‐directed electric field, would have longer precipitation duration than non‐resonant electrons. We further calculate the energy spectrum and the total fluxes of the precipitating electrons directly driven by ULF waves, and demonstrate that the effect could be potentially comparable to that caused by other magnetospheric waves. Key Points: We investigate electron precipitation driven by poloidal‐mode ultralow‐frequency waves that perturb the electron dynamics over bounce and drift timescalesPrecipitation occurs when electrons encounter westward electric fields, which enhance their cross‐field energy and reduce the mirror heightsDrift‐resonant electrons can continuously encounter westward electric fields to have longer precipitation duration than non‐resonant ones [ABSTRACT FROM AUTHOR]

Chorus waves outside the plasmapause influence the Earth's radiation belt dynamics by interacting with energetic electrons via cyclotron and Landau resonance. Recent numerical diffusion experiments indicate that the diffusion process is sensitive to the spatial and temporal scale of variability in the wave‐particle interaction, which is reported to be more efficient than that based on the traditional average model. Using Van Allen Probes A and B data from November 2012 to July 2019, the spatial and temporal scale size of chorus waves are calculated by the correlation between the wave amplitudes detected by two satellites with varying spatial separation or time lag. We found that, the chorus wave is incoherent when the spatial extent is greater than 433 km or the time lag lasts ∼10 s, which are significantly smaller than that of plasmaspheric hiss. In addition, the spatial correlations of chorus tend to be higher near noon or with lower geomagnetic activity. The temporal correlations of chorus are always statistically near zero, which are not influenced by the location and geomagnetic activity. Our results can help refine the model of the interactions between energetic particles and chorus waves in the radiation belt. Key Points: Chorus waves tend to be incoherent when the spatial extent is greater than 433 km or the time lag lasts 10 s at <∼6.5The spatial scale size of chorus wave is relatively larger near noon or with lower geomagnetic activityThe temporal scale size of chorus wave is always statistically near zero, not influenced by L‐shell, magnetic local time, or AL* index [ABSTRACT FROM AUTHOR]

We use data from eight satellites to statistically examine the role of chorus as a potential source of plasmaspheric hiss. We find that the strong equatorial (|λm| < 6°) chorus wave power in the frequency range 50 < f < 200 Hz does not extend to high latitudes in any magnetic local time sector and is unlikely to be the source of the low frequency plasmaspheric hiss in this frequency range. In contrast, strong equatorial chorus wave power in the medium frequency range 200 < f < 2,000 Hz is observed to extend to high latitudes and low altitudes in the pre‐noon sector, consistent with ray tracing modeling from a chorus source and supporting the chorus to hiss generation mechanism. At higher frequencies, chorus may contribute to the weak plasmaspheric hiss seen on the dayside in the frequency range 2,000 < f < 3,000 Hz band but is not responsible for the weak plasmaspheric hiss on the nightside in the frequency range 3,000 < f < 4,000 Hz. Plain Language Summary: Plasma waves in space, known as plasmaspheric hiss, are responsible for the formation of the slot region between the inner and outer radiation belt. The waves occur in the frequency range from 20 Hz to several kHz and are typically observed close to the planet in the high density plasmasphere from 2 to 4 RE(Earth radii) in the magnetic equatorial plane. In this study, we use data from eight satellites to statistically examine the role of a different plasma wave, known as chorus, as a potential source of plasmaspheric hiss. Chorus is observed further from the planet, in a lower density region known as the plasma trough and ranging from 5 to 10 RE from the planet in the equatorial plane. We find that chorus waves in the frequency range 50 < f < 200 Hz are well separated from the plasmaspheric hiss closer to the planet and are unlikely to be the source of low frequency plasmaspheric hiss. In contrast, chorus waves in the medium frequency range 200 < f < 2,000 Hz are observed to extend to high latitudes and low altitudes in the pre‐noon sector, consistent with ray tracing modeling from a chorus source and supporting the chorus to hiss generation mechanism. Key Points: Chorus is an important source of medium frequency plasmaspheric hiss (200 < f < 2,000 Hz)Chorus is unlikely to be the source of low frequency plasmaspheric hiss (50 < f < 200 Hz)We identify the strong emissions in the 2,000–4,000 Hz band on the dawnside during active conditions as chorus waves outside the plasmapause [ABSTRACT FROM AUTHOR]

We extend our database of whistler mode chorus, based on data from seven satellites, by including ∼3 years of data from Radiation Belt Storm Probes (RBSP)‐A and RBSP‐B and an additional ∼6 years of data from Time History of Events and Macroscale Interactions during Substorms (THEMIS)‐A, THEMIS‐D, and THEMIS‐E. The new database allows us to probe the near‐equatorial region in detail, revealing new features. In the equatorial source region, |λm|<6°, strong wave power is most extensive in the 0.1–0.4fce bands in the region 21–11 magnetic local time (MLT) from the plasmapause out to L∗ = 8 and beyond, especially near dawn. At higher frequencies, in the 0.4–0.6fce frequency bands, strong wave power is more tightly confined, typically being restricted to the postmidnight sector in the region 4

We analyze an energetic electron flux enhancement event in the inner radiation belt observed by Van Allen Probes during an intense geomagnetic storm. The energetic electron flux at L~1.5 increased by a factor of 3 with pronounced butterfly pitch angle distributions (PADs). Using a three‐dimensional radiation belt model, we simulate the electron evolution under the impact of radial diffusion, local wave‐particle interactions including hiss, very low frequency transmitters, and magnetosonic waves, as well as Coulomb scattering. Consistency between observation and simulation suggests that inward radial diffusion plays a dominant role in accelerating electrons up to 900 keV and transporting the butterfly PADs from higher L shells to form the butterfly PADs at L~1.5. However, local wave‐particle interactions also contribute to drive butterfly PADs at L ≳ 1.9. Our study provides a feasible mechanism to explain the electron flux enhancement in the inner belt and the persistent presence of the butterfly PADs at L~1.5. Plain Language Summary: Electron flux enhancements can occur in the Earth's inner belt and slot region during geomagnetically active times. Recent studies have reported that butterfly pitch angle distributions (PADs) of energetic electrons exist persistently at L~1.5. However, it is still not well understood about the underlying mechanism that causes such electron enhancement at L < 2.5 and butterfly PADs that are always observed at L~1.5. In this letter, we present two‐month observations of electron flux, demonstrating that butterfly PADs were first formed at higher L shells and then gradually transported inward to lower L shells. By performing a three‐dimensional radiation belt simulation and further comparing the results with observation, we have found that inward radial diffusion plays a dominant role in electron flux enhancement, while local wave‐particle interactions barely contribute to electron flux enhancement but can drive butterfly PADs at L ≳ 1.9. Our study provides a feasible mechanism to explain the electron flux enhancement in the inner belt and the persistent presence of the butterfly PADs at L~1.5. Key Points: The flux enhancement up to 900 keV at L < 2.5 during active times is reproduced by our simulation using enhanced inward radial diffusionThe persistent butterfly PADs at L ≃ 1.5 are mainly due to the inward radial transport of those formed locally at higher L shellsLocal wave‐particle interaction plays a minor role in the electron flux enhancement in the inner radiation belt but can drive butterfly PADs [ABSTRACT FROM AUTHOR]