This study presents ensemble modeling of outer radiation belt dynamics observed by Van Allen Probes throughout 2017 using DREAM3D simulations. We utilize a recently developed empirical radial diffusion coefficient (DLL) model with statistical distributions, employing two outer boundary (OB) conditions: Van Allen Probes data at L*=5.5 and GOES data at L*=6, for two magnetic moments μ=512 keV/G and μ=1237 keV/G. The results demonstrate that OB location critically influences model performance. A model using Van Allen Probes OB at L*=5.5 better reproduces observations, particularly for high μ electrons. In this scenario, radial diffusion alone can largely explain the dynamics because the OB is located near the phase space density (PSD) peak region. Stronger DLL outside the plasmasphere effectively captures inward/outward radial diffusion to/from the OB, while an intermediate DLL around the 30th percentile best matches electron PSD inside the plasmasphere. With GOES OB at L*=6, not only does strong DLL remain crucial for achieving good performance, but chorus heating also becomes critical. Model performance inside the plasmasphere is the best for the intermediate DLL but consistently worse than that outside the plasmasphere, suggesting a need for improved DLL and loss inputs in the plasmasphere.

Abstract Quasilinear diffusion coefficients can be used to model the response of charged particles to resonant wave‐particle interactions. The calculation of these coefficients is sufficiently complicated and arduous to render it prohibitive to many potential users, because of the expense in time spent developing the code. The PIRAN software package (”Particles In ResonANce”) is written using Python, and allows the user to calculate local and bounce‐averaged relativistic diffusion coefficients in energy and pitch‐angle space via the two main current proposed methods in the literature. The code is predominantly based upon the formalisms and methods presented in Glauert and Horne (2005, https://doi.org/10.1029/2004JA010851) and Cunningham (2023, https://doi.org/10.1029/10.1029/2023JA031703). We solve for diffusion coefficients using exact relativistic formulae. We use Gaussian spectra in wave frequency and in tangent of the wave normal angle and solve the full cold‐plasma dispersion relation. At present the code supports fully tested calculations for electron diffusion coefficients based on whistler‐mode waves in a fully ionized proton‐electron cold plasma. However the codebase architecture is built such that future developments to include other wave modes and other plasma compositions should involve incremental additions. The initial release of PIRAN may not have the same number of features as some other numerical codes, but is has the advantages of being a fully open‐source diffusion coefficient code that: (a) supports calculation of both local and bounce‐averaged diffusion coefficients via both of the two proposed methods; (b) is written fully in Python; (c) has detailed user pages, commit history and changelog on GitHub.

We use the full NASA Van Allen Probes mission (2012-2019) to extract the electron plasma density from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) and Electric Field and Waves (EFW) instruments and discuss the evolution of the plasmasphere. We generate new statistics including mean and standard deviations of the plasma density with respect to L-shell, magnetic local time (MLT), and various geomagnetic indices. These statistics are generated to be applied in radiation belt physics and space weather codes (with fits provided). The mean plasmasphere is circular around Earth with respect to MLT for Kp < 1. The mean 100 cm-3 level line is above L = 5 and mean 10 cm-3 level expands above the Van Allen Probes apogee for Kp < 1. The outer electron belt lies within the plasmasphere for 60% of all times. As activity increases (Kp > 2), a gradual MLT asymmetry forms with higher mean density in the afternoon sector due to plumes expanding outward. Conversely, the mean density decreases on the dawn and night sectors. The mean density is between similar to 500 and similar to 50 cm-3 between L similar to 4 and L similar to 6 during quiet and moderately active times (Kp < 3), representing similar to 80% of all times. Statistics in regions of high density below L = 2 are underdefined for intense activity. The highest standard deviation of density represents a factor 2.5 to 3 times the mean above L = 5 and for active times. We find the percent difference between the EFW and EMFISIS densities is bounded by +/- 20% for quiet and moderate activity (Kp < 5) and goes up to +/- 100% for extreme activity. The Earth's plasmasphere, discovered in the 1950s, is a region of cold plasma made of ions and electrons of a few electronvolts in energy, originating from upwelling ionized gas from the ionosphere and forming a rotating torus around the Earth. The radial profile of the electron cold plasma density within the plasmasphere decays from 10,000 electrons per cubic centimeter at similar to 1,000 km altitude to 10s electrons per cubic centimeter at its outer edge, sometimes exceeding similar to 36,000 km in altitude at the equator. The state of the plasmasphere is highly dependent on geomagnetic conditions, with geomagnetic storms and substorms eroding parts of this plasma. Here, we analyze 7 years of NASA Van Allen Probes measurements of the electron plasma density and generate statistics with respect to L-shell, magnetic local time, and geomagnetic indices. In this way, we show statistical variations of the plasmasphere, a strong magnetic local time dependence, and erosion with increasing geomagnetic activity. New mean electron densities and their standard deviation are generated and fitted with model functions that can be incorporated into space weather codes. This is important because the electron density is a key parameter influencing the strength of wave-particle interactions that accelerate and scatter energetic particles in the inner magnetosphere.

We compared the performance of DREAM3D simulations in reproducing the long-term radiation belt dynamics observed by Van Allen Probes over the entire year of 2017 with various boundary conditions (BCs) and model inputs. Specifically, we investigated the effects of three different outer boundary conditions, two different low-energy boundary conditions for seed electrons, four different radial diffusion (RD) coefficients (DLL), four hiss wave models, and two chorus wave models from the literature. Using the outer boundary condition driven by GOES data, our benchmark simulation generally well reproduces the observed radiation belt dynamics inside L* = 6, with a better model performance at lower mu than higher mu, where mu is the first adiabatic invariant. By varying the boundary conditions and inputs, we find that: (a) The data-driven outer boundary condition is critical to the model performance, while adding in the data-driven seed population doesn't further improve the performance. (b) The model shows comparable performance with DLL from Brautigam and Albert (2000, ), Ozeke et al. (2014, ), and Liu et al. (2016, ), while with DLL from Ali et al. (2016, ) the model shows less RD compared to data. (c) The model performance is similar with data-based hiss models, but the results show faster loss is still needed inside the plasmasphere. (d) The model performs similarly with the two different chorus models, but better capturing the electron enhancement at higher mu using the Wang et al. (2019, ) model due to its stronger wave power, since local heating for higher energy electrons is under-reproduced in the current model. Relativistic electrons in the outer radiation belt are very dynamic involving various acceleration and loss processes under the influence of radial diffusion (RD), hiss, and chorus waves. The physical processes are regarded as diffusive in behavior. The DREAM3D code solves the Fokker-Plank equation to investigate the radiation belt dynamics in the aspect of the diffusive dynamics of electrons. A variety of empirical models and boundary conditions have been developed and included in the simulations in the literature. In this study, we compare the DREAM3D performance in reproducing the observed radiation belt dynamics with various empirical models of the RD coefficients, hiss and chorus wave, and boundary conditions. In conclusion, we find the data-driven outer boundary condition is very important to reproduce the observed radiation belt variations. For the RD coefficients, all DLL exhibit comparable performances while DLL from Ali et al. (2016, ) shows slower RD due to its smaller magnitude. All the hiss wave models lead to effective loss inside the plasmasphere, but stronger losses are needed. For the chorus wave models, the two models are comparable with a small difference in model performance due to the different levels of wave power. This work compares the performance of long-term radiation belt simulations using various inputs and boundary conditions Using GOES outer boundary condition, the benchmark simulations reproduce the radiation belt dynamics inside L* = 6 observed by Van Allen Probes The data-driven OB condition is critical to the model performance, and stronger loss inside the plasmasphere could improve the performance

NASA's Van Allen Probes observed significant, long-lived fluxes of inner belt electrons up to similar to 1 MeV after geomagnetic storms in March and June 2015. Reanalysis of Magnetic Electron Ion Spectrometer (MagEIS) data with improved background correction showed a clearer picture of the relativistic electron population that persisted through 2016 and into 2017 above the Fennell et al. (2015, ) limit. The intensity and duration of these enhancements allow estimation of decay timescales for comparison with simulated decay rates and theoretical lifetimes. We compare decay timescales from these data and DREAM3D simulations based on them using geomagnetic activity-dependent pitch angle diffusion coefficients derived from plasmapause-indexed wave data (Malaspina et al., 2016, , 2018, ) and phase space densities derived from MagEIS observations. Simulated decay rates match observed decay rates more closely than the theoretical lifetime due to significantly nonequilibrium pitch angle distributions in simulation and data. We conclude that nonequilibrium effects, rather than a missing diffusion or loss process, account for observed short decay rates.

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.

A new empirical density model is developed for the inner zone between 1 < L < 3 using plasma densities inferred from the upper hybrid resonance on Arase, and hiss‐inferred density values from Van Allen Probes. The Van Allen Probes hiss‐inferred densities are first recalibrated and validated against Arase observations, using both a conjunction event and statistical analyses. The newly developed density model includes dependencies on L , magnetic latitude, and magnetic local time (MLT). Between 1.5 < L < 3.0, the equatorial density variation with L is shown to be equivalent to that of the Ozhogin et al. (2012, https://doi.org/10.1029/2011JA017330 ) model. However, for L < 1.5, this dependence changes as the plasma density increases at a faster rate with decreasing L. The latitudinal dependence of the plasma density is shown to present a flatter profile than previous models, meaning lower densities extend to higher latitudes. This dependence is well‐modeled by updated fitting coefficients. A clear MLT dependence of the plasma density is identified, which was not found or included in some previous models. This variation is consistent with the diurnal variation of the ionosphere, peaking near MLT = 14 and becoming larger in amplitude with decreasing L. A function describing this MLT dependence is presented. Overall, the new L , latitude, and MLT‐dependent empirical model can provide density values in areas outside the validity region of many previous models, making it a useful resource for accurately determining diffusion coefficients and predicting electron dynamics and their lifetimes in the inner radiation belt.

This review focusses strictly on existing plasma density models, including ionospheric source models, empirical density models, physics-based and machine-learning density models. This review is framed in the context of radiation belt physics and space weather codes. The review is limited to the most commonly used models or to models recently developed and promising. A great variety of conditions is considered such as the magnetic local time variation, geomagnetic conditions, ionospheric source regions, radial and latitudinal dependence, and collisional vs. collisionless conditions. These models can serve to complement satellite observations of the electron plasma density when data are lacking, are for most of them commonly used in radiation belt physics simulations, and can improve our understanding of the plasmasphere dynamics.

∗ Primary Author 1 Astrophysical and Planetary Sciences Department, University of Colorado, Boulder, CO 2 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 3 Southwest Research Institute, San Antonio, TX 4 Space Science Research Institute, Boulder, CO 5 NASA Marshall Spaceflight Research Center, Huntsville, AL 6 Los Alamos National Laboratory, Los Alamos, NM 7 Space Sciences Laboratory, University of California, Berkeley, Berkeley, CA 8 College of Engineering, Boston University, Boston, MA

Dropout events are dramatic decreases in radiation belt electron populations that can occur in as little as 30 minutes. Loss to magnetopause due to a combination of magnetopause shadowing and outward radial transport plays a significant role in these events. We examine the dropout of relativistic electron populations during the October 2012 geomagnetic storm using simulated electron phase space density, evaluating the contribution of different processes to losses across the magnetopause. We compare loss contribution from outward transport calculated using a standard empirical radial diffusion model that assumes a dipolar geomagnetic field to an event-specific radial diffusion model evaluated with a non-dipolar geomagnetic field. We additionally evaluate the contribution of Shabansky type 1 particles, which bounce along magnetic field lines with local equatorial maxima, to the loss calculated during this event. We find that the empirical radial diffusion model with a dipolar background field underestimates the contribution of radial diffusion to this dropout event by up to 10% when compared to the event-specific, non-dipolar radial diffusion model. We additionally find that including Shabansky type 1 particles in the initial electron phase space density, that is, allowing some magnetic field lines distorted from the typical single-minima configuration in drift shell construction, increases the calculated loss by an average of 0.75%. This shows that the treatment of the geomagnetic field significantly impacts the calculation of electron losses to the magnetopause during dropout events, with the non-dipolar treatment of radial diffusion being essential to accurately quantify the loss of outer radiation belt populations.

We deduce the cold electron plasma density from NASA Van Allen Probes measurements throughout 2012-2019. We then extract two of the plasmasphere boundaries. We first use the gradient method for locating the plasmapause at L pp and, then, the $100\mathrm{~cm}^{-3}$ density threshold for the plasmasphere outer edge located at L 100 . The sharp gradient of the plasmapause is only defined in 53% of cases, while L 100 is defined for $\sim 85\%$ of cases. Differences and similarities between L pp and L 100 are discussed. L 100 is demonstrated to bound the plasmasphere at large L-shell in the dusk where L pp gradients often lack. We generate new empirical density models of the plasmasphere boundaries binned by L-shell, magnetic local time (MLT), and the maximum of the Kp index over 24 hours (Kp*).

This summary article gathers a series of new results related to the characterization of the electromagnetic properties of lightning strokes both on Earth and in space through lightning-generated whistlers.

Lightning superbolts are the most powerful and rare lightning events with intense optical emission, first identified from space. Superbolt events occurred in 2010-2018 could be localized by extracting the high energy tail of the lightning stroke signals measured by the very low frequency ground stations of the World-Wide Lightning Location Network. Here, we report electromagnetic observations of superbolts from space using Van Allen Probes satellite measurements, and ground measurements, and with two events measured both from ground and space. From burst-triggered measurements, we compute electric and magnetic power spectral density for very low frequency waves driven by superbolts, both on Earth and transmitted into space, demonstrating that superbolts transmit 10-1000 times more powerful very low frequency waves into space than typical strokes and revealing that their extreme nature is observed in space. We find several properties of superbolts that notably differ from most lightning flashes; a more symmetric first ground-wave peak due to a longer rise time, larger peak current, weaker decay of electromagnetic power density in space with distance, and a power mostly confined in the very low frequency range. Their signal is absent in space during day times and is received with a long-time delay on the Van Allen Probes. These results have implications for our understanding of lightning and superbolts, for ionosphere-magnetosphere wave transmission, wave propagation in space, and remote sensing of extreme events.

We compare ESA PROBA‐V observations of electron flux at LEO with those from the NASA Van Allen Probes mostly at MEO for October 2013. Dropouts are visible at all energy during four storms from both satellites. Equatorially trapped electron fluxes are higher than at LEO by 10 2 (<1 MeV) to 10 5 (>2.5 MeV). We observe a quite isotropic structure of the outer belt during quiet times, contrary to the inner belt, and pitch angle dependence of high energy injection. We find a very good overlap of the outer belt at MEO and LEO at ∼0.5 MeV. We use test‐particle simulations of the energetic electrons trapped in the terrestrial magnetic field to study the outer radiation belt electron flux changes during geomagnetic storms. We show that the Dst (Disturbance storm time) effect during the main phase of a geomagnetic storm results in a betatron mechanism causing outward radial drift and a deceleration of the electrons. This outward drift motion is energy independent, pitch angle‐dependent, and represents a significant distance (∼1 L‐shell at L = 5 for moderate storms). At fixed L‐shell, this causes a decay of the LEO precipitating flux (adiabatic outward motion), followed by a return to the normal state (adiabatic inward motion) during main and recovery phases. Dst effect, associated with magnetopause shadowing and radial diffusion can explain the main characteristics of outer radiation belt electron dropouts in October 2013. We also use Fokker‐Planck simulations with event‐driven diffusion coefficients at high temporal resolution, to distinguish instantaneous loss from the gradual scattering that depopulates the slot region and the outer belt after storms. Simulations reproduce the slot formation and the gradual loss in the outer belt. The typical energy dependence of these losses leads to the absence of scattering for relativistic and ultra‐relativistic electrons in the outer belt, oppositely to dropouts.

We study the propagation and attenuation of lightning-generated whistler (LGW) waves in near-Earth space (L ≤ 3) through the statistical study of three specific quantities extracted from data recorded by NASA’s Van Allen Probes mission, from 2012 to 2019: the LGW electric and magnetic power attenuation with respect to distance from a given lightning stroke, the LGW wave normal angle in space, and the frequency-integrated LGW refractive index. We find that LGW electric field wave power decays with distance mostly quadratically in space, with a power varying between -1 and -2, while the magnetic field wave power decays mostly linearly in space, with a power varying between 0 and -1. At night only, the electric wave power decays as a quadratic law and the magnetic power as a linear law, which is consistent with electric and magnetic ground measurements. Complexity of the dependence of the various quantities is maximal at the lowest L-shells (L < 1.5) and around noon, for which LGW are the rarest in Van Allen Probes measurements. In-space near-equatorial LGW wave normal angle statistics are shown for the first time with respect to magnetic local time (MLT), L-shell (L), geographic longitude, and season. A distribution of predominantly electrostatic waves is peaked at large wave normal angle. Conversely, the distribution of electromagnetic waves with large magnetic component and small electric component is peaked at small wave normal angle. Outside these limits, we show that, as the LGW electric power increases, the LGW wave normal angle increases. But, as the LGW magnetic power increases, the LGW wave normal angle distribution becomes peaked at small wave normal angle with a secondary peak at large wave normal angle. The LGW mean wave-normal angle computed over the whole data set is 41.6° with a ∼24° standard deviation. There is a strong MLT-dependence, with the wave normal angle smaller for daytime (34.4° on average at day and 46.7° at night). There is an absence of strong seasonal and continental dependences of the wave-normal angle. The statistics of the LGW refractive index show a mean LGW refractive index is 32 with a standard deviation of ∼26. There is a strong MLT-dependence, with larger refractive index for daytime 36) than for nighttime (28). Smaller refractive index is found during Northern hemisphere summer for L-shells above 1.8, which is inconsistent with Chapman ionization theory and consistent with the so-called winter/seasonal anomaly. Local minima of the mean refractive index are observed over the three continents. Cross-correlation of these wave parameters in fixed (MLT, L) bins shows that the wave normal angle and refractive index are anti-correlated; large (small) wave normal angles correspond with small (large) refractive indexes. High power attenuation during LGW propagation from the lightning source to the spacecraft is correlated with large refractive index and anti-correlated with small wave normal angle. Correlation and anti-correlation show a smooth and continuous path from one regime (i.e. large wave normal angle, small refractive index, low attenuation) to its opposite (i.e. small wave normal angle, large refractive index, large attenuation), supporting consistency of the results.

This study focuses on the radiation effects of Sr+ ions–generated from high-altitude nuclear explosions (HANE)–on satellite solar cells in low-Earth orbits (LEO). Along four selected satellite orbits, ion fluences are sampled inside the evolving Sr+ ion distributions for days, determined from our newly developed HANE environment model. These fluences, along with the help of radiation transport codes including the MULASSIS and SRIM models, enable us to quantify the radiation damages by determining the values of total ionizing doses and the equivalent 1 MeV electron fluences for displacement damages. Comparing the dose values to existing experimental data, we conclude that HANE-generated Sr+ ions have limited darkening effects to quartz solar cell coverglasses in LEO with apogees of 100s to 1000 km. In addition, with the extremely high equivalent fluences, we also conclude that these Sr ions may cause severe or even fatal displacement damage to exposed solar photovoltaic (PV) cells on satellites in LEO. The radiation effects of Sr+ ions are much less significant for the orbits with high apogees beyond ten thousand km. We also conducted model parameter sensitivity studies on the charge exchange cross-sections, neutral atmosphere density profiles and explosion local time positions, and the above conclusions stay unchanged. The methodology developed in this study can be extended to other HANE-generated heavy ion species in the future.

This talk will show a statistical analysis of both electric and magnetic field wave amplitudes of very low frequency lightning‐generated whistlers (LGWs) based on the equivalent of 11.5 years of observations made by the Van Allen Probes. We complement this analysis with data from the ground‐based World Wide Lightning Location Network (WWLLN) to explore differences between satellite and ground‐based measurements. We will discuss how LGW mean amplitudes were generally found to be low compared with other whistler mode waves even though there exists extreme events (1 out of 5,000) that can reach 100 pT and contribute strongly to the mean power below L = 2. We will reveal a region of low wave amplitude existing below L=2 thanks to the denser dayside ionosphere, which prevents the intense equatorial lightning VLF waves from propagating through it. Below L = 1.5 at all MLT, LGW amplitudes are found to be weak while the ground‐level lightning activity is maximal. This suggests a difficulty of lightning VLF waves to penetrate / propagate / remain at low L‐shells, certainly due at least to the denser ionosphere during daytime. On the contrary, the mean LGW magnetic power (or RMS) remains nearly constant with respect to L‐shell. We will explain that this is due to strong to extreme LGWs that dominate the wave mean power to the point of compensating the decay of LGW occurrence at low L‐shell. Even though extreme LGW were found to be very powerful, particularly at low L and during night, the mean electric/magnetic power remains low compared with other whistler waves. This implies that LGW resonant effects on electrons are consequently long‐term effects that contribute to “age” trapped inner belt electron populations.

The very low‐frequency transmitter in the Northwest Cape of Australia (NWC) has previously been observed to pitch‐angle scatter electrons with energies from 30–400 keV, creating enhanced fluxes measured by low‐Earth orbiting (LEO) satellites. Here we use observations from the Energetic Particle Telescope on PROBA‐V. We compare the measured flux, as a function of local magnetic field strength, when the NWC transmitter is “on” versus “off,” and find enhanced fluxes only when NWC is “on” and located on the nightside. The enhanced fluxes occur in the population gradually transitioning from “permanently trapped” to “quasi‐trapped.” We show that electrons up to 800 keV, substantially higher energy than previously studied, are scattered by resonant interactions with NWC to produce enhanced fluxes. The enhanced fluxes appear at multiple L‐shells for each energy channel, consistent with resonance conditions at distinct wave normal angles, that indicate ducted interactions at L < 1.55 and unducted interactions at L > 1.65.

We provide a statistical analysis of both electric and magnetic field wave amplitudes of very low frequency lightning‐generated waves (LGWs) based on the equivalent of 11.5 years of observations made by the Van Allen Probes encompassing ~24.6 × 106 survey mode measurements. We complement this analysis with data from the ground‐based World Wide Lightning Location Network to explore differences between satellite and ground‐based measurements. LGW mean amplitudes are found to be low compared with other whistler mode waves (1 ± 1.6 pT and 19 ± 59 μV/m). Extreme events (1/5,000) can reach 100 pT and contributes strongly to the mean power below L = 2. We find excellent correlations between World Wide Lightning Location Network‐based power and wave amplitudes in space at various longitudes. We reveal strong dayside ionospheric damping of the LGW electric field. LGW amplitudes drop for L < 2, contrary to the Earth's intense equatorial lightning activity. We conclude that it is difficult for equatorial LGW to propagate and remain at L < 2.

Ganguli and Crabtree have written a comment about a recent article by the authors listed above on radiation-belt remediation. They have objected to our evaluation of the Naval Research Laboratory’s chemical release concept which states that this concept may be impractical due to an apparently low overall efficiency. In their comment, they provide a scientific argument and refer to the published literature to counter our statement. Here, we provide more details on our numerical calculations and experimental results which led to this evaluation.