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The main objective of SHIELDS project is to develop a new capability to understand, model, and predict the spacecraft Surface Charging Environment (SCE).
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Three-dimensional particle-in-cell simulations of decaying whistler turbulence are carried out on a collisionless, homogeneous, magnetized, electron-ion plasma model. In addition, the simulations use an initial ensemble of relatively long wavelength whistler modes with a broad range of initial propagation directions with an initial electron beta β e = 0.05. The computations follow the temporal evolution of the fluctuations as they cascade into broadband turbulent spectra at shorter wavelengths. Three simulations correspond to successively larger simulation boxes and successively longer wavelengths of the initial fluctuations. The computations confirm previous results showing electron heating is preferentially parallel to the background magnetic field B o , and ion heating is preferentially perpendicular to B o . The new results here are that larger simulation boxes and longer initial whistler wavelengths yield weaker overall dissipation, consistent with linear dispersion theory predictions of decreased damping, stronger ion heating, consistent with a stronger ion Landau resonance, and weaker electron heating.
We simulate electromagnetic ion cyclotron (EMIC) wave growth and evolution within three regions, the plasmasphere (or plasmaspheric plume), the plasmapause, and the low-density plasmatrough outside the plasmapause. First, we use a ring current simulation with a plasmasphere model to model the particle populations that give rise to the instability for conditions observed on 9 June 2001. Then, using two different models for the cold ion composition, we do a full scale hybrid code simulation in dipole coordinates of the EMIC waves on a meridional plane at MLT = 18 and at 1900 UT within a range of L shell from L = 4.9 to 6.7. EMIC waves were observed during June 9, 2001 by Geostationary Operational Environmental Satellite (GOES) spacecraft. While an exact comparison between observed and simulated spectra is not possible here, we do find significant similarities between the two, at least at one location within the region of largest wave growth. We find that the plasmapause is not a preferred region for EMIC wave growth, though waves can grow in that region. The density gradient within the plasmapause does, however, affect the orientation of wave fronts and wave vector both within the plasmapause and in adjacent regions. There is a preference for EMIC waves to be driven in the He+ band (frequencies between the O+ and He+ gyrofrequencies) within the plasmasphere, although they can also grow in the plasmatrough. If present, H+ band waves are more likely to grow in the plasmatrough. This fact, plus L dependence of the frequency and possible time evolution toward lower frequency waves, can be explained by a simple model. Large O+ concentration limits the frequency range of or even totally quenches EMIC waves. This is more likely to occur in the plasmatrough at solar maximum. Such large O+ concentration significantly affects the H+ cutoff frequency and hence the width in frequency of the stop band above the He+ gyrofrequency. EMIC wave surfaces predicted by cold plasma theory are altered by the finite temperature of the ring current H+.
Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field RAM-SCB, a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field. By applying quasi-linear theory, the bounce- and MLT-averaged electron pitch angle, mixed term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (~1 MeV) and ring current (~100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyro-resonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L = 4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the March 17 2013 storm and for L ≲ 4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.
Relativistic electrons have been thought to more easily resonate with electromagnetic ion cyclotron EMIC waves if the total density is large. We show that, for a particular EMIC mode, this dependence is weak due to the dependence of the wave frequency and wave vector on the density. A significant increase in relativistic electron minimum resonant energy might occur for the H band EMIC mode only for small density, but no changes in parameters significantly decrease the minimum resonant energy from a nominal value. The minimum resonant energy depends most strongly on the thermal velocity associated with the field line motion of the hot ring current protons that drive the instability. High density due to a plasmasphere or plasmaspheric plume could possibly lead to lower minimum resonance energy by causing the He band EMIC mode to be dominant. We demonstrate these points using parameters from a ring current simulation.
During the small storm on 14–15 April 2014, Van Allen Probe A measured a continuously distinct proton ring distribution and enhanced magnetosonic (MS) waves along its orbit outside the plasmapause. Inside the plasmasphere, strong MS waves were still present but the distinct proton ring distribution was falling steeply with distance. We adopt a sum of subtracted bi-Maxwellian components to model the observed proton ring distribution and simulate the wave trajectory and growth. MS waves at first propagate toward lower L shells outside the plasmasphere, with rapidly increasing path gains related to the continuous proton ring distribution. The waves then gradually cross the plasmapause into the deep plasmasphere, with almost unchanged path gains due to the falling proton ring distribution and higher ambient density. These results present the first report on how MS waves penetrate into the plasmasphere with the aid of the continuous proton ring distributions during weak geomagnetic activities.
Fast mode magnetosonic waves are typically confined close to the magnetic equator and exhibit harmonic structures at multiples of the local, equatorial proton cyclotron frequency. Here, we report observations of magnetosonic waves well off the equator at geomagnetic latitudes from -16.5°to -17.9° and L shell ~2.7–4.6. The observed waves exhibit discrete spectral structures with multiple frequency spacings. The predominant frequency spacings are ~6 and 9 Hz, neither of which is equal to the local proton cyclotron frequency. Backward ray tracing simulations show that the feature of multiple frequency spacings is caused by propagation from two spatially narrow equatorial source regions located at L ≈ 4.2 and 3.7. The equatorial proton cyclotron frequencies at those two locations match the two observed frequency spacings. Finally, our analysis provides the first observations of the harmonic nature of magnetosonic waves well away from the equatorial region and suggests that the propagation from multiple equatorial sources contributes to these off-equatorial magnetosonic emissions with varying frequency spacings.
We report that past studies of radiation belt relativistic electrons have favored active storm time periods, while the effects of small geomagnetic storms (Dst >₋50 nT) have not been statistically characterized. In this timely study, given the current weak solar cycle, we identify 342 small storms from 1989 through 2000 and quantify the corresponding change in relativistic electron flux at geosynchronous orbit. Surprisingly, small storms can be equally as effective as large storms at enhancing and depleting fluxes. Slight differences exist, as small storms are 10% less likely to result in flux enhancement and 10% more likely to result in flux depletion than large storms. Nevertheless, it is clear that neither acceleration nor loss mechanisms scale with storm drivers as would be expected. Small geomagnetic storms play a significant role in radiation belt relativistic electron dynamics and provide opportunities to gain new insights into the complex balance of acceleration and loss processes.
Our study demonstrates the feasibility and reliability of using observations from low Earth orbit (LEO) to forecast and nowcast relativistic electrons in the outer radiation belt. Furthermore, we first report a high cross-energy, cross-pitch-angle coherence discovered between the trapped MeV electrons and precipitating approximately hundreds (~100s) of keV electrons—observed by satellites with very different altitudes—with correlation coefficients as high as ≳ 0.85. We then tested the feasibility of applying linear prediction filters to LEO data to predict the arrival of new MeV electrons during geomagnetic storms, as well as their evolving distributions afterward, based on the coherence. Reliability of these predictive filters is quantified by the performance efficiency with values as high as 0.74 when driven merely by LEO observations (or up to 0.94 with the inclusion of in situ MeV electron measurements). Finally, a hypothesis based upon the wave-particle resonance theory is proposed to explain the coherence, and a first-principle electron tracing model yields supporting evidence.
Enabled by the comprehensive measurements from the Magnetic Electron Ion Spectrometer (MagEIS), Helium Oxygen Proton Electron mass spectrometer (HOPE), and Radiation Belt Storm Probes Ion Composition Experiment (RBSPICE) instruments onboard Van Allen Probes in the heart of the radiation belt, the relative contributions of ions with different energies and species to the ring current energy density and their dependence on the phases of geomagnetic storms are quantified. The results show that lower energy (<50 keV) protons enhance much more often and also decay much faster than higher-energy protons. During the storm main phase, ions with energies <50 keV contribute more significantly to the ring current than those with higher energies; while the higher-energy protons dominate during the recovery phase and quiet times. The enhancements of higher-energy proton fluxes as well as energy content generally occur later than those of lower energy protons, which could be due to the inward radial diffusion. For the 29 March 2013 storm we investigated in detail that the contribution from O + is ~25% of the ring current energy content during the main phase and the majority of that comes from <50 keV O + . This indicates that even during moderate geomagnetic storms the ionosphere is still an important contributor to the ring current ions. Using the Dessler-Parker-Sckopke relation, the contributions of ring current particles to the magnetic field depression during this geomagnetic storm are also calculated. In conclusion, the results show that the measured ring current ions contribute about half of the Dst depression.
A statistical survey of electron pitch angle distributions (PADs) is performed based on the pitch angle-resolved flux observations from the Magnetic Electron Ion Spectrometer (MagEIS) instrument on board the Van Allen Probes during the period from 1 October 2012 to 1 May 2015. By fitting the measured PADs to a sin n α form, where α is the local pitch angle and n is the power law index, we investigate the dependence of PADs on electron kinetic energy, magnetic local time (MLT), the geomagnetic Kp index, and L shell. The difference in electron PADs between the inner and outer belt is distinct. In the outer belt, the common averaged n values are less than 1.5, except for large values of the Kp index and high electron energies. The averaged n values vary considerably with MLT, with a peak in the afternoon sector and an increase with increasing L shell. In the inner belt, the averaged n values are much larger, with a common value greater than 2. The PADs show a slight dependence on MLT, with a weak maximum at noon. A distinct region with steep PADs lies in the outer edge of the inner belt where the electron flux is relatively low. The distance between the inner and outer belt and the intensity of the geomagnetic activity together determine the variation of PADs in the inner belt. Finally, besides being dependent on electron energy, magnetic activity, and L shell, the results show a clear dependence on MLT, with higher n values on the dayside.
In this study, we investigate the possibility of nonlinearity in chorus waves during a geomagnetic storm on 1 November 2012. The data we use were measured by the Van Allen Probe B. Wave data and plasma sheet electron data are analyzed. Chorus waves were frequently measured in the morning side during the main phase of this storm. Large–amplitude chorus waves were seen of the order of ~0.6 nT and >7 mV/m, which are similar to or larger than the typical ULF waves. The waves quite often consist of rising tones during the burst sampling. Since the rising tone is known as a signature of nonlinearity, a large portion of the waves are regarded as nonlinear at least during the burst sampling periods. These results underline the importance of nonlinearity in the dynamics of chorus waves. We further compare the measurement and the nonlinear theories, based on the inhomogeneity ratio, our own calculation derived from the field equation and the backward wave oscillator model. The wave quantities examined are frequency, amplitude, frequency drift rate, and duration. Furthermore, this type of study is useful to more deeply understand wave-particle interactions and hence may lead to predicting the generation and loss of radiation belt electrons in the future.
The 18–19 October 1998 GEM (Geospace Environment Modeling) storm was associated with a long interval of remarkably steady southward interplanetary magnetic field. Here in this study we demonstrate that classical substorms occurred throughout the interval and that the storm appears to be composed of the typical two-mode response consisting of a recurrent loading/unloading cycle on a timescale of approximately 2–4 h together with an episodic/bursty continuously driven component operating on a timescale of 5–15 min. The loading/unloading activity is manifested as typical poleward expanding “embedded” substorms (embedded into the auroral oval) emerging from the equatorward regions of the auroral distribution, while the continuously driven component is manifested by the episodic ejection of streamers equatorward from poleward boundary activations. The streamers subsequently produce torches and eastward drifting omega bands which likely moderate the need for substorms to occur more frequently than observed.
In this paper, 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 1D 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 vs 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 (τ Diffusion /τ 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 ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E ~ [0.6, 1] MeV for L = [3, 4] at Kp = 3, and E ~ 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.
We present observations from the Van Allen Probes spacecraft that identify a region of intense whistler mode activity within a large density enhancement outside of the plasmasphere. We speculate that this density enhancement is part of a remnant plasmaspheric plume, with the observed wave being driven by a weakly anisotropic electron injection that drifted into the plume and became nonlinearly unstable to whistler emission. Particle measurements indicate that a significant fraction of thermal (<100 eV) electrons within the plume were subject to Landau acceleration by these waves, an effect that is naturally explained by whistler emission within a gradient and high-density ducting inside a density enhancement.
Recent observations from the Van Allen Probes Helium Oxygen Proton Electron (HOPE) instrument revealed a persistent depletion in the 1–10 eV ion population in the postmidnight sector during quiet times in the 2 < L < 3 region. This study explores the source of this ion depletion by developing an algorithm to classify 26 months of pitch angle distributions measured by the HOPE instrument. We correct the HOPE low energy fluxes for spacecraft potential using measurements from the Electric Field and Waves (EFW) instrument. A high percentage of low count pitch angle distributions is found in the postmidnight sector coupled with a low percentage of ion distributions peaked perpendicular to the field line. A peak in loss cone distributions in the dusk sector is also observed. Here, these results characterize the nature of the dearth of the near 90° pitch angle 1–10 eV ion population in the near-Earth postmidnight sector. This study also shows, for the first time, low-energy HOPE differential number fluxes corrected for spacecraft potential and 1–10 eV H + fluxes at different levels of geomagnetic activity.