Earth's Radiation Belts Research Articles

Sub‐MeV Electron Precipitation Driven by EMIC Waves Through Nonlinear Fractional Resonances

AbstractElectromagnetic ion cyclotron waves in the Earth's outer radiation belt drive rapid electron losses through wave‐particle interactions. The precipitating electron flux can be high in the hundreds of keV energy range, well below the typical minimum resonance energy. One of the proposed explanations relies on nonresonant scattering, which causes pitch‐angle diffusion away from the fundamental cyclotron resonance. Here we propose the fractional sub‐cyclotron resonance, a second‐order nonlinear effect that scatters particles at resonance order n = 1/2, as an alternate explanation. Using test‐particle simulations, we evaluate the precipitation ratios of sub‐MeV electrons for wave packets with various shapes, amplitudes, and wave normal angles. We show that the nonlinear sub‐cyclotron scattering produces larger ratios than the nonresonant scattering when the wave amplitude reaches sufficiently large values. The ELFIN CubeSats detected several events with precipitation ratio patterns matching our simulation, demonstrating the importance of sub‐cyclotron resonances during intense precipitation events.

Large Amplitude Whistler Waves in Earth's Plasmasphere and Plasmaspheric Plumes

AbstractWhistler mode waves in the plasmasphere and plumes drive significant losses of energetic electrons from the Earth's radiation belts into the upper atmosphere. In this study, we conducted a survey of amplitude‐dependent whistler wave properties and analyzed their associated background plasma conditions and electron fluxes in the plasmasphere and plumes. Our findings indicate that extremely large amplitude (>400 pT) whistler waves (a) tend to occur at L > 4 over the midnight‐dawn‐noon sectors and have small wave normal angles; (b) are more likely to occur during active geomagnetic conditions associated with higher fluxes of anisotropic electrons at 10 s keV energies; and (c) tend to occur at higher latitudes up to 20° with increasing amplitude. These results suggest that extremely large amplitude whistler waves in the plasmasphere and plumes could be generated locally by injected electrons during substorms and further amplified when propagating to higher latitudes.

Distribution of Seed Electron Phase Space Density Minima in Earth's Radiation Belts

AbstractWe conducted a statistical analysis of local phase space density (PSD) minima across a wide energy range (∼20 keVs to ∼10 MeV), using observations from the Van Allen Probes and the Geostationary Operational Environmental Satellite. We identified deepening minima in PSD profiles of multi‐MeV (∼5% occurrence) and of “seed” electrons (up to 15% occurrence, corresponding to ∼70–100 s keV) and compared their distribution with a 3D diffusion model using the Versatile Electron Radiation Belts (VERB) code. The comparison of the observed and modeled distributions suggests that the PSD minima of seed electrons are likely associated with hiss waves and the corresponding L‐shell dependent electron lifetimes. However, the observed distribution was not fully reproduced by the model, potentially indicating other fast loss mechanisms of seed electrons.

A Sub‐relativistic Electron Three‐Belt Event in the Earth's Radiation Belts: Observation and Explanation

AbstractThe Van Allen Probes mission contributed to the discovery of the relativistic (∼500 keV–2 MeV) and ultra‐relativistic (∼>2 MeV) electron three‐belt structure in Earth's radiation belts. This structure results from the partial depletion of the preexisting outer belt and the replenishment of a new outer belt. Ultra‐low frequency and very‐low frequency waves are believed to play important roles in these processes, and substorm injections are usually not responsible for the formation of the external outer belt. In this study, based on observations from the Arase and NOAA‐18 (National Oceanic and Atmospheric Administration‐18) satellites, we report an electron three‐belt event in the energy range of ∼100–200 keV (i.e., sub‐relativistic electrons). According to the evolution of the phase space density and the dawn‐dusk asymmetric flux enhancement during this event, we conclude that the depletion of the upper part of the original outer belt was due to outward radial diffusion accompanied by magnetopause shadowing effect and convection, and the formation of the external outer belt was due to increased electron flux from convection as well as substorm injections. This discovery and its preliminary explanation may help understand the electron three‐belt structure in radiation belts more comprehensively.

Low-frequency whistler waves driven by energetic electrons in plasmas of solely electron cyclotron wave heating

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts.

Nonresonant Scattering of Energetic Electrons by Electromagnetic Ion Cyclotron Waves: Spacecraft Observations and Theoretical Framework

AbstractElectromagnetic ion cyclotron (EMIC) waves lead to rapid scattering of relativistic electrons in Earth's radiation belts, due to their large amplitudes relative to other waves that interact with electrons of this energy range. A central feature of electron precipitation driven by EMIC waves is deeply elusive. That is, moderate precipitating fluxes at energies below the minimum resonance energy of EMIC waves occur concurrently with strong precipitating fluxes at resonance energies in low‐altitude spacecraft observations. This paper expands on a previously reported solution to this problem: nonresonant scattering due to wave packets. The quasi‐linear diffusion model is generalized to incorporate nonresonant scattering by a generic wave shape. The diffusion rate decays exponentially away from the resonance, where shorter packets lower decay rates and thus widen the energy range of significant scattering. Using realistic EMIC wave packets from δf particle‐in‐cell simulations, test particle simulations are performed to demonstrate that intense, short packets extend the energy of significant scattering well below the minimum resonance energy, consistent with our theoretical prediction. Finally, the calculated precipitating‐to‐trapped flux ratio of relativistic electrons is compared to ELFIN observations, and the wave power spectra is inferred based on the measured flux ratio. We demonstrate that even with a narrow wave spectrum, short EMIC wave packets can provide moderately intense precipitating fluxes well below the minimum resonance energy.

Archimedean Spiral Distribution of Energetic Particles in Earth's Inner Radiation Belt

AbstractArchimedean spirals are common in various fields such as biology, engineering, astronomy, and space physics. Here we report the discovery of patterns resembling the general Archimedean spirals in particle distributions in the Earth radiation belt. Our analytic theory and numerical simulations demonstrate that electrons with initially asymmetric spatial distributions form such spirals in the inner magnetosphere, where particles at smaller radial distances move more slowly in angular velocity. These spirals result in time‐varying peaks and valleys in particle fluxes, referred to as “zebra stripes,” which are well consistent with Van Allen Probes measurements. Although the initial asymmetric distribution may be seeded by the electric field in the magnetosphere, the spiral formation does not require them. Furthermore, we show that, due to the same fundamental motion of charged particles in regions dominated by dipole fields, this spiral phenomenon may also appear in the proton distributions, as well as in planetary magnetospheres.

On the Two Approaches to Incorporate Wave‐Particle Resonant Effects Into Global Test Particle Simulations

AbstractEnergetic electron dynamics in the Earth's radiation belts and near‐Earth plasma sheet are controlled by multiple processes operating on very different time scales: from storm‐time magnetic field reconfiguration on a timescale of hours to individual resonant wave‐particle interactions on a timescale of milliseconds. The most advanced models for such dynamics either include test particle simulations in electromagnetic fields from global magnetospheric models, or those that solve the Fokker‐Plank equation for long‐term effects of wave‐particle resonant interactions. The most prospective method, however, would be to combine these two classes of models, to allow the inclusion of resonant electron scattering into simulations of electron motion in global magnetospheric fields. However, there are still significant outstanding challenges that remain regarding how to incorporate the long term effects of wave‐particle interactions in test‐particle simulations. In this paper, we describe in details two approaches that incorporate electron scattering in test particle simulations: stochastic differential equation (SDE) approach and the mapping technique. Both approaches assume that wave‐particle interactions can be described as a probabilistic process that changes electron energy, pitch‐angle, and thus modifies the test particle dynamics. To compare these approaches, we model electron resonant interactions with field‐aligned whistler‐mode waves in dipole magnetic fields. This comparison shows advantages of the mapping technique in simulating the nonlinear resonant effects, but also underlines that more significant computational resources are needed for this technique in comparison with the SDE approach. We further discuss applications of both approaches in improving existing models of energetic electron dynamics.

Design and construction of the near-earth space plasma simulation system of the Space Plasma Environment Research Facility

Our earth is immersed in the near-earth space plasma environment, which plays a vital role in protecting our planet against the solar-wind impact and influencing space activities. It is significant to investigate the physical processes dominating the environment, for deepening our scientific understanding of it and improving the ability to forecast the space weather. As a crucial part of the National Major Scientific and Technological Infrastructure–Space Environment Simulation Research Infrastructure (SESRI) in Harbin, the Space Plasma Environment Research Facility (SPERF) builds a system to replicate the near-earth space plasma environment in the laboratory. The system aims to simulate the three-dimensional (3-D) structure and processes of the terrestrial magnetosphere for the first time in the world, providing a unique platform to reveal the physics of the 3-D asymmetric magnetic reconnection relevant to the earth's magnetopause, wave–particle interaction in the earth's radiation belt, particles’ dynamics during the geomagnetic storm, etc. The paper will present the engineering design and construction of the near-earth space plasma simulation system of the SPERF, with a focus on the critical technologies that have been resolved to achieve the scientific goals. Meanwhile, the possible physical issues that can be studied based on the apparatus are sketched briefly. The earth-based system is of great value in understanding the space plasma environment and supporting space exploration.

Observations of Relativistic Electron Enhancement and Butterfly Pitch Angle Distributions at Low L (<3)

AbstractElectrons in Earth's outer radiation belt are highly dynamic, with fluxes changing by up to orders of magnitude. The penetration of electrons from the outer belt to the inner belt is one such change observed during geomagnetic storms and was previously observed in electrons up to 1 MeV for some strong storms observed by the Van Allen Probes. We analyze pulse height analysis data from the Relativistic Electric and Proton Telescope (REPT) on the Van Allen Probes to produce electron flux measurements with lower minimum energy and significantly improved resolution compared to the standard REPT data and show that electron penetrations into the inner belt (L ≤ 2) extend to at least 1.3 MeV and penetrations into the slot region (2 < L < 2.8) extend to at least 1.5 MeV during certain geomagnetic storms. We also demonstrate that these penetrations are associated with butterfly pitch angle distributions from 1 to 1.3 MeV.

АНАЛИЗ РАДИАЦИОННЫХ НАГРУЗОК В КАЮТЕ МКС ПРИ ИСПОЛЬЗОВАНИИ ЗАЩИТЫ ИЗ КОМПОЗИТНОГО МАТЕРИАЛА

The paper reports the results of calculating doses in the location of a cylindrical container of a protective composite (teflon of 1 cm in thickness and 4.05 g/cm3 density) in the left crew quarter of the ISS Service module (space experiment "Protective composite"). Calculations were compared with the data of passive PILLE-MKS detectors installed inside the container and on the nearby wall. Calculation was performed using ray tracing for the detectors' locations with consideration for the input of galactic cosmic rays and particles in Earth's radiation belts in the conditions modeling the space station compartment. The calculation was made for the ISS orbit in the period between February 21 and September 19, 2022 on the background of increasing solar activity. According to the PILLE-ISS measurements, the protective effect of the composite in terms of absorbed dose made up 1.39 ± 0.03, largely due to a reduced input of Earth's radiation belts which agrees with the calculations.

Characterizing Radiation‐Belt Energetic Electron Precipitation Spectra: A Comparison of Quasi‐Linear Diffusion Theory With In Situ Measurements

AbstractHigh energy electron precipitation from the Earth's radiation belts is important for loss from the radiation belts and atmospheric chemistry. We follow up investigations presented in Reidy et al. (2021, https://doi.org/10.1029/2020ja028410) where precipitating flux is calculated inside the field of view of the POES T0 detector using quasi‐linear theory and pitch angle diffusion coefficients (Dαα) from the British Antarctic Survey (BAS). These results showed good agreements at >30 keV for L* >5 on the dawnside but the flux were too low at higher energies. We have investigated the effect of changing parameters in the calculation of the precipitating flux to improve the results for the higher energies using comparisons of in situ flux and cold plasma measurements from GOES‐15 and RBSP. We find that the strength of the diffusion coefficients rather than the shape of the source spectrum has the biggest effect on the calculated precipitation. In particular we find decreasing the cold plasma density used in the calculation of Dαα increases the diffusion and hence the precipitation at the loss cone for the higher energies, improving our results. The method of calculating Dαα is also examined, comparing co‐located rather than averaged RBSP measurements. We find that the method itself has minimal effect but using RBSP derived Dαα improved our results over using Dαα calculated using the entire BAS wave data base; this is potentially due to better measurements of the cold plasma density from RBSP than the other spacecraft included in the BAS wave data base (e.g., THEMIS).

АНАЛИЗ ВОЗМОЖНЫХ УРОВНЕЙ ОБЛУЧЕНИЯ КОСМОНАВТОВ ПРИ КРАТКОСРОЧНОЙ ЛУННОЙ МИССИИ

Probable dose loads to cosmonauts in a short-term lunar mission including the transit and stay on the surface were estimated using actual measurements and model calculations. It was found that doses of radiation received in a 21-day mission with a 14-day stay on the Moon in the period of minimal solar activity will make about 130 mSv; in the period of solar maximum and in case of a solar event radiation doses may reach 9–12 Svwith the maximum admissible dose of 250 mSv over a month. Increase of mass thickness of radiation shield of the command module from 10 to 20 g/cm2 (aluminum equivalent) and of the EVA spacesuit from 0.2 to 0.5-1.0 g/cm2 (aluminum equivalent) can reduce 1.4 times the total dose to cosmonauts in the period of solar minimum. Minimization of crew radiation levels requires a consideration of the solar activity forecast in order to choose the launch "windows" when high-energy electrons flow in the Earth's external radiation belt is minimal, and space weather along the route to the Moon.

Energy Transfer Between Various Electron Populations Via Resonant Interaction With Whistler Mode Wave

AbstractElectron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi‐monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave‐particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles.

Relativistic kinematic effects in the interaction time of whistler-mode chorus waves and electrons in the outer radiation belt

Abstract. Whistler-mode chorus waves propagate outside the plasmasphere, interacting with energetic electrons in the outer radiation belt. This leads to local changes in the phase space density distribution due to energy or pitch angle diffusion. The wave–particle interaction time (Tr) is crucial in estimating time-dependent processes such as the energy and pitch angle diffusion. Although the wave group and particle velocities are a fraction of the speed of light, the kinematics description of the wave–particle interaction for relativistic electrons usually considers the relativistic Doppler shift in the resonance condition and relativistic motion equation. This relativistic kinematics description is incomplete. In this paper, to the literature we add a complete relativistic description of the problem that relies on the relativistic velocity addition (between the electron and the wave) and the implications of the different reference frames for the estimates of the interaction time. We use quasi-linear test particle equations and the special relativity theory applied to whistler-mode chorus waves parallel propagating in cold-plasma magnetosphere interaction with relativistic electrons. Also, we consider that the resonance occurs in the electron's reference frame. At the same time, the result of such interaction and their parameters are measured in the local inertial reference frame of the satellite. The change pitch angle and the average diffusion coefficient rates are then calculated from the relativistic interaction time. The interaction time equation is consistent with previous works in the limit of non-relativistic interactions (Tnr). For the sake of application, we provide the interaction time and average diffusion coefficient Daa for four case studies observed during the Van Allen Probes era. Our results show that the interaction time is generally longer when applying the complete relativistic approach, considering a non-relativistic calculation. From the four case studies, the ratio Tr/Tnr varies in the range 1.7–3.0 and Daa/Daanr in the range 1.9–5.4. Accurately calculating the interaction time with full consideration of special relativity can enhance the modeling of the electron flux in Earth's outer radiation belt. Additionally, the change in pitch angle depends on the time of interaction, and similar discrepancies can be found when the time is calculated with no special relativity consideration. The results described here have several implications for modeling relativistic outer-radiation-belt electron flux resulting from the wave–particle interaction. Finally, since we considered only one wave cycle interaction, the average result from some interactions can bring more reliable results in the final flux modeling.

Direct Observation of Rising‐Tone Chorus Triggered by Enhanced Solar Wind Pressure

AbstractChorus waves play a significant role in both electron precipitation and acceleration in Earth's radiation belts. Their generation includes the initial linear process and subsequent nonlinear process. After the amplitude of whistler‐mode waves reaches a sufficient value in the linear phase, the nonlinear process takes effect and results in the frequency chirping of chorus waves. Here we present the first report on the generation and intensification of rising‐tone chorus driven by two sudden increases of solar wind dynamic pressure observed by Van Allen Probes on 20 December 2015. First, whistler‐mode waves are excited by the anisotropic thermal electrons (∼10s keV), which is quite consistent with the linear theoretical expectation. Then, rising‐tone chorus waves are nonlinearly generated from the existing whistler‐mode waves, triggered by the first increase of solar wind dynamic pressure. Subsequently, the second increase of solar wind pressure further intensifies the rising‐tone chorus. Based on the nonlinear theoretical model and Ts04 magnetic field model, we demonstrate that the decreasing inhomogeneity of the background magnetic field due to the increasing solar wind dynamic pressure is the major cause to trigger rising tones, which essentially reduces the wave amplitude threshold of the nonlinear process. Our study emphasizes the significance of solar wind dynamic pressure in the Earth's radiation belts from a micro perspective.

Role of “positive phase bunching” effect for long-term electron flux dynamics due to resonances with whistler-mode waves

Resonant interactions with electromagnetic whistler-mode waves are a primary driver of energetic electron dynamics in the Earth's radiation belts. The most intense waves can resonate with electrons nonlinearly, and effects of such nonlinear resonant interactions significantly differ from the classical quasi-linear diffusion. There have been continuous efforts on the theoretical investigation and implementation of these effects into radiation belt models, but not all nonlinear effects have been revealed yet. The two most investigated effects are phase trapping and phase bunching, which are responsible for electron acceleration and precipitation into the Earth's atmosphere, respectively, i.e., for the first cyclotron resonance with waves generated at the equator and propagating to higher latitudes, phase trapping increases electrons' energy, whereas phase bunching decreases the electron pitch-angle (and magnetic moment). However, recent studies reported a new effect called positive phase bunching, which may increase the electron pitch-angle and move them away from the loss-cone. This paper aims to characterize possible contributions of this effect to long-term electron dynamics, including multiple resonant interactions. Using an iterated mapping technique, we show that although the positive phase bunching effect can modify electron trajectories, it does not change the average rate of electron mixing in phase space. Thus, this effect may be safely neglected in long-term simulations of radiation belt dynamics. We also discuss possible verification of the positive phase bunching effect using short (single resonance), bursty electron precipitation events.

Dependence of Electron Flux Dropouts in the Earth's Outer Radiation Belt on Energy and Driving Parameters During Geomagnetic Storms

AbstractUsing 5‐year of measurements from Van Allen Probes, we present a survey of the statistical dependence of the Earth's outer radiation belt electron flux dropouts during geomagnetic storms on electron energy and various driving parameters including interplanetary magnetic field Bz, PSW, SYM‐H, and AE. By systematically investigating the dropouts over energies of 1 keV–10 MeV at L‐shells spanning 4.0–6.5, we find that the dropouts are naturally divided into three regions. The dropouts show much higher occurrence rates at energies below ∼100 keV and above ∼1 MeV compared to much smaller occurrence rate at intermediate energies around hundreds of keV. The flux decays more dramatically at energies above ∼1 MeV compared to the energies below ∼100 keV. The flux dropouts of electrons below ∼100 keV strongly depend on magnetic local time (MLT), which demonstrate high occurrence rates on the nightside (18–06 MLT), with the highest occurrence rate associated with northward Bz, strong PSW and SYM‐H, and weak AE conditions. The strongest flux decay of these dropouts is found on the nightside, which strongly depends on PSW and SYM‐H. However, there is no clear MLT dependence of the occurrence rate of relativistic electron flux dropouts above ∼1 MeV, but the flux decay of these dropouts is more significant on the dayside, with stronger decay associated with southward IMF Bz, strong PSW, SYM‐H, and AE conditions. Our statistical results are crucial for understanding of the fundamental physical mechanisms that control the outer belt electron dynamics and developing future potential radiation belt forecasting capability.

A Statistical Study on the Acceleration Conditions of Ultrarelativistic Electrons in the Earth's Outer Radiation Belt During Geomagnetic Storms

AbstractUsing the data from Van Allen Probes, we statistically study the acceleration conditions of ultrarelativistic electrons (Ek > 3 MeV) in the Earth's outer radiation belt. Based on the different high energy cutoffs of ultrarelativistic electrons, the acceleration events of ultrarelativistic electrons are divided into the four groups of “3.4 MeV events,” “5.2 MeV events,” “6.3 MeV events,” and “7.7 MeV events.” According to different solar wind and substorm conditions during the recovery stage, we classify solar wind into three categories: no high‐speed flows, short‐duration high‐speed flows, and long‐duration high‐speed flows. Substorms are divided into continuous substorm activity and non‐continuous substorm activity. Our statistical results show that (a) The different solar wind speeds can cause enhancements of ultrarelativistic electrons with different energies. The high solar wind speed is more important in the acceleration of ultrarelativistic electrons with higher energies (7.7 MeV) than lower energies (3.4, 5.2, and 6.3 MeV). (b) The different substorm activities during the recovery stage can cause enhancements of ultrarelativistic electrons with different energies. Continuous intense substorms in the early recovery stage can contribute to the rapid recovery and enhancements of ultrarelativistic electrons. The timing, intensity, and duration of substorms during the recovery stage are important to the acceleration of ultrarelativistic electrons. (c) Relativistic (1 MeV) electrons are the direct “source” of ultrarelativistic electrons (3.4, 5.2, and 6.3 MeV) in the outer radiation belt. These can help us further understand the electron dynamics of the Earth’s outer radiation belt.

Global Empirical Models of Wave Amplitudes and Normal Angles of Banded Plasmaspheric Hiss Obtained From Van Allen Probes Observations

AbstractThe unique banded structure of plasmaspheric hiss with an upper band above ∼200 Hz and a lower band below ∼150 Hz has been recently reported. Based on observations from the twin Van Allen Probes from 15 September 2012 to 30 June 2019, we statistically investigate the global distributions of amplitude and power‐weighted wave normal angle (WNA) of banded hiss waves with respect to L, MLT, MLAT, and AE*. The results indicate that amplitudes of dayside banded hiss significantly depend on the substorm level (AE* index), while the variation of WNAs on the AE* index is slight. The WNAs of upper band hiss show a peak at L ∼ 3, while the WNAs of lower band hiss are relatively uniform at L < 4. The WNAs of both bands decrease with increasing L values at L > 4. We further develop the global empirical models of banded hiss wave amplitudes and WNAs to fit the statistical results, which show good agreement with satellite observations. These results can be essentially useful to evaluate the role of banded plasmaspheric hiss in the dynamic variations of Earth's radiation belt electrons.