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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.
Electromagnetic ion cyclotron waves have long been recognized to play a crucial role in the dynamic loss of ring current protons. While the field-aligned propagation approximation of electromagnetic ion cyclotron waves was widely used to quantify the scattering loss of ring current protons, in this study, we find that the wave normal distribution strongly affects the pitch angle scattering efficiency of protons. Increase of peak normal angle or angular width can considerably reduce the scattering rates of <= 10 keV protons. For >10 keV protons, the field-aligned propagation approximation results in a pronounced underestimate of the scattering of intermediate equatorial pitch angle protons and overestimates the scattering of high equatorial pitch angle protons by orders of magnitude. Our results suggest that the wave normal distribution of electromagnetic ion cyclotron waves plays an important role in the pitch angle evolution and scattering loss of ring current protons and should be incorporated in future global modeling of ring current dynamics.
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.
Ring current electrons (1–100 keV) have received significant attention in recent decades, but many questions regarding their major transport and loss mechanisms remain open. In this study, we use the four‐dimensional Versatile Electron Radiation Belt code to model the enhancement of phase space density that occurred during the 17 March 2013 storm. Our model includes global convection, radial diffusion, and scattering into the Earth's atmosphere driven by whistler‐mode hiss and chorus waves. We study the sensitivity of the model to the boundary conditions, global electric field, the electric field associated with subauroral polarization streams, electron loss rates, and radial diffusion coefficients. The results of the code are almost insensitive to the model parameters above 4.5 RERE, which indicates that the general dynamics of the electrons between 4.5 RE and the geostationary orbit can be explained by global convection. We found that the major discrepancies between the model and data can stem from the inaccurate electric field model and uncertainties in lifetimes. We show that additional mechanisms that are responsible for radial transport are required to explain the dynamics of ≥40‐keV electrons, and the inclusion of the radial diffusion rates that are typically assumed in radiation belt studies leads to a better agreement with the data. The overall effect of subauroral polarization streams on the electron phase space density profiles seems to be smaller than the uncertainties in other input parameters. This study is an initial step toward understanding the dynamics of these particles inside the geostationary orbit.
Statistical Analysis of Hiss Waves in Plasmaspheric Plumes Using Van Allen Probe Observations
(2019)
Plasmaspheric hiss waves commonly observed in high‐density regions in the Earth's magnetosphere are known to be one of the main contributors to the loss of radiation belt electrons. There has been a lot of effort to investigate the distributions of hiss waves in the plasmasphere, while relatively little attention has been given to those in the plasmaspheric plume. In this study, we present for the first time a statistical analysis of the occurrence and the spatial distribution of wave amplitudes and wave normal angles for hiss waves in plumes using Van Allen Probes observations during the period of October 2012 to December 2016. Statistical results show that a wide range of hiss wave amplitudes in plumes from a few picotesla to >100 pT is observed, but a modest (<20 pT) wave amplitude is more commonly observed regardless of geomagnetic activity in both the midnight‐to‐dawn and dusk sector. By contrast, stronger amplitude hiss occurs preferentially during geomagnetically active times in the dusk sector. The wave normal angles are distributed over a broad range from 0° to 90° with a bimodal distribution: a quasi‐field‐aligned population (<20°) with an occurrence rate of <60% and an oblique one (>50°) with a relative low occurrence rate of ≲20%. Therefore, from a statistical point of view, we confirm that the hiss intensity (a few tens of picotesla) and field‐aligned hiss wave adopted in previous simulation studies are a reasonable assumption but stress that the activity dependence of the wave amplitude should be considered.
Models of ring current electron dynamics unavoidably contain uncertainties in boundary conditions, electric and magnetic fields, electron scattering rates, and plasmapause location. Model errors can accumulate with time and result in significant deviations of model predictions from observations. Data assimilation offers useful tools which can combine physics-based models and measurements to improve model predictions. In this study, we systematically analyze performance of the Kalman filter applied to a log-transformed convection model of ring current electrons and Van Allen Probe data. We consider long-term dynamics of mu = 2.3 MeV/G and K = 0.3 G(1/2) R-E electrons from 1 February 2013 to 16 June 2013. By using synthetic data, we show that the Kalman filter is capable of correcting errors in model predictions associated with uncertainties in electron lifetimes, boundary conditions, and convection electric fields. We demonstrate that reanalysis retains features which cannot be fully reproduced by the convection model such as storm-time earthward propagation of the electrons down to 2.5 R-E. The Kalman filter can adjust model predictions to satellite measurements even in regions where data are not available. We show that the Kalman filter can adjust model predictions in accordance with observations for mu = 0.1, 2.3, and 9.9 MeV/G and constant K = 0.3 G(1/2) R-E electrons. The results of this study demonstrate that data assimilation can improve performance of ring current models, better quantify model uncertainties, and help deeper understand the physics of the ring current particles.
Plain Language Summary Radiation belts of the Earth, which are the zones of charged energetic particles trapped by the geomagnetic field, comprise enormous and dynamic systems. While the inner radiation belt, composed mainly of high-energy protons, is relatively stable, the outer belt, filled with energetic electrons, is highly variable and depends substantially on solar activity. Hence, extended reliable observations and the improved models of the electron intensities in the outer belt depending on solar wind parameters are necessary for prediction of their dynamics. The Cluster mission has been measuring electron flux intensities in the radiation belts since its launch in 2000, thus providing a huge dataset that can be used for radiation belts analysis. Using 16 years of electron measurements by the Cluster mission corrected for background contamination, we derived a uniform linear-logarithmic dependence of electron fluxes in the outer belt on the solar wind dynamic pressure.
In this paper we report a rare and fortunate event of fast magnetosonic (MS, also called equatorial noise) waves modulated by compressional ultralow frequency (ULF) waves measured by Van Allen Probes. The characteristics of MS waves, ULF waves, proton distribution, and their potential correlations are analyzed. The results show that ULF waves can modulate the energetic ring proton distribution and in turn modulate the MS generation. Furthermore, the variation of MS intensities is attributed to not only ULF wave activities but also the variation of background parameters, for example, number density. The results confirm the opinion that MS waves are generated by proton ring distribution and propose a new modulation phenomenon.
Space radiation is one of the main concerns for human space flights. The prediction of the radiation dose for the actual spacecraft geometry is very important for the planning of long-duration missions. We present a numerical method for the fast calculation of the radiation dose rate during a space flight. We demonstrate its application for dose calculations during the first and the second sessions of the MATROSHKA-R space experiment with a spherical tissue-equivalent phantom. The main advantage of the method is the short simulation time, so it can be applied for urgent radiation dose calculations for low-Earth orbit space missions. The method uses depth-dose curve and shield-and-composition distribution functions to calculate a radiation dose at the point of interest. The spacecraft geometry is processed into a shield-and-composition distribution function using a ray-tracing method. Depth-dose curves are calculated using the GEANT4 Monte-Carlo code (version 10.00.P02) for a double-layer aluminum-water shielding. Aluminum-water shielding is a good approximation of the real geometry, as water is a good equivalent for biological tissues, and aluminum is the major material of spacecraft bodies.