Ring current electron trajectories associated with VLF emissions

Abstract. Using the data from satellite CRRES and three geostationary LANL spacecraft, the propagation of an electron cloud from midnight to the evening sector is investigated. An electron cloud was injected during a weak isolated substorm that developed on a quiet geomagnetic background. It is found that within the local time sector from 03:00 until at least 08:00 MLT, the propagation of electrons at perpendicular pitch-angles is well described by a simple model of drift in the dipole magnetic field. The flux levels in the field-aligned electrons increase simultaneously with the flux at perpendicular pitch angles, which is attributed to the pitch angle diffusion by the whistler mode. This pitch-angle diffusion leads to precipitation of electrons from a drifting cloud and an increase in the ionospheric electron density, simultaneously observed above Tromsø, Norway, by the EISCAT UHF radar in the morning sector (04:40–05:25 MLT). The precipitation develops as quasi-periodic pulses with a period of about 100 s. We discuss the models of pulsating precipitation due to the whistler cyclotron instability and show that our observations can be explained by such a model.

The evolution of the bounce‐averaged ring current/radiation belt proton distribution is simulated during resonant interactions with ducted plasmaspheric hiss. The plasmaspheric hiss is assumed to be generated by ring current electrons and to be damped by the energetic protons. Thus energy is transferred between energetic electrons and protons using the plasmaspheric hiss as a mediary. The problem is not solved self‐consistently. During the simulation period, interactions with ring current electrons (not represented in the model) are assumed to maintain the wave amplitudes in the presence of damping by the energetic protons, allowing the wave spectrum to be held fixed. Diffusion coefficients in pitch angle, cross pitch angle/energy, and energy were previously calculated by Kozyra et al. (1994) and are adopted for the present study. The simulation treats the energy range, E ≥ 80 keV, within which the wave diffusion operates on a shorter timescale than other proton loss processes (i.e., Coulomb drag and charge exchange). These other loss processes are not included in the simulation. An interesting result of the simulation is that energy diffusion maximizes at moderate pitch angles near the edge of the atmospheric loss cone. Over the simulation period, diffusion in energy creates an order of magnitude enhancement in the bounce‐averaged proton distribution function at moderate pitch angles. The loss cone is nearly empty because scattering of particles at small pitch angles is weak. The bounce‐averaged flux distribution, mapped to ionospheric heights, results in elevated locally mirroring proton fluxes. OGO 5 observed order of magnitude enhancements in locally mirroring energetic protons at altitudes between 350 and 1300 km and invariant latitudes between 50° and 60° (Lundblad and Soraas, 1978). The proton distributions were highly anisotropic in pitch angle with nearly empty loss cones. The similarity between the observed distributions and those resulting from this simulation raises the possibility that interactions with plasmaspheric hiss play a role in forming and maintaining the characteristic zones of anisotropic proton precipitation in the subauroral ionosphere. Further assessment of the importance of this process depends on knowledge of the distribution in space and time of ducted plasmaspheric hiss in the inner magnetosphere.

Multi‐spacecraft data demonstrate that intense chorus waves are excited during electron injection events that drive rapid radiation belt electron loss across a limited energy range from 100 to 300 keV on sub‐drift timescales through strong pitch angle diffusion. We use a conjunction of Van Allen Probe A, B, and Arase spacecraft to study the variation of electron fluxes along an electron injection path in the energy range of 30 keV–1 MeV during the 20 April 2018, geomagnetic storm. At 100 keV, the 90 fluxes remained almost constant; for 100–300 keV, the fluxes decreased at all pitch angles; and at 300 keV, the fluxes showed a decrease following the injection closer to local midnight, and an increase further along the drift trajectory toward dawn. We calculate electron pitch angle and momentum diffusion coefficients in the observed waves using a quasi‐linear approximation: fast losses only occurred at lower pitch angles at 100 keV but reached the core distribution for 100–300 keV. For 300 keV, the overall pitch angle diffusion is weak, but energy diffusion acts to increase the electron flux along the injection path. The results indicate that intense chorus waves drive loss on timescales of 10s of minutes through strong pitch angle diffusion that is localized in energy and local time, consistent with the observations. Overall, electron injection events should be associated with intense losses in a limited energy range, the resulting atmospheric impacts having strong local‐time dependence, with preferential energy deposition in the morning sector during substorm injections.

The rate of energy injection into the geomagnetic ring current has been determined for the years 1958 and 1964 using a method based on Dst and knowledge of the decay rate for the ring current energy. At all levels of magnetic activity, the temporal behavior of the energy injection is similar to Dp in that it is burst-like; also there is a positive but imperfect correlation between Dp and the rate of energy injection into the ring current. The onset times of energy-injection bursts typically occur during the same hour or after the onset times of Dp bursts, and it is often possible to identify an injection burst as being associated with a particular Dp burst and then the peaks in both types of activity are simultaneous within one hour. During the quiet year of 1964, the average injection rate, on a monthly basis, was fairly constant and was near 1.2 × 1017 ergs sec−1. The rate during the active year 1958 was highly variable with the over-all average being 1.7 × 1017 ergs sec−1. Maximum hourly average injection rates of 1 × 1019 ergs sec−1 occurred during great magnetic storms. Although the injection of energy into the ring current, averaged over the entire ring, increases during a magnetospheric substorm, examination of longitudinal differences in the injection indicate temporary losses from the midnight and morning sectors at the onset of some substorms. Also it is found that when a magnetic storm follows a prolonged period of magnetic quiet, there is often precursor activity lasting 4 to 60 hours.

Magnetosonic (MS) waves are common plasma waves in the Earth's magnetosphere. The self‐consistent excitation of MS waves has been studied by 2D particle‐in‐cell simulations in the meridian and equatorial planes of a dipole magnetic field. However, the direction of wave propagation is artificially limited in the previous 2D simulations. Therefore, the 3D simulation of MS waves needs to be investigated. In this paper, we investigate the excitation and evolution of MS waves in the Earth's dipole magnetic field based on a 3D general curvilinear particle‐in‐cell simulation. We find that the MS waves are excited primarily within 3° of the equator when the thermal velocity of the ring distribution is much less than the ring velocity of the ring distribution. These waves propagate along both the radial and azimuthal directions nearly perpendicular to the background magnetic field. In the linear stage, the growth rates of MS waves are almost equal in the radial and azimuthal directions. Compared with the waves propagating along the radial direction, the waves propagating along the azimuthal direction can grow for a longer time, resulting in a larger wave amplification in this direction after saturation. The simulation results provide a valuable insight to understand the self‐consistent evolution of MS waves in the Earth's dipole magnetic field, and the findings are useful for understanding the plasma wave‐particle interaction in the Earth's radiation belts.

<p>Pitch angle distributions (PADs) of trapped particles play an important role in understanding the processes driving the dynamics of Earth’s radiation belts and ring current. The Van Allen Probes mission has provided electron observations of PADs with an unprecedented coverage in energy (from tens of keV to several MeV) and pitch angles during the mission’s lifespan. We approximate the equatorial electron PADs using the Fourier sine series expansion up to degree 5. The corresponding coefficients can be directly related to the main PAD shapes (pancake, butterfly, flat-top and cap), and the approximated PADs can be easily integrated and converted to omnidirectional flux. Using the entire Van Allen Probes MagEIS data set in 2012-2019, we analyze the response of the equatorial electron PAD shapes to 129 geomagnetic storms with minimum Dst< -50nT. At lower energies (<100 keV), the PADs are stable throughout geomagnetic storms and mainly exhibit a pancake shape. At higher energies, the storm-time PAD evolution depends on the magnetic local time (MLT). At dayside, the pancake distributions become steeper during the main phase and then recover to their original broader form during recovery phase, likely due to the inward radial diffusion. At nightside MLT, the butterfly distributions become more pronounced during the main phase due to the combination of drift-shell splitting and magnetopause shadowing. We present a simple polynomial regression model of PAD shapes driven by the solar wind dynamic pressure. The model allows reconstructions of the full equatorial PADs based on uni-directional measurements at low equatorial pitch angles (applicable to LEO satellite data), as well as from omnidirectional electron flux observations and significantly outperforms the standard sin(alpha) approximation.</p>

We present a detailed investigation of bounce-resonant pitch angle scattering of ring current electrons caused by electromagnetic ion cyclotron (EMIC) waves. It is found that H+ band EMIC waves can resonate with near-equatorially mirroring electrons over a wide range of L shells (i.e., 3≤L≤6) and energies and lead to the efficient transport of ring current electrons (i.e., ∼10 keV to 100 keV) from near 90° pitch angles to lower pitch angles. Computations of the bounce-resonant pitch angle scattering rates show a strong dependence on the L shell, electron energy, and resonance harmonics. When the L-shell increases, the orders of bounce resonance contributing to the whole scattering coefficient decrease, and meanwhile, it becomes difficult for the bounce resonance of higher orders to occur. Furthermore, when the electron energy increases, the bounce resonance orders decrease. Our results demonstrate that bounce-resonant scattering by H+ band EMIC waves can be an important loss mechanism for ∼10–100 keV electrons because of the absence of cyclotron resonance for ring current electrons interacting with EMIC waves. We conclude that bounce resonant scattering by H+ band EMIC waves should be incorporated into future modeling efforts of the ring current electron dynamics.

We simulate ring current dynamics during the 22 April 2001 geomagnetic storm (Dstmin = −102 nT) using our global ring current–atmosphere interactions model (RAM) extended to relativistic energies and electrons. The model retains four dimensions by solving the bounce‐averaged kinetic equation as a function of radial distance in the equatorial plane, magnetic local time (MLT), energy, and pitch angle. RAM includes time‐dependent convective transport and radial diffusion, all major loss processes, and is coupled with a dynamic 2‐D plasmasphere model. The global electric fields, as well as the boundary conditions at geosynchronous orbit, are specified from the Rice Convection Model (RCM) driven by a plasma sheet source population that depends on interplanetary conditions. The 1–30 keV electron fluxes simulated with RAM during the main phase of the storm at 4 ≤ L ≤ 6.5 agree reasonably well with THEMIS statistical data for active times (AE* > 300 nT). We calculate the pitch angle anisotropy of ring current electrons and the linear growth rate of whistler mode chorus in the equatorial plane at L ≤ 6.5 and for all MLT. Intense chorus waves are generated outside the plasmasphere (L > 4) in the premidnight to dawn local time sector by ring current electrons with ∼5 keV resonant energy. The chorus intensification on the dayside is smaller, and it is caused by higher‐energy ∼10 keV electrons. We present first results of the path‐integrated amplification of chorus obtained with the HOTRAY code using RAM outputs at selected locations. Significant chorus amplification with wave gain G ≥ 200 dB is obtained near local midnight after the fresh injections of ring current electrons from the plasma sheet. The global distribution of enhanced chorus waves on the nightside shows good agreement with recent surveys of near‐equatorial plasma wave data from satellites.

The 4–6 June 1991 magnetic storm, which occurred during solar maximum conditions, is analyzed to investigate two observed features of magnetic storms that are not completely understood: (1) the mass‐dependent decay of the ring current during the early recovery phase and (2) the role of preconditioning in multistep ring current development. A kinetic ring current drift‐loss model, driven by dynamic fluxes at the nightside outer boundary, was used to simulate this storm interval. A strong partial ring current developed and persisted throughout the main and early recovery phases. The majority of ions in the partial ring current make one pass through the inner magnetosphere on open drift paths before encountering the dayside magnetopause. The ring current exhibited a three‐phase decay in this storm. A short interval of charge‐exchange loss constituted the first phase of the decay followed by a classical two‐phase decay characterized by an abrupt transition between two very different decay timescales. The short interval dominated by charge‐exchange loss occurred because an abrupt northward turning of the interplanetary magnetic field (IMF) trapped ring current ions on closed trajectories, and turned‐off sources and “flow‐out” losses. If this had been the end of the solar wind disturbance, decay timescales would have gradually lengthened as charge exchange preferentially removed the short‐lived species; a distinctive two‐phase decay would not have resulted. However, the IMF turned weakly southward, drift paths became open, and a standard two‐phase decay ensued as the IMF rotated slowly northward again. As has been shown before, a two‐phase decay is produced as open drift paths are converted to closed in a weakening convection electric field, driving a transition from the fast flow‐out losses associated with the partial ring current to the slower charge‐exchange losses associated with the trapped ring current. The open drift path geometry during the main phase and during phase 1 of the two‐phase decay has important consequences for the evolution of ring current composition and for preconditioning issues. In this particular storm, ring current composition changes measured by the Combined Release and Radiation Effects Satellite (CRRES) during the main and recovery phase of the storm resulted largely from composition changes in the plasma sheet transmitted into the inner magnetosphere along open drift paths as the magnetic activity declined. Possible preconditioning elements were investigated during the multistep development of this storm, which was driven by the sequential arrival of three southward IMF Bz intervals of increasing peak strength. In each case, previous intensifications (preexisting ring currents) were swept out of the magnetosphere by the enhanced convection associated with the latest intensification and did not act as a significant preconditioning element. However, plasma sheet characteristics varied significantly between subsequent intensifications, altering the response of the magnetosphere to the sequential solar wind drivers. A denser plasma sheet (ring current source population) appeared during the second intensification, compensating for the weaker IMF Bz at this time and producing a minimum pressure‐corrected Dst* value comparable to the third intensification (driven by stronger IMF Bz but a lower density plasma sheet source). The controlling influence of the plasma sheet dynamics on the ring current dynamics and its role in altering the inner magnetospheric response to solar wind drivers during magnetic storms adds a sense of urgency to understanding what processes produce time‐dependent responses in the plasma sheet density, composition, and temperature.

Martin and Speiser (1988) have predicted ridges in the velocity space distribution function as a signature of the interaction of energetic ions with an X type neutral line in the geomagnetic tail. In this paper we study the properties of these ridges as the observation point is moved relative to the X line, as phase angle is varied, and the effect of the ridges on initial distributions with a loss cone. With the ridges, one can remotely sense not only the presence of an X line, but also, potentially, the distance from the X line, whether the observer is earthward or tailward of the X line, and the vertical position within the current sheet. For example, we find that for single particle dynamics in a current sheet with neutral line, the phase space ridge is predicted to be found throughout the current sheet if it is not destroyed by collective behavior. The ridge is predicted to be found for distributions plotted in ν⊥, ν∥ space and also in νx, νy, νz space. Additionally, valleys are found in νx, νy, νz space, which are also signatures of a neutral line, and which depend on the initial flowing distribution. An initially tailward flowing distribution causes asymmetries in distributions earthward versus tailward of the neutral line. These asymmetries are due to the fact that part of the distribution below (at smaller pitch angles than) the ridge comes from initially earthward (tailward) particles when the modeling point is earthward (tailward) of the neutral line. The accelerated beam is not predicted inside the current sheet at x = L (one separatrix distance earthward of the neutral line), but close to the sheet center a perpendicular bulk flow is predicted. Spatially, the ridge is found to move to larger pitch angles as the observation point approaches the neutral line in the plasma sheet boundary layer. As the observation point moves toward the current sheet center, the ridge stays at about the same pitch angle, but then tends to be diminished very near the center where a perpendicular bulk flow is found. Chaotic pitch angle scattering can fill even a relatively large (10°), initially empty loss cone. This loss cone filling is more complete when orbits are calculated in a thicker current sheet. Thus chaotic pitch angle scattering may be a dominant mechanism to produce nightside proton isotropy in the auroral zones, as suggested by Sergeev et al. (1983).

This paper attempts to summarize the current understanding of the storm/substorm relationship by clearing up a considerable amount of controversy and by addressing the question of how solar wind energy is deposited into and is dissipated in the constituent elements that are critical to magnetospheric and ionospheric processes during magnetic storms. (1) Four mechanisms are identified and discussed as the primary causes of enhanced electric fields in the interplanetary medium responsible for geomagnetic storms. It is pointed out that in reality, these four mechanisms, which are not mutually exclusive, but interdependent, interact differently from event to event. Interplanetary coronal mass ejections (ICMEs) and corotating interaction regions (CIRs) are found to be the primary phenomena responsible for the main phase of geomagnetic storms. The other two mechanisms, i.e., HILDCAA (high‐intensity, long‐duration, continuous auroral electrojet activity) and the so‐called Russell‐McPherron effect, work to make the ICME and CIR phenomena more geoeffective. The solar cycle dependence of the various sources in creating magnetic storms has yet to be quantitatively understood. (2) A serious controversy exists as to whether the successive occurrence of intense substorms plays a direct role in the energization of ring current particles or whether the enhanced electric field associated with southward IMF enhances the effect of substorm expansions. While most of the Dst variance during magnetic storms can be solely reproduced by changes in the large‐scale electric field in the solar wind and the residuals are uncorrelated with substorms, recent satellite observations of the ring current constituents during the main phase of magnetic storms show the importance of ionospheric ions. This implies that ionospheric ions, which are associated with the frequent occurrence of intense substorms, are accelerated upward along magnetic field lines, contributing to the energy density of the storm‐time ring current. An apparently new controversy regarding the relative importance of the two processes is thus created. It is important to identify the role of substorm occurrence in the large‐scale enhancement of magnetospheric convection driven by solar wind electric fields. (3) Numerical schemes for predicting geomagnetic activity indices on the basis of solar/solar wind/interplanetary magnetic field parameters continue to be upgraded, ensuring reliable techniques for forecasting magnetic storms under real‐time conditions. There is a need to evaluate the prediction capability of geomagnetic indices on the basis of physical processes that occur during storm time substorms. (4) It is crucial to differentiate between storms and nonstorm time substorms in terms of energy transfer/conversion processes, i.e., mechanical energy from the solar wind, electromagnetic energy in the magnetotail, and again, mechanical energy of particles in the plasma sheet, ring current, and aurora. To help answer the question of the role of substorms in energizing ring current particles, it is crucial to find efficient magnetospheric processes that heat ions up to some minimal energies so that they can have an effect on the strength of the storm time ring current. (5) The question of whether the Dst index is an accurate and effective measure of the storm time ring current is also controversial. In particular, it is demonstrated that the dipolarization effect associated with substorm expansion acts to reduce the Dst magnitude, even though the ring current may still be growing.

VLF-emissions associated with ring current electrons: Off-equatorial observations

The extra magnetic energy present in the magnetosphere during a magnetic storm is shown to be the same as if the disturbing field existed without the main field of the Earth: that is, the “joint” energy of the two fields is zero. The disturbance field energy is considered for both the first and the main phase of a storm, on the basis of idealized models of the electric currents that cause the disturbance. The currents, actually distributed throughout volumes, are taken to flow only on surfaces. Numerical estimates of the field energy are given, for a weak storm and for a great storm. The magnetic moment of the field of the ring current is also considered; it is inferred that it is only a small fraction of the Earth's dipole moment. The field energy of magnetic storms is found to be less than the kinetic energy associated with the ring current at the peak of the main phase.

Large increases of electron 100 ev ≲ Ee ≲. 40 kev energy fluxes over L ≃ 2.8 to L ≃ 4.0 were observed at the onset of magnetic storms on October 1 and October 29, 1961, with instrumentation on Explorer 12. The omnidirectional energy fluxes at L = 3.5 were ∼1000 ergs(cm2 sec)−1 for these two events, the duration of these events was approximately one day, and the peak energy flux was positioned at L ≃3.0. The large enhancement of electron 100 ev ≲ Ee ≲ 40 kev energy fluxes on October 1 is coincident with large decreases of electron Ee ≳ 1.6 Mev intensities and with increases of electron 40 kev ≲ Ee ≲ 100 kev intensities in the outer radiation zone. Although no spectral information concerning the electron 100 ev ≈ Ee ≤ 40 kev fluxes is available, estimates of the decrease of the magnetic field on the surface of the earth at the magnetic equator for monoenergetic electron intensities corresponding to the observed energy fluxes are ∼60 γ for Ee = 500 ev and ∼30γ for Ee = 2 kev during the main phase of the magnetic storm. The observations reported here suggest that these electrons form a ring current centered at ∼3 RE, which is responsible for some fraction of the main phase and the rapid-decay component DR1 of magnetic storms. An upper limit on the increases of the proton Ep≳ 400 ev energy fluxes is ∼100 ergs (cm2 sec)−1 at L∼3 during the main phases of these two magnetic storms, an upper limit that is not low enough to eliminate a low-energy proton ring current of similar or greater magnitude when compared with the above low-energy electron ring current.

Electron lifetimes are important for understanding the dominant loss processes of radiation belt electrons to the atmosphere and for accurate radiation belt modeling. We estimate electron lifetimes from the precipitating population measured in Low Earth Orbit (LEO) from the Polar Orbiting Environmental Satellites (POES). We compare our estimates to previous estimates from the Radiation Belt Storm Probes (RBSP) by Claudepierre et al. (2020b, https://doi.org/10.1029/2019GL086053). We also present the first complete pitch angle resolved lifetimes in the radiation belts. Quasi‐linear theory predicts the pitch angle distribution decays uniformly, therefore if steady‐state decay is realized, POES and RBSP should measure similar lifetimes. Lifetime estimates from LEO are shown to be in good agreement with those from Van Allen Probes in the outer belt and pitch angle resolved lifetimes indicate that steady‐state decay is realized. However, a systematic slight overestimation of the POES lifetimes reveal that the POES instruments may suffer from bremsstrahlung contamination. At L = 2–3, no decay intervals were identified in the POES electron fluxes and the near loss cone RBSP electron fluxes. We show that at these L‐shells, where lifetimes are long, there is an apparent decoupling of the perpendicular and parallel flux. Large pitch angle anisotropy and processes that affect low pitch angle electrons are two explanations for this apparent decoupling. Electron lifetime models that use pitch angle independent lifetimes, derived from the equatorially mirroring electron flux, likely underestimate the amount of precipitating flux and may not capture the dynamics of low equatorial pitch angle electrons at L < 3.