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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.
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.
Using over-5-year EMFISIS wave measurements from Van Allen Probes, we present a detailed survey to identify the controlling factors among the geomagnetic indices and solar wind parameters for the 1-min root mean square amplitudes of lower band chorus (LBC) and upper band chorus (UBC).
A set of important features are automatically determined by feature selection techniques, namely, Random Forest and Maximum Relevancy Minimum Redundancy. Our analysis results indicate the AE index with zero-time-delay dominates the intensity evolution of LBC and UBC, consistent with the evidence that chorus waves prefer to occur and amplify during enhanced substorm periods. Regarding solar wind parameters, solar wind speed and IMF B-z are identified as the controlling factors for chorus wave intensity. Using the combination of all these important features, a predictive neural network model of chorus wave intensity is established to reconstruct the temporal variations of chorus wave intensity, for which application of Random Forest produces the overall best performance.
Plain Language Summary
Whistler mode chorus waves are electromagnetic waves observed in the low-density region near the geomagnetic equator outside the plasmapause. The dynamics of Earth's radiation belts are largely influenced by chorus waves owing to their dual contributions to both radiation belt electron acceleration and loss. In this study, we use feature selection techniques to identify the controlling geomagnetic and solar wind factors for magnetospheric chorus waves. Feature selection techniques implement the processes which can select the features most influential to the output.
In this study, the inputs are geomagnetic indices and solar wind parameters and the output is the chorus wave intensity. The results indicate that AE index with zerotime delay dominates the chorus wave intensity. Furthermore, solar wind speed and IMF B-z are identified as the most important solar wind drivers for chorus wave intensity.
On basis of the combination of all these important geomagnetic and solar wind controlling factors, we develop a neural network model of chorus wave intensity, and find that the model with the inputs identified using the Random Forest method produces the overall best performance.
Simulations of the inner magnetospheric energetic electrons using the IMPTAM-VERB coupled model
(2019)
In this study, we present initial results of the coupling between the Inner Magnetospheric Particle Transport and Acceleration Model (IMPTAM) and the Versatile Electron Radiation Belt (VERB-3D) code. IMPTAM traces electrons of 10-100 keV energies from the plasma sheet (L = 9 Re) to inner L-shell regions. The flux evolution modeled by IMPTAM is used at the low energy and outer L* computational boundaries of the VERB code (assuming a dipole approximation) to perform radiation belt simulations of energetic electrons. The model was tested on the March 17th, 2013 storm, for a six-day period. Four different simulations were performed and their results compared to satellites observations from Van Allen probes and GOES. The coupled IMPTAM-VERB model reproduces evolution and storm-time features of electron fluxes throughout the studied storm in agreement with the satellite data (within similar to 0.5 orders of magnitude). Including dynamics of the low energy population at L* = 6.6 increases fluxes closer to the heart of the belt and has a strong impact in the VERB simulations at all energies. However, inclusion of magnetopause losses leads to drastic flux decreases even below L* = 3. The dynamics of low energy electrons (max. 10s of keV) do not affect electron fluxes at energies >= 900 keV. Since the IMPTAM-VERB coupled model is only driven by solar wind parameters and the Dst and Kp indexes, it is suitable as a forecasting tool. In this study, we demonstrate that the estimation of electron dynamics with satellite-data-independent models is possible and very accurate.
Predicting the electron population of Earth's ring current during geomagnetic storms still remains a challenging task.
In this work, we investigate the sensitivity of 10 keV ring current electrons to different driving processes, parameterised by the Kp index, during several moderate and intense storms.
Results are validated against measurements from the Van Allen Probes satellites. Perturbing the Kp index allows us to identify the most dominant processes for moderate and intense storms respectively.
We find that during moderate storms (Kp < 6) the drift velocities mostly control the behaviour of low energy electrons, while loss from wave-particle interactions is the most critical parameter for quantifying the evolution of intense storms (Kp > 6). Perturbations of the Kp index used to drive the boundary conditions at GEO and set the plasmapause location only show a minimal effect on simulation results over a limited L range.
It is further shown that the flux at L & SIM; 3 is more sensitive to changes in the Kp index compared to higher L shells, making it a good proxy for validating the source-loss balance of a ring current model.