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Van Allen Probes measurements revealed the presence of the most unusual structures in the ultra-relativistic radiation belts. Detailed modeling, analysis of pitch angle distributions, analysis of the difference between relativistic and ultra-realistic electron evolution, along with theoretical studies of the scattering and wave growth, all indicate that electromagnetic ion cyclotron (EMIC) waves can produce a very efficient loss of the ultra-relativistic electrons in the heart of the radiation belts. Moreover, a detailed analysis of the profiles of phase space densities provides direct evidence for localized loss by EMIC waves. The evolution of multi-MeV fluxes shows dramatic and very sudden enhancements of electrons for selected storms. Analysis of phase space density profiles reveals that growing peaks at different values of the first invariant are formed at approximately the same radial distance from the Earth and show the sequential formation of the peaks from lower to higher energies, indicating that local energy diffusion is the dominant source of the acceleration from MeV to multi-MeV energies. Further simultaneous analysis of the background density and ultra-relativistic electron fluxes shows that the acceleration to multi-MeV energies only occurs when plasma density is significantly depleted outside of the plasmasphere, which is consistent with the modeling of acceleration due to chorus waves.
We present two new empirical models of radiation belt electron flux at geostationary orbit. GOES-15 measurements of 0.8 MeV electrons were used to train a Nonlinear Autoregressive with Exogenous input (NARX) neural network for both modeling GOES-15 flux values and an upper boundary condition scaling factor (BF). The GOES-15 flux model utilizes an input and feedback delay of 2 and 2 time steps (i.e., 5 min time steps) with the most efficient number of hidden layers set to 10. Magnetic local time, Dst, Kp, solar wind dynamic pressure, AE, and solar wind velocity were found to perform as predicative indicators of GOES-15 flux and therefore were used as the exogenous inputs. The NARX-derived upper boundary condition scaling factor was used in conjunction with the Versatile Electron Radiation Belt (VERB) code to produce reconstructions of the radiation belts during the period of July-November 1990, independent of in-situ observations. Here, Kp was chosen as the sole exogenous input to be more compatible with the VERB code. This Combined Release and Radiation Effects Satellite-era reconstruction showcases the potential to use these neural network-derived boundary conditions as a method of hindcasting the historical radiation belts. This study serves as a companion paper to another recently published study on reconstructing the radiation belts during Solar Cycles 17-24 (Saikin et al., 2021, ), for which the results featured in this paper were used.
In this study we analyze the storm-time evolution of equatorial electron pitch angle distributions (PADs) in the outer radiation belt region using observations from the Magnetic Electron Ion Spectrometer (MagEIS) instrument aboard the Van Allen Probes in 2012-2019. The PADs are approximated using a sum of the first, third and fifth sine harmonics. Different combinations of the respective coefficients refer to the main PAD shapes within the outer radiation belt, namely the pancake, flat-top, butterfly and cap PADs. We conduct a superposed epoch analysis of 129 geomagnetic storms and analyze the PAD evolution for day and night MLT sectors. PAD shapes exhibit a strong energy-dependent response. At energies of tens of keV, the PADs exhibit little variation throughout geomagnetic storms. Cap PADs are mainly observed at energies < 300 keV, and their extent in L shrinks with increasing energy. The cap distributions transform into the pancake PADs around the main phase of the storm on the nightside, and then come back to their original shapes during the recovery phase. At higher energies on the dayside, the PADs are mainly pancake during pre-storm conditions and become more anisotropic during the main phase. The quiet-time butterfly PADs can be observed on the nightside at L> 5.6. During the main phase, butterfly PADs have stronger 90 degrees-minima and can be observed at lower L-shells (down to L = 5), then transitioning into flat-top PADs at L similar to 4.5 - 5 and pancake PADs at L < 4.5. The resulting PAD coefficients for different energies, locations and storm epochs can be used to test the wave models and physics-based radiation belt codes in terms of pitch angle distributions.
Different modeling methodologies possess different strengths and weakness. For instance, data based models may provide superior accuracy but have a limited spatial coverage while physics based models may provide lower accuracy but provide greater spatial coverage. This study investigates the coupling of a data based model of the electron fluxes at geostationary orbit (GEO) with a numerical model of the radiation belt region to improve the resulting forecasts/pastcasts of electron fluxes over the whole radiation belt region. In particular, two coupling methods are investigated. The first assumes an average value for L* for GEO, namely LGEO* L-GEO* = 6.2. The second uses a value of L* that varies with geomagnetic activity, quantified using the Kp index. As the terrestrial magnetic field responds to variations in geomagnetic activity, the value of L* will vary for a specific location. In this coupling method, the value of L* is calculated using the Kp driven Tsyganenko 89c magnetic field model for field line tracing. It is shown that this addition can result in changes in the initialization of the parameters at the Versatile Electron Radiation Belt model outer boundary. Model outputs are compared to Van Allen Probes MagEIS measurements of the electron fluxes in the inner magnetosphere for the March 2015 geomagnetic storm. It is found that the fixed LGEO* L-GEO* coupling method produces a more realistic forecast.
In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012-2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat-top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two-step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni-directional flux observations and is applicable to low-PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni- or omnidirectional measurement at off-equatorial latitudes. The model can be used for converting the long-term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics-based modeling in the form of boundary conditions, and for data assimilation purposes.
Data assimilation aims to blend incomplete and inaccurate data with physics-based dynamical models. In the Earth's radiation belts, it is used to reconstruct electron phase space density, and it has become an increasingly important tool in validating our current understanding of radiation belt dynamics, identifying new physical processes, and predicting the near-Earth hazardous radiation environment. In this study, we perform reanalysis of the sparse measurements from four spacecraft using the three-dimensional Versatile Electron Radiation Belt diffusion model and a split-operator Kalman filter over a 6-month period from 1 October 2012 to 1 April 2013. In comparison to previous works, our 3-D model accounts for more physical processes, namely, mixed pitch angle-energy diffusion, scattering by Electromagnetic Ion Cyclotron waves, and magnetopause shadowing. We describe how data assimilation, by means of the innovation vector, can be used to account for missing physics in the model. We use this method to identify the radial distances from the Earth and the geomagnetic conditions where our model is inconsistent with the measured phase space density for different values of the invariants mu and K. As a result, the Kalman filter adjusts the predictions in order to match the observations, and we interpret this as evidence of where and when additional source or loss processes are active. The current work demonstrates that 3-D data assimilation provides a comprehensive picture of the radiation belt electrons and is a crucial step toward performing reanalysis using measurements from ongoing and future missions.
Significant progress has been made in recent years in understanding acceleration mechanisms in the Earth's radiation belts. In particular, a number of studies demonstrated the importance of the local acceleration by analyzing the radial profiles of phase space density (PSD) and observing building up peaks in PSD. In this study, we focus on understanding of the local loss using very similar tools. The profiles of PSD for various values of the first adiabatic invariants during the previously studied 17 January 2013 storm are presented and discussed. The profiles of PSD show clear deepening minimums consistent with the scattering by electromagnetic ion cyclotron waves. Long-term evolution shows that local minimums in PSD can persist for relatively long times. During considered interval of time the deepening minimums were observed around L* = 4 during 17 January 2013 storm and around L* = 3.5 during 1 March 2013 storm. This study shows a new method that can help identify the location, magnitude, and time of the local loss and will help quantify local loss in the future. This study also provides additional clear and definitive evidence that local loss plays a major role for the dynamics of the multi-MeV electrons.
Understanding of wave environments is critical for the understanding of how particles are accelerated and lost in space. This study shows that in the vicinity of Europa and Ganymede, that respectively have induced and internal magnetic fields, chorus wave power is significantly increased. The observed enhancements are persistent and exceed median values of wave activity by up to 6 orders of magnitude for Ganymede. Produced waves may have a pronounced effect on the acceleration and loss of particles in the Jovian magnetosphere and other astrophysical objects. The generated waves are capable of significantly modifying the energetic particle environment, accelerating particles to very high energies, or producing depletions in phase space density. Observations of Jupiter’s magnetosphere provide a unique opportunity to observe how objects with an internal magnetic field can interact with particles trapped in magnetic fields of larger scale objects.
Chorus waves play an important role in the dynamic evolution of energetic electrons in the Earth's radiation belts and ring current. Using more than 5 years of Van Allen Probe data, we developed a new analytical model for upper‐band chorus (UBC; 0.5fce < f < fce) and lower‐band chorus (LBC; 0.05fce < f < 0.5fce) waves, where fce is the equatorial electron gyrofrequency. By applying polynomial fits to chorus wave root mean square amplitudes, we developed regression models for LBC and UBC as a function of geomagnetic activity (Kp), L, magnetic latitude (λ), and magnetic local time (MLT). Dependence on Kp is separated from the dependence on λ, L, and MLT as Kp‐scaling law to simplify the calculation of diffusion coefficients and inclusion into particle tracing codes. Frequency models for UBC and LBC are also developed, which depends on MLT and magnetic latitude. This empirical model is valid in all MLTs, magnetic latitude up to 20°, Kp ≤ 6, L‐shell range from 3.5 to 6 for LBC and from 4 to 6 for UBC. The dependence of root mean square amplitudes on L are different for different bands, which implies different energy sources for different wave bands. This analytical chorus wave model is convenient for inclusion in quasi‐linear diffusion calculations of electron scattering rates and particle simulations in the inner magnetosphere, especially for the newly developed four‐dimensional codes, which require significantly improved wave parameterizations.
The evolution of the radiation belts in L-shell (L), energy (E), and equatorial pitch angle (alpha(0)) is analyzed during the calm 11-day interval (4-15 March) following the 1 March 2013 storm. Magnetic Electron and Ion Spectrometer (MagEIS) observations from Van Allen Probes are interpreted alongside 1D and 3D Fokker-Planck simulations combined with consistent event-driven scattering modeling from whistler mode hiss waves. Three (L, E, alpha(0)) regions persist through 11 days of hiss wave scattering; the pitch angle-dependent inner belt core (L similar to <2.2 and E < 700 keV), pitch angle homogeneous outer belt low-energy core (L > similar to 5 and E similar to < 100 keV), and a distinct pocket of electrons (L similar to [4.5, 5.5] and E similar to [0.7, 2] MeV). The pitch angle homogeneous outer belt is explained by the diffusion coefficients that are roughly constant for alpha(0) similar to <60 degrees, E > 100 keV, 3.5 < L < L-pp similar to 6. Thus, observed unidirectional flux decays can be used to estimate local pitch angle diffusion rates in that region. Top-hat distributions are computed and observed at L similar to 3-3.5 and E = 100-300 keV.