Abstract Determination of electron phase space density (PSD) at a wide range of L‐shells with high temporal resolution is central to understanding acceleration, transport, and loss processes in Earth's radiation belts. However, cross‐mission comparisons of PSD are complicated by instrumental biases and differing orbital coverages. In this study, we develop and validate a cross‐calibrated PSD data set combining measurements from the Arase and Van Allen Probes missions across overlapping energy ranges. Using conjunctions between Arase's MEP‐e and HEP instruments with Van Allen Probe's MagEIS instrument, we quantify systematic differences in PSD observation for fixed adiabatic invariants and derive energy channel‐specific correction functions. The cross‐calibration procedure reduces systematic biases between instruments to below 5% and leads to statistically meaningful reductions in random error, with uncertainty estimates provided for each channel. This results in a continuous combined PSD product spanning energies from 35 keV to 1.6 MeV. The resulting data set provides internally consistent cross‐mission PSD observations, extending reliable coverage of the outer belt to higher L‐shells accessible to Arase.

The proton radiation belt contains high fluxes of adiabatically trapped protons varying in energy from similar to one to hundreds of megaelectron volts (MeV). At large radial distances, magnetospheric field lines become stretched on the nightside of Earth and exhibit a small radius of curvature RC near the equator. This leads protons to undergo field line curvature (FLC) scattering, whereby changes to the first adiabatic invariant accumulate as field strength becomes nonuniform across a gyroorbit. The outer boundary of the proton belt at a given energy corresponds to the range of magnetic L shell over which this transition to nonadiabatic motion takes place, and is sensitive to the occurrence of geomagnetic storms. In this work, we first find expressions for nightside equatorial RC and field strength Be as functions of Dst and L* to fit the TS04 field model. We then apply the Tu et al. (2014, ) condition for nonadiabatic onset to solve the outer boundary L*, and refine our expression for RC to achieve agreement with Van Allen Probes observations of 1-50 MeV proton flux over the 2014-2018 era. Finally, we implement this nonadiabatic onset condition into the British Antarctic Survey proton belt model (BAS-PRO) to solve the temporal evolution of proton fluxes at L <= 4. Compared with observations, BAS-PRO reproduces storm losses due to FLC scattering, but there is a discrepancy in mid-2017 that suggests a similar to 5 MeV proton source not accounted for. Our work sheds light on outer zone proton belt variability at 1-10 MeV and demonstrates a useful tool for real-time forecasting. Over 2014-2018, large geomagnetic storms resulted in field line curvature scattering of MeV trapped protons at L greater than or similar to 2.5 The nonadiabatic region subject to scattering can be predicted using an onset condition with Dst dependence The BAS-PRO model simulates scattering of outer zone proton flux during 2014-2018 using a method that can be applied in real time

Abstract We perform ensemble simulations of radiation belt electron acceleration using the quasi‐linear approach during the storm on 9 October 2012, where chorus waves dominated electron acceleration at L = 5.2. Based on a superposed epoch analysis of 11 similar storms when both multi‐MeV electron flux enhancements and chorus wave activities were observed by Van Allen Probes, we use percentiles to sample the normalized input distributions for the four key inputs to estimate their relative perturbations. Using 11 points in each input parameter including chorus wave amplitude Bw, chorus wave peak frequency fm, background magnetic field B0, and electron density Ne, we ran 114 simulations to quantify the impact of uncertainties in the input parameters on the resulting simulated electron acceleration by chorus. By comparing the simulations to observations, our ensemble simulations reveal that inaccuracies in all four input parameters significantly affect the simulated electron acceleration, with the largest simulation errors attributed to the uncertainties in Bw, Ne, and fm. The simulation can deviate from the observations by four orders of magnitude, while members with largest probability density (smallest perturbations in the input) provide reasonable estimations of output fluxes with log accuracy errors concentrated between ∼−2.0 and 0.5. Quantifying the uncertainties in our study is a prerequisite for the validation of our radiation belt electron model and improvements of accurate electron flux predictions.

Many Machine Learning (ML) systems, especially neural networks, are fundamentally regarded as black boxes since it is difficult to grasp how they function once they have been trained. Here, we tackle the issue of the interpretability of a high-accuracy ML model created to model the flux of Earth's radiation belt electrons. The Outer RadIation belt Electron Neural net model (ORIENT) uses only solar wind conditions and geomagnetic indices as input. Using the Deep SHAPley additive explanations (DeepSHAP) method, we show that the `black box' ORIENT model can be successfully explained. Two significant electron flux enhancement events observed by Van Allen Probes during the storm interval of 17 to 18 March 2013 and non storm interval of 19 to 20 September 2013 are investigated using the DeepSHAP method. The results show that the feature importances calculated from the purely data driven ORIENT model identify physically meaningful behavior consistent with current physical understanding.

We perform an ensemble of quasi‐linear diffusion simulations of the radiation belt electron flux decay for ∼6 days at L = 3.5 during the recovery phase of the storm on 7 November 2015, where plasmaspheric hiss dominantly drives the electron flux decay process. Based on Van Allen Probes measurements, we use percentiles to sample distributions of the four key input parameters, which are the hiss wave amplitude B w , hiss wave peak frequency f m , background magnetic field B 0 , and electron density N e , with 11 points representing that range of each input, leading to 11 4 (∼14,600) ensemble members. By developing a Lookup Table method to rapidly calculate the time‐dependent diffusion coefficients, the changing wave environment at every time step is incorporated into our ensemble simulations. The comparison between the ensemble simulations and observations reveals the influence of uncertainties in the input parameters on the simulated electron fluxes. Our results demonstrate that the perturbations in B w are the primary contributors for discrepancies between modeled and observed electron fluxes, while the simulation errors caused by variations in f m and N e are strongly energy‐dependent. The simulated electron flux using the wave parameters observed at the 50th percentile agrees with observations, and most of the simulation errors increase with decreasing observational probability density of the parameters, with the largest log accuracy ratio of ∼14. Our physics‐based ensemble modeling provides the essential information about the robustness of radiation belt simulation and forecast considering the uncertainties in the plasma wave measurement or parameterization.

Abstract Geomagnetically induced currents (GICs) at middle latitudes have received increased attention after reported power grid disruptions due to geomagnetic disturbances. However, quantifying the risk to the electric power grid at middle latitudes is difficult without understanding how the GIC sensors respond to geomagnetic activity on a daily basis. Therefore, in this study the question “Do measured GICs have distinguishable and quantifiable long‐period and short‐period characteristics?” is addressed. The study focuses on the long‐term variability of measured GIC, and establishes the extent to which the variability relates to quiet‐time geomagnetic activity. GIC quiet‐day curves (QDCs) are computed from measured data for each GIC node, covering all four seasons, and then compared with the seasonal variability of thermosphere‐ionosphere‐electrodynamics general circulation model (TIE‐GCM)‐simulated neutral wind and height‐integrated current density. The results show strong evidence that the middle‐latitude nodes routinely respond to the tidal‐driven Sq variation, with a local time and seasonal dependence on the direction of the ionospheric currents, which is specific to each node. The strong dependence of GICs on the Sq currents demonstrates that the GIC QDCs may be employed as a robust baseline from which to quantify the significance of GICs during geomagnetically active times and to isolate those variations to study independently. The QDC‐based significance score computed in this study provides power utilities with a node‐specific measure of the geomagnetic significance of a given GIC observation. Finally, this study shows that the power grid acts as a giant sensor that may detect ionospheric current systems.

Riometers are ground‐based passive radio receivers that detect cosmic noise emanating from distant stars and galaxies. Some of the radiowave energy from these galactic sources is absorbed in the lower ionosphere by free electrons, precipitated from magnetospheric sources. The eastward motion of magnetospheric electrons, due to the combined effects of convection and gradient and curvature drift, results in a delay in signal between ground stations separated by 100s and 1,000s of kilometers. In this study, the signal delay is used to infer the energy of trapped electrons by employing a full bounce‐averaged drift velocity computation using two semi‐empirical magnetic field models, an empirical electric field, and 13 Riometer stations in the NORSTAR ground observation network. It is shown statistically, that riometers respond to 20–80 keV electrons, and that the inferred energy rises with an increase in absorption. The inferred energy is also shown to depend on magnetic local time, and the choice of the magnetic field model. This study quantifies the capability to infer magnetically trapped electron energies from riometer signals. This important population of 10s of keV electrons acts as a source of electromagnetic wave energy, necessary for acceleration of trapped electrons to higher energies where they may be hazardous to space hardware.

The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.

Using Van Allen Probes' observations and established plasmapause location (Lpp) models, we investigate the relationship between the location of the initial enhancement (IE) of energetic electrons and the innermost (among all magnetic local time sectors) Lpp over five intense storm periods. Our study reveals that the IE events for ~30‐keV to ~2‐MeV electrons always occurred outside of the innermost Lpp. On average, the inner extent of the IE events (LIE) for <800‐keV electrons was closer to the innermost Lpp when compared to the LIE for >800‐keV electrons that was found consistently at ~1.5 RE outside of the innermost Lpp. The IE of tens of kiloelectron volts electrons was observed before the IE of hundreds of kiloelectron volt electrons, and the IE of >800‐keV electrons was observed on average 12.6 ± 2.3 hr after the occurrence of the earliest IE event. In addition, we report an overall electron (~30 keV to ~2 MeV) flux increase outside the plasmasphere during the selected storm periods, in contrast to the little change of energy spectrum evolution inside the plasmasphere; this demonstrates the important role of the plasmasphere in shaping energetic electron dynamics. Our investigation of the LIE‐Lpp relationship also provides insights into the underlying physical processes responsible for the dynamics of ~30‐keV to ~2‐MeV electrons.

Whistler mode exohiss are the structureless hiss waves observed outside the plasma pause with featured equatorward Poynting flux. An event of the amplification of exohiss as well as chorus waves was recorded by Van Allen Probes during the recovery phase of a weak geomagnetic storm. Amplitudes of both types of the waves showed a significant increase at the regions of electron density enhancements. It is found that the electrons resonant with exohiss and chorus showed moderate pitch angle anisotropies. The ratio of the number of electrons resonating with exohiss to total electron number presented in-phase correlation with density variations, which suggests that exohiss can be amplified due to electron density enhancement in terms of cyclotron instability. The calculation of linear growth rates further supports above conclusion. We suggest that exohiss waves have potential to become more significant due to the background plasma fluctuation.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.

This study is focused on understanding the coupling between different electron populations in the inner magnetosphere and the various physical processes that determine evolution of electron fluxes at different energies. Observations during the 17 March 2013 storm and simulations with a newly developed Versatile Electron Radiation Belt-4D (VERB-4D) are presented. Analysis of the drift trajectories of the energetic and relativistic electrons shows that electron trajectories at transitional energies with a first invariant on the scale of similar to 100 MeV/G may resemble ring current or relativistic electron trajectories depending on the level of geomagnetic activity. Simulations with the VERB-4D code including convection, radial diffusion, and energy diffusion are presented. Sensitivity simulations including various physical processes show how different acceleration mechanisms contribute to the energization of energetic electrons at transitional energies. In particular, the range of energies where inward transport is strongly influenced by both convection and radial diffusion are studied. The results of the 4-D simulations are compared to Van Allen Probes observations at a range of energies including source, seed, and core populations of the energetic and relativistic electrons in the inner magnetosphere.

The response of high-energy particle precipitation to substorm onset is investigated using observations of cosmic noise absorption by a 7 x 7 beam imaging riometer in Kilpisjarvi, Finland, and substorm onset information obtained from the IMAGE satellite. A new method is developed for automatic detection of absorption responses to substorm onsets. Superposed epoch analysis shows that absorption exhibits some fading prior to and a clear response preceding substorm onset. These features are interpreted as being due to the stretching of magnetic field lines and a rapid dipolarization during the late growth phase of a substorm. A distinct dependence on substorm onset location is discovered with response delay increasing with distance from substorm onset and all responses to closest substorms (within 250 km) preceding substorm onset by 1-5 min. The absorption propagation is further examined using the average velocity from the onset to the riometer location as well as instantaneous velocities for a short period of time when substorm-enhanced absorption reaches the field of view. Comparison of the two velocity estimates shows that the absorption propagation is slower and oriented in more poleward directions away from substorm onset, with some evidence of near instantaneous expansion in zonal directions over large distances of similar to 2000 km from onset followed by a slower expansion primarily in poleward and westward directions. The observations suggest that during substorms precipitating electrons in the high-energy part of the spectrum behave differently from their low-energy counterparts and that they exhibit some evidence of predictable behavior.