Sarah A. Glauert

Quasi‐linear diffusion theory is widely used in radiation belt modeling to describe resonant interactions between charged particles and electromagnetic waves. The diffusion rates depend on the wave spectrum and properties of the background plasma. For decades many studies have used variations of a longstanding method to specify the wave spectrum. Recently, a new method was proposed, and it was suggested the resulting diffusion rates can differ by orders of magnitude. Large differences in the diffusion rates would cause significant changes in the relativistic electron flux predicted by radiation belt models. We calculate quasi‐linear diffusion rates using three methods to specify the wave spectrum: two variations of the longstanding method and the new method. All three methods have the same wave power at each frequency, but the weighting of wave energy with respect to wave normal angle is different. We use input parameters typical of wave observations in the inner magnetosphere, including lower band and upper band chorus, hiss waves, electromagnetic ion cyclotron waves and fast magnetosonic waves. We find very small differences between the new method and the method used to calculate diffusion rates for the British Antarctic Survey Radiation Belt Model. We conclude that the uncertainties in modeling global variations in the radiation belts are more likely due to statistical sampling of wave data, rather than the method of calculating diffusion rates.

The Combined Release and Radiation Effects Satellite (CRRES) observed the response of the Van Allen radiation belts to peak solar activity within solar cycle 22. This study analyses relativistic and ultra‐relativistic electron occurrence and loss timescales within the CRRES High Energy Electron Fluxometer (HEEF) data set, including during several strong and severe geomagnetic storms that all, remarkably, flooded the slot region with multi‐MeV electrons. These allow the first definitive multi‐MeV electron lifetimes to be calculated in this region and indicate an elevated risk to satellites in slot region orbits during periods of heightened solar activity. The HEEF outer belt loss timescales are broadly in agreement with those from later solar cycles, but differences include longer‐lasting sub‐MeV electrons near the inner region of the outer belt and faster‐decaying multi‐MeV electrons near geosynchronous orbit. These differences are associated with higher levels of geomagnetic activity, a phenomenon that enables the spread in the results to be parameterised accordingly. The timescales generally appear well‐bounded by Kp‐dependent theoretical predictions, but the variability within the spread is not always well‐ordered by geomagnetic activity. This suggests the limitations of using pitch‐angle diffusion to account for the decay of elevated electrons following geomagnetic storms, and the need for more sophisticated space weather indices for radiation belt forecasting.

A large proton belt enhancement occurred on 24 March 1991 following an interplanetary shock that impacted the dayside magnetopause at 03:40 UT. Its formation was measured by the proton telescope aboard CRRES and attributed to the injection and inward transport of solar energetic particles (SEPs) by an azimuthally propagating electric field pulse induced by the shock's compression of the magnetosphere. This led to an increase in the flux of high energy (25 MeV) protons by several orders of magnitude at which has been well‐studied. However, a flux enhancement by up to one order of magnitude was also seen in 1–20 MeV protons at . Protons in this energy range pose a hazard to orbiting spacecraft as a major contributor to solar cell nonionizing dose. The 1–20 MeV enhancement cannot be explained by the inward transport of a solar proton source, because a newly injected source population at the required energy would have a drift velocity too low to interact with the pulse. Instead, we hypothesize that the 1–20 MeV enhancement was caused by the redistribution of radiation belt protons to different drift shells by the pulse. To test this hypothesis, we apply a novel method to predict the change in phase space density during a shock event which utilizes reverse‐time particle tracing simulations. Our results show that the 1–20 MeV enhancement can be accounted for by internal redistribution as hypothesized. We thus identify a new mechanism for proton belt enhancements that does not depend on a SEP source and present a way to model it.

Increases in the flux of high energy electrons in the Earth's radiation belts cause satellite charging which can lead to an electrostatic discharge, anomalies and disruption to service. For geostationary orbit (GEO) there are guidelines on how much shielding to protect electronic components, but not for lower orbits. Here we use data from GPS satellite NS41, the AE9 radiation model, and LANL satellite data to create a reasonable worst‐case electron flux spectrum between 60 keV and 8 MeV. We calculate the charging currents for satellites in circular equatorial orbit between 4.25 and 7.0 Re and show that the recommended guideline of 2.8 mm (110 mil) of Al shielding is sufficient to keep charging below recommended guidelines at GEO. Approximately 4.5 mm (177 mil) of Al shielding would be needed for satellites in circular equatorial orbit at 4.5 Re. We show that the maximum electric field could exceed the breakdown field in cables and dielectrics just under the spacecraft surface on a timescale of 1–2 hr presenting a risk of anomalies. Radiation induced conductivity reduces the risk but is highly uncertain. A magnetic storm, series of storms or high speed stream accompanied by a large solar energetic particle event would present a much higher risk of anomalies on several satellites.

The cold plasma density can significantly alter the rate of diffusion of radiation belt electrons by chorus waves within the magnetosphere, and the range of energies at which diffusion is effective. We describe a coupled density and radiation belt model based on the British Antarctic Survey Radiation Belt Model that uses spatially and temporally varying values of to drive a statistical model of electron diffusion due to chorus waves. We demonstrate that this approach of including the variance in recreates the acceleration of electrons up to MeV energies better than other previous approaches to including .

The plasma density is one of the most fundamental quantities of any plasma yet measuring it in space is exceptionally difficult when the density is low. Measurements from particle detectors are contaminated by spacecraft photoelectrons and methods using plasma wave emissions are hampered by natural plasma instabilities which dominate the wave spectrum. Here we present a new method which calculates the density from magnetosonic waves near the lower hybrid resonance frequency. The method works most effectively when the ratio of the plasma to cyclotron frequency is fpe / fce < 3.5. The method provides a lower bound on the plasma density. Using the new method we show that wave acceleration of electrons to relativistic energies is increased by orders of magnitude. The method enables years of satellite data to be re‐analyzed for the Earth and the effectiveness of wave acceleration at the Earth, Jupiter and Saturn to be re‐assessed.

As the number of satellites on orbit grows it is increasingly important to understand their operating environment. Physics‐based models can simulate the behavior of the Earth's radiation belts by solving a Fokker‐Planck equation. Three‐dimensional models use diffusion coefficients to represent the interactions between electromagnetic waves and the electrons. One‐dimensional radial diffusion models neglect the effects of energy diffusion and represent the losses due to the waves with a loss timescale. Both approaches may use pitch angle distributions (PADs) to create boundary conditions, to map observations from low to high equatorial pitch angles and to calculate phase‐space density from observations. We present a comprehensive set of consistent PADs and loss timescales for 2 ≤ L* ≤ 7, 100 keV ≤ E ≤ 5 MeV and all levels of geomagnetic activity determined by the Kp index. These are calculated from drift‐averaged diffusion coefficients that represent all the VLF waves that typically interact with radiation belt electrons and show good agreement with data. The contribution of individual waves is demonstrated; magnetosonic waves have little effect on loss timescales when lightning‐generated whistlers are present, and chorus waves contribute to loss even in low levels of geomagnetic activity. The PADs vary in shape depending on the dominant waves. When chorus is dominant the distributions have little activity dependence, unlike the corresponding loss timescales. Distributions peaked near 90° are formed by plasmaspheric hiss for L* ≤ 3 and E < 1 MeV, and by EMIC waves for L* > 3 and E > 1 MeV. When hiss dominates, increasing activity broadens the distribution but when EMIC waves dominate increasing activity narrows the distribution.

The proton radiation belt contains high fluxes of adiabatically trapped protons varying in energy from ∼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 R_C 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 R_C and field strength B_e as functions of Dst and L* to fit the TS04 field model. We then apply the Tu et al. (2014, https://doi.org/10.1002/2014ja019864) condition for nonadiabatic onset to solve the outer boundary L*, and refine our expression for R_C 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 ∼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.

Earth’s radiation belts consist of high-energy charged particles trapped by Earth’s magnetic field. Strong pitch angle diffusion of electrons caused by wave-particle interaction in Earth’s radiation belts has primarily been considered as a loss process, as trapped electrons are rapidly diffused into the loss cone and lost to the atmosphere. However, the wave power necessary to produce strong diffusion should also produce rapid energy diffusion, and has not been considered in this context. Here we provide evidence of strong diffusion using satellite data. We use two-dimensional Fokker-Planck simulations of electron diffusion in pitch angle and energy to show that scaling up chorus wave power to the strong diffusion limit produces rapid acceleration of electrons, sufficient to outweigh the losses due to strong diffusion. The rate of losses saturates at the strong diffusion limit, whilst the rate of acceleration does not. This leads to the surprising result of an increase, not a decrease in the trapped electron population during strong diffusion due to chorus waves as expected when treating strong diffusion as a loss process. Our results suggest there is a tipping point in chorus wave power between net loss and net acceleration that global radiation belt models need to capture to better forecast hazardous radiation levels that damage satellites.

High energy electron precipitation from the Earth's radiation belts is important for loss from the radiation belts and atmospheric chemistry. We follow up investigations presented in Reidy et al. (2021, https://doi.org/10.1029/2020ja028410) where precipitating flux is calculated inside the field of view of the POES T0 detector using quasi‐linear theory and pitch angle diffusion coefficients (D_αα) from the British Antarctic Survey (BAS). These results showed good agreements at >30 keV for L* >5 on the dawnside but the flux were too low at higher energies. We have investigated the effect of changing parameters in the calculation of the precipitating flux to improve the results for the higher energies using comparisons of in situ flux and cold plasma measurements from GOES‐15 and RBSP. We find that the strength of the diffusion coefficients rather than the shape of the source spectrum has the biggest effect on the calculated precipitation. In particular we find decreasing the cold plasma density used in the calculation of D_αα increases the diffusion and hence the precipitation at the loss cone for the higher energies, improving our results. The method of calculating D_αα is also examined, comparing co‐located rather than averaged RBSP measurements. We find that the method itself has minimal effect but using RBSP derived D_αα improved our results over using D_αα calculated using the entire BAS wave data base; this is potentially due to better measurements of the cold plasma density from RBSP than the other spacecraft included in the BAS wave data base (e.g., THEMIS).