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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.
New wave frequency and amplitude models for the nightside and dayside chorus waves are built based on measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. The corresponding 3D diffusion coefficients are systematically obtained. Compared with previous commonly-used (typical) parameterizations, the new parameterizations result in differences in diffusion rates that depend on the energy and pitch angle. Furthermore, one-year 3D diffusive simulations are performed using the Versatile Electron Radiation Belt (VERB) code. Both typical and new wave parameterizations simulation results are in a good agreement with observations at 0.9 MeV. However, the new parameterizations for nightside chorus better reproduce the observed electron fluxes. These parameterizations will be incorporated into future modeling efforts.
The "Lomonosov" space project is lead by Lomonosov Moscow State University in collaboration with the following key partners: Joint Institute for Nuclear Research, Russia, University of California, Los Angeles (USA), University of Pueblo (Mexico), Sungkyunkwan University (Republic of Korea) and with Russian space industry organi-zations to study some of extreme phenomena in space related to astrophysics, astroparticle physics, space physics, and space biology. The primary goals of this experiment are to study: -Ultra-high energy cosmic rays (UHECR) in the energy range of the Greizen-ZatsepinKuzmin (GZK) cutoff; -Ultraviolet (UV) transient luminous events in the upper atmosphere; -Multi-wavelength study of gamma-ray bursts in visible, UV, gamma, and X-rays; -Energetic trapped and precipitated radiation (electrons and protons) at low-Earth orbit (LEO) in connection with global geomagnetic disturbances; -Multicomponent radiation doses along the orbit of spacecraft under different geomagnetic conditions and testing of space segments of optical observations of space-debris and other space objects; -Instrumental vestibular-sensor conflict of zero-gravity phenomena during space flight. This paper is directed towards the general description of both scientific goals of the project and scientific equipment on board the satellite. The following papers of this issue are devoted to detailed descriptions of scientific instruments.
Modeling and observations have shown that energy diffusion by chorus waves is an important source of acceleration of electrons to relativistic energies. By performing long-term simulations using the three-dimensional Versatile Electron Radiation Belt code, in this study, we test how the latitudinal dependence of chorus waves can affect the dynamics of the radiation belt electrons. Results show that the variability of chorus waves at high latitudes is critical for modeling of megaelectron volt (MeV) electrons. We show that, depending on the latitudinal distribution of chorus waves under different geomagnetic conditions, they cannot only produce a net acceleration but also a net loss of MeV electrons. Decrease in high-latitude chorus waves can tip the balance between acceleration and loss toward acceleration, or alternatively, the increase in high-latitude waves can result in a net loss of MeV electrons. Variations in high-latitude chorus may account for some of the variability of MeV electrons.
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.
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.
Fast-localized electron loss, resulting from interactions with electromagnetic ion cyclotron (EMIC) waves, can produce deepening minima in phase space density (PSD) radial profiles. Here, we perform a statistical analysis of local PSD minima to quantify how readily these are associated with radiation belt depletions. The statistics of PSD minima observed over a year are compared to the Versatile Electron Radiation Belts (VERB) simulations, both including and excluding EMIC waves. The observed minima distribution can only be achieved in the simulation including EMIC waves, indicating their importance in the dynamics of the radiation belts. By analyzing electron flux depletions in conjunction with the observed PSD minima, we show that, in the heart of the outer radiation belt (L* < 5), on average, 53% of multi-MeV electron depletions are associated with PSD minima, demonstrating that fast localized loss by interactions with EMIC waves are a common and crucial process for ultra-relativistic electron populations.
In this study, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1-D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3, and 6. We find that the equilibrium states at moderately low Kp, when plotted versus L shell (L) and energy (E), display the same interesting S shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L shell. Equilibrium electron flux profiles are governed by the Biot number (tau(Diffusion)/tau(loss)), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E>300 keV and moderate Kp (<= 3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp = 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E similar to [200, 300] keV for L= [3.7, 4] at Kp= 1, E similar to[0.6, 1] MeV for L = [3, 4] at Kp = 3, and E similar to 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.