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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.
The Cluster mission has produced a large data set of electron flux measurements in the Earth's magnetosphere since its launch in late 2000. Electron fluxes are measured using Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector as a function of energy, pitch angle, spacecraft position, and time. However, no adiabatic invariants have been calculated for Cluster so far. In this paper we present a step-by-step guide to calculations of adiabatic invariants and conversion of the electron flux to phase space density (PSD) in these coordinates. The electron flux is measured in two RAPID/IES energy channels providing pitch angle distribution at energies 39.2-50.5 and 68.1-94.5 keV in nominal mode since 2004. A fitting method allows to expand the conversion of the differential fluxes to the range from 40 to 150 keV. Best data coverage for phase space density in adiabatic invariant coordinates can be obtained for values of second adiabatic invariant, K, similar to 10(2), and values of the first adiabatic invariant mu in the range approximate to 5-20 MeV/G. Furthermore, we describe the production of a new data product "LSTAR," equivalent to the third adiabatic invariant, available through the Cluster Science Archive for years 2001-2018 with 1-min resolution. The produced data set adds to the availability of observations in Earth's radiation belts region and can be used for long-term statistical purposes.
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.
Whistler mode exohiss are the structureless hiss waves observed outside the plasma pause with featured equatorward Poynting flux. An event of the amplification of exohiss as well as chorus waves was recorded by Van Allen Probes during the recovery phase of a weak geomagnetic storm. Amplitudes of both types of the waves showed a significant increase at the regions of electron density enhancements. It is found that the electrons resonant with exohiss and chorus showed moderate pitch angle anisotropies. The ratio of the number of electrons resonating with exohiss to total electron number presented in-phase correlation with density variations, which suggests that exohiss can be amplified due to electron density enhancement in terms of cyclotron instability. The calculation of linear growth rates further supports above conclusion. We suggest that exohiss waves have potential to become more significant due to the background plasma fluctuation.
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.
We present the Neural-network-based Upper hybrid Resonance Determination (NURD) algorithm for automatic inference of the electron number density from plasma wave measurements made on board NASA's Van Allen Probes mission. A feedforward neural network is developed to determine the upper hybrid resonance frequency, fuhr, from electric field measurements, which is then used to calculate the electron number density. In previous missions, the plasma resonance bands were manually identified, and there have been few attempts to do robust, routine automated detections. We describe the design and implementation of the algorithm and perform an initial analysis of the resulting electron number density distribution obtained by applying NURD to 2.5 years of data collected with the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrumentation suite of the Van Allen Probes mission. Densities obtained by NURD are compared to those obtained by another recently developed automated technique and also to an existing empirical plasmasphere and trough density model.
We perform a statistical study calculating electromagnetic ion cyclotron (EMIC) wave amplitudes based off in situ plasma measurements taken by the Van Allen Probes’ (1.1–5.8 Re) Helium, Oxygen, Proton, Electron (HOPE) instrument. Calculated wave amplitudes are compared to EMIC waves observed by the Electric and Magnetic Field Instrument Suite and Integrated Science on board the Van Allen Probes during the same period. The survey covers a 22-month period (1 November 2012 to 31 August 2014), a full Van Allen Probe magnetic local time (MLT) precession. The linear theory proxy was used to identify EMIC wave events with plasma conditions favorable for EMIC wave excitation. Two hundred and thirty-two EMIC wave events (103 H+-band and 129 He+-band) were selected for this comparison. Nearly all events selected are observed beyond L = 4. Results show that calculated wave amplitudes exclusively using the in situ HOPE measurements produce amplitudes too low compared to the observed EMIC wave amplitudes. Hot proton anisotropy (Ahp) distributions are asymmetric in MLT within the inner (L < 7) magnetosphere with peak (minimum) Ahp, ∼0.81 to 1.00 (∼0.62), observed in the dawn (dusk), 0000 < MLT ≤ 1200 (1200 < MLT ≤ 2400), sectors. Measurements of Ahp are found to decrease in the presence of EMIC wave activity. Ahp amplification factors are determined and vary with respect to EMIC wave-band and MLT. He+-band events generally require double (quadruple) the measured Ahp for the dawn (dusk) sector to reproduce the observed EMIC wave amplitudes.
Since more than 15 years, the Cluster mission passes through Earth's radiation belts at least once every 2 days for several hours, measuring the electron intensity at energies from 30 to 400 keV. These data have previously been considered not usable due to contamination caused by penetrating energetic particles (protons at >100 keV and electrons at >400 keV). In this study, we assess the level of distortion of energetic electron spectra from the Research with Adaptive Particle Imaging Detector (RAPID)/Imaging Electron Spectrometer (IES) detector, determining the efficiency of its shielding. We base our assessment on the analysis of experimental data and a radiation transport code (Geant4). In simulations, we use the incident particle energy distribution of the AE9/AP9 radiation belt models. We identify the Roederer L values, L⋆, and energy channels that should be used with caution: at 3≤L⋆≤4, all energy channels (40–400 keV) are contaminated by protons (≃230 to 630 keV and >600 MeV); at L⋆≃1 and 4–6, the energy channels at 95–400 keV are contaminated by high-energy electrons (>400 keV). Comparison of the data with electron and proton observations from RBSP/MagEIS indicates that the subtraction of proton fluxes at energies ≃ 230–630 keV from the IES electron data adequately removes the proton contamination. We demonstrate the usefulness of the corrected data for scientific applications.
We present the dependence of the magnetosonic wave amplitudes both outside and inside the plasmapause on the solar wind and AE index using Van Allen Probe-A spacecraft during the time period of 1 October 2012 to 31 December 2015, based on a correlation and regression analysis. Solar wind parameters considered are the southward interplanetary magnetic field (IMF B-S), solar wind number density (N-SW), and bulk speed (V-SW). We find that the wave amplitudes outside (inside) the plasmapause are well correlated with the preceding AE, IMF B-S, and N-SW with time delays, each corresponding to 2-3 h (3-4 h), 4-5 h (3-4 h), and 2-3 h (8-9 h), while the correlation with V-SW is ambiguous both inside and outside the plasmapause. As measured by the correlation coefficient, the IMF B-S is the most influential solar wind parameter that affects the dayside wave amplitudes both outside and inside the plasmapause, while N-SW contributes to enhancing the duskside waves outside the plasmapause. The AE effect on wave amplitudes is comparable to that of IMF B-S. More interestingly, regression with time histories of the solar wind parameters and the AE index preceding the wave measurements outside the plasmapause shows significant dependence on the IMF B-S, N-SW, and AE: the region of peak coefficients is changed with time delay for IMF B-S and AE, while isolated peaks around duskside remain gradually decrease with time for N-SW. In addition, the regression with magnetosonic waves inside the plasmapause shows high coefficients around prenoon sector with preceding IMF B-S and V-SW.
In this paper, we address the question of whether spacecraft potential depends on the ambient electron density. In Maxwellian space plasmas, the onset of spacecraft charging does not depend on the ambient electron density. The balance of electron currents causes the incoming electrons to balance with the outgoing secondary electrons. The onset is controlled by the critical or anticritical temperature of the ambient electrons, but not the electron density. Above the critical temperature, charging to negative potential occurs. If the energy of the incoming electrons increases to well beyond the second crossing point of the secondary electron yield (SEY), the value of SEY decreases to well below unity. When the secondary electron current is negligible compared with the primary electron current, the spacecraft potential is governed solely by the balance of the incoming electrons and the sum of the currents of the repelled electrons and the attracted ions. In neutral space plasma, the electron and ion charges cancel each other. But if the space plasma deviates from being neutral, then the densities can have effect on the spacecraft potential. If the ambient plasma deviates significantly from equilibrium, a non-Maxwellian electron distribution may result. For a kappa distribution, one can show that the spacecraft charging level is independent of the ambient electron density. For a double Maxwellian distribution, the spacecraft charging level depends on the electron densities. For a conducting spacecraft charging in sunlight, the charging level is low and positive. It also depends on the ambient electron density. For a dielectric spacecraft in sunlight, the high-level negative-voltage charging on the shadowed side may extend to the sunlit side and block the photoelectrons trying to escape from the sunlit side. In this case, the charging level does not depend on ambient electron density. Using coordinated environmental and spacecraft charging data obtained from the Los Alamos National Laboratory geosynchronous satellites, we showed some results confirming that spacecraft potential is indeed often independent of the ambient electron density.