Planetary Radiation Belts Research Articles

Checking Key Assumptions of the Kennel‐Petschek Flux Limit With ELFIN CubeSats

AbstractIn planetary radiation belts, the Kennel‐Petschek flux limit is expected to set an upper limit on trapped electron fluxes at 80–600 keV in the presence of efficient electron loss through pitch‐angle diffusion by whistler‐mode chorus waves generated around the magnetic equator by the same 80–600 keV electron population. Comparisons with maximum measured fluxes have been relatively successful, but several key assumptions of the Kennel‐Petschek model have not been experimentally tested. The Kennel‐Petschek model notably assumes an exponential growth of chorus waves as the trapped electron flux increases, and a fixed maximum wave power gain of about 3. Here, we describe a method for inferring the near‐equatorial wave power gain using only measurements of trapped, precipitating, and backscattered electron fluxes at low altitude. Next, we make use of Electron Losses and Fields Investigation (ELFIN) CubeSats measurements of such electron fluxes during two moderate geomagnetic storms with sustained electron injections to infer the corresponding chorus wave power gains as a function of time, energy, and equatorial trapped electron flux. We show that wave power increases exponentially with trapped flux, with a wave power gain roughly proportional to the theoretical linear convective gain, and that the maximum inferred gain near the upper flux limit is roughly 10, with a factor of 2 uncertainty. Therefore, two key theoretical underpinnings of the Kennel‐Petschek model are borne out by the present results, although the strong inferred gains should correspond to higher flux limits than in traditional estimates.

Radial Transport in the Earth’s Radiation Belts: Linear, Quasi-linear, and Higher-order Processes

Observational studies of the Earth’s radiation belts indicate that Alfvénic fluctuations in the frequency range of 2–25 mHz accelerate electrons to relativistic energies. For decades, statistical models of radiation belts have quantified the impact of Alfvénic waves in terms of quasi-linear diffusion. However, quasi-linear models are inadequate to quantify Alfvénic radial transport occurring on timescales comparable to the azimuthal drift period of 0.1–10 MeV electrons. With recent advances in observational methodologies offering coverage of the Earth’s radiation belts on fast timescales, a theoretical framework that distinguishes between fast and diffusive radial transport can be tested for the first time in situ. In this report, we present a drift-kinetic description of radial transport for planetary radiation belts. We characterize fast linear processes and determine the conditions under which higher-order effects become dynamically significant. In the linear regime, wave–particle interactions are categorized in terms of resonant and nonresonant responses. We demonstrate that the phenomenon of zebra stripes is nonresonant and can originate from injection events in the inner radiation belts. We derive a radial diffusion coefficient for a field model that satisfies Faraday’s law and that contains two terms: one scaling as L 10 independent of the azimuthal number m, and a second scaling as m 2 L 6. In the higher-order regime, azimuthally symmetric waves with properties consistent with in situ measurements can energize 10–100 keV electrons in less than a drift period. This process provides new evidence that acceleration by Alfvénic waves in radiation belts cannot be fully contained within diffusive models.

Diffusive scattering of energetic electrons by intense whistler-mode waves in an inhomogeneous plasma

Electron resonant interactions with electromagnetic whistler-mode waves play an important role in electron flux dynamics in various space plasma systems: planetary radiation belts, bow shocks, solar wind and magnetic reconnection regions. Two key wave characteristics determining the regime of wave–particle interactions are the wave intensity and the wave coherency. The classical quasi-linear diffusion approach describes well electron diffusion by incoherent and low-amplitude waves, whereas the nonlinear resonant models describe electron phase bunching and trapping by highly coherent intense waves. This study is devoted to the investigation of the regime of electron resonant interactions with incoherent but intense waves. Although this regime is characterized by electron diffusion, we show that diffusion rates scale linearly with the wave amplitude,$D\propto B_w$, in contrast to the quasi-linear diffusion scaling$D_{QL}\propto B_w^2$. Using observed wave amplitude distributions, we demonstrate that the quasi-linear diffusion model significantly overestimates electron scattering by incoherent, but intense whistler-mode waves. We discuss the results obtained in the context of simulations of long-term electron flux dynamics in space plasma systems.

Ganymede's Radiation Cavity and Radiation Belts

AbstractWhile planetary radiation belts are all embedded within the low energy solar wind, Ganymede is in the unique situation of being surrounded by the energetic particles of Jupiter's magnetosphere. Here we study Ganymede's environment based the recent flyby of Juno, as well as through reanalysis of past measurements from the Galileo spacecraft. We find that Ganymede is surrounded by a radiation cavity with intensities that are lower compared to Jupiter. Particles are lost in the cavity due to absorption by Ganymede that is likely enhanced by scattering. In the core of the cavity we find radiation belts. Their intensities are comparable to Jupiter for ions but lower for electrons. The radiation belts form peaks in phase space density, which indicates that they cannot be produced through steady inward influx and accumulation of Jupiter particles. Other processes are needed such as local acceleration, or time dependent transport and loss processes.

Maximum Energies of Trapped Particles Around Magnetized Planets and Small Bodies

AbstractEnergetic charged particles trapped in planetary radiation belts are hazardous to spacecraft. Planned missions to iron‐rich asteroids with possible strong remanent magnetic fields require an assessment of trapped particles energies. Using laboratory measurements of iron meteorites, we estimate the largest possible asteroid magnetic moment. Although weak compared to moments of planetary dynamos, the small body size may yield strong surface fields. We use hybrid simulations to confirm the formation of a magnetosphere with an extended quasi‐dipolar region. However, the short length scale of the field implies that energetic particle motion would be nonadiabatic, making existing radiation belt theories not applicable. Our idealized particle simulations demonstrate that chaotic motions lead to particle loss at lower energies than those predicted by adiabatic theory, which may explain the energies of transiently trapped particles observed at Mercury, Ganymede, and Earth. However, even the most magnetized asteroids are unlikely to stably trap hazardous particles.

Estimating Inner Magnetospheric Radial Diffusion Using a Hybrid-Vlasov Simulation

Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.

The Short‐Time Prediction of the Energetic Electron Flux in the Planetary Radiation Belt Based on Stacking Ensemble‐Learning Algorithm

AbstractHigh energy electrons in planetary radiation belts are a major threat to satellites and communications in deep space applications. In order to predict the variations of energetic electron fluxes for different energy channels, we proposed a new ensemble machine leaning model for differential electron flux from 30 keV to 4 MeV in the Earth's radiation belts based on the RBSP‐A observation data from March 2013 to December 2017. The deep neural network (DNN), the convolutional neural network (CNN), the combination of CNN and DNN (CNN&DNN), the linear regression (LR), and the light gradient boosting machine (LightGBM) are among the machine learning models chosen. We carefully compared the electron flux predictions for 20 energy levels and all five models can present valid short‐time flux forecasts. The DNN model has the poorest result. The LR model is good for short‐term forecasting but not so good for long‐term forecasting. The LightGBM ensemble model is highly stable, and it has always outperformed other independent models in terms of forecast accuracy. Then the comparison by adding AE and SYM‐H indexes is given and the influence of geomagnetic activity conditions can be negligible for this short‐time prediction. Furthermore, we applied these five models on Saturn and finally got very similar prediction results. Our results will be significantly useful in instrument designs and system control of future scientific satellites in deep space explorations.

Transitional regime of electron resonant interaction with whistler-mode waves in inhomogeneous space plasma.

Resonances with electromagnetic whistler-mode waves are the primary driver for the formation and dynamics of energetic electron fluxes in various space plasma systems, including shock waves and planetary radiation belts. The basic and most elaborated theoretical framework for the description of the integral effect of multiple resonant interactions is the quasilinear theory, which operates through electron diffusion in velocity space. The quasilinear diffusion rate scales linearly with the wave intensity, D_{QL}∼B_{w}^{2}, which should be small enough to satisfy the applicability criteria of this theory. Spacecraft measurements, however, often detect whistle-mode waves sufficiently intense to resonate with electrons nonlinearly. Such nonlinear resonant interactions imply effects of phase trapping and phase bunching, which may quickly change the electron fluxes in a nondiffusive manner. Both regimes of electron resonant interactions (diffusive and nonlinear) are well studied, but there is no theory quantifying the transition between these two regimes. In this paper we describe the integral effect of nonlinear electron interactions with whistler-mode waves in terms of the timescale of electron distribution relaxation, ∼1/D_{NL}. We determine the scaling of D_{NL} with wave intensity B_{w}^{2} and other main wave characteristics, such as wave-packet size. The comparison of D_{QL} and D_{NL} provides the range of wave intensity and wave-packet sizes where the electron distribution evolves at the same rates for the diffusive and nonlinear resonant regimes. The obtained results are discussed in the context of energetic electron dynamics in the Earth's radiation belt.

Radial Diffusion of Planetary Radiation Belts’ Particles by Fluctuations with Finite Correlation Time

Abstract Radial diffusion in planetary radiation belts is a dominant transport mechanism resulting in the energization and losses of charged particles by large-scale electromagnetic fluctuations. In this study, we revisit the radial diffusion formalism by relaxing the assumption of zero correlation time in the spectrum of fluctuations responsible for the transport of charged particles. We derive a diffusion coefficient by assuming fluctuations that (1) are time homogeneous, (2) too small to trap the particles, and (3) can decorrelate on timescales comparable to the transit time of the particles. We demonstrate through self-similar solutions of the Fokker–Planck equation that autocorrelation time τ c much larger than the linear transit time/particle drift period τ L = Ω D − 1 results in characteristic time for transport independent of the drift frequency and faster than for short correlation time. In both instances, that is for short (τ L ≫ τ c ) and long (τ L ≪ τ c ) autocorrelation time, the diffusion of particles is subdiffusive since the variance of increments along the magnetic drift shells L*, scales as 〈ΔL*2〉 ∼ t s , with s < 1. However, in the absence of sources and sinks, particle transport for both short and long autocorrelation times result in equilibrium distribution along L* with differences of less than 10% across lower magnetic drift shells. The main consequence of incorporating finite correlation time appears in intermediate times much longer than the drift period but before the distribution function reaches equilibrium and indicates the importance of quantifying observationally the spectral properties of fluctuations for the modeling of planetary radiation belts.

In Situ Observations of Whistler‐Mode Chorus Waves Guided by Density Ducts

AbstractIn this paper, we report the proof of the existence of density ducts in the Earth's magnetosphere by studying in situ observations of whistler‐mode chorus waves using NASA's Van Allen Probe‐A data. Chorus waves, originally excited inside the density ducts with wave normal angles (WNAs) smaller than the Gendrin angle at the near‐equatorial region, are efficiently confined to a limited area inside density ducts (i.e., ducted regions), and remain with small WNAs as they propagate toward higher latitudes. The ducted region becomes narrower for the higher‐frequency waves. Chorus waves with WNAs larger than the Gendrin angle are not guided by density ducts. Our study reveals that density ducts can effectively control the property and distribution of chorus waves, and may ultimately regulate electron dynamics in the Earth's or other planetary radiation belts.

The Formation of Saturn’s and Jupiter’s Electron Radiation Belts by Magnetospheric Electric Fields

Abstract The existence of planetary radiation belts with relativistic electron components means that powerful acceleration mechanisms are operating within their volume. Mechanisms that bring charged particles planetward toward stronger magnetic fields can cause their heating. On the basis that electron fluxes in Saturn’s radiation belts are enhanced over discrete energy intervals, previous studies have suggested that rapid inward plasma flows may be controlling the production of their most energetic electrons. However, rapid plasma inflows languish in the planet’s inner magnetosphere, and they are not spatially appealing as a mechanism to form the belts. Here we show that slow, global-scale flows resulting from transient noon-to-midnight electric fields successfully explain the discretized flux spectra at quasi- and fully relativistic energies, and that they are ultimately responsible for the bulk of the highest energy electrons trapped at Saturn. This finding is surprising, given that plasma flows at Saturn are dominated by the planetary rotation; these weak electric field perturbations were previously considered impactful only over a very narrow electron energy range where the magnetic drifts of electrons cancel out with corotation. We also find quantitative evidence that ultrarelativistic electrons in Jupiter's radiation belts are accelerated by the same mechanism. Given that similar processes at Earth drive a less efficient electron transport compared to Saturn and Jupiter, the conclusion is emerging that global-scale electric fields can provide powerful relativistic electron acceleration, especially at strongly magnetized and fast-rotating astrophysical objects.

The evolution of Saturn’s radiation belts modulated by changes in radial diffusion

Globally magnetized planets, such as the Earth 1 and Saturn 2 , are surrounded by radiation belts of protons and electrons with kinetic energies well into the million electronvolt range. The Earth’s proton belt is supplied locally from galactic cosmic rays interacting with the atmosphere 3 , as well as from slow inward radial transport 4 . Its intensity shows a relationship with the solar cycle 4,5 and abrupt dropouts due to geomagnetic storms 6,7 . Saturn’s proton belts are simpler than the Earth’s because cosmic rays are the principal source of energetic protons 8 with virtually no contribution from inward transport, and these belts can therefore act as a prototype to understand more complex radiation belts. However, the time dependence of Saturn’s proton belts had not been observed over sufficiently long timescales to test the driving mechanisms unambiguously. Here we analyse the evolution of Saturn’s proton belts over a solar cycle using in-situ measurements from the Cassini Saturn orbiter and a numerical model. We find that the intensity in Saturn’s proton radiation belts usually rises over time, interrupted by periods that last over a year for which the intensity is gradually dropping. These observations are inconsistent with predictions based on a modulation in the cosmic-ray source, as could be expected 4,9 based on the evolution of the Earth’s proton belts. We demonstrate that Saturn’s intensity dropouts result instead from losses due to abrupt changes in magnetospheric radial diffusion. Saturn’s proton radiation belts are quite an isolated system and can be used as a laboratory for endogenous impacts on planetary radiation belts. Their evolution over a solar cycle shows variations associated with changes in magnetospheric radial diffusion.

Subcritical Growth of Electron Phase-space Holes in Planetary Radiation Belts

Abstract The discovery of long-lived electrostatic coherent structures with large-amplitude electric fields ( mV/m) by the Van Allen Probes has revealed alternative routes through which planetary radiation belts’ acceleration can take place. Following previous reports showing that small phase-space holes, with , could result from electron interaction with large-amplitude whistlers, we demonstrate one possible mechanism through which holes can grow nonlinearly (i.e., ) and subcritically as a result of momentum exchange between hot and cold electron populations. Our results provide an explanation for the common occurrence and fast growth of large-amplitude electron phase-space holes in the Earth’s radiation belts.

ON THE CONNECTION BETWEEN MICROBURSTS AND NONLINEAR ELECTRONIC STRUCTURES IN PLANETARY RADIATION BELTS

ABSTRACT Using a dynamical-system approach, we have investigated the efficiency of large-amplitude whistler waves for causing microburst precipitation in planetary radiation belts by modeling the microburst energy and particle fluxes produced as a result of nonlinear wave–particle interactions. We show that wave parameters, consistent with large-amplitude oblique whistlers, can commonly generate microbursts of electrons with hundreds of keV-energies as a result of Landau trapping. Relativistic microbursts (>1 MeV) can also be generated by a similar mechanism, but require waves with large propagation angles θ kB > 50 ° ?> and phase-speeds v Φ ≥ c / 9 ?> . Using our result for precipitating density and energy fluxes, we argue that holes in the distribution function of electrons near the magnetic mirror point can result in the generation of double layers and electron solitary holes consistent in scales (of the order of Debye lengths) to nonlinear structures observed in the radiation belts by the Van Allen Probes. Our results indicate a relationship between nonlinear electrostatic and electromagnetic structures in the dynamics of planetary radiation belts and their role in the cyclical production of energetic electrons ( E ≥ 100 ?> keV) on kinetic timescales, which is much faster than previously inferred.

Observation of particle acceleration in laboratory magnetosphere

The self-organization of magnetospheric plasma is brought about by inward diffusion of magnetized particles. Not only creating a density gradient toward the center of a dipole magnetic field, the inward diffusion also accelerates particles and provides a planetary radiation belt with high energy particles. Here, we report the first experimental observation of a “laboratory radiation belt” created in the ring trap 1 device. By spectroscopic measurement, we found an appreciable anisotropy in the ion temperature, proving the betatron acceleration mechanism which heats particles in the perpendicular direction with respect to the magnetic field when particles move inward. The energy balance model, including the heating mechanism, explains the observed ion temperature profile.

What characterizes planetary space weather?

Space weather has become a mature discipline for the Earth space environment. With increasing efforts in space exploration, it is becoming more and more necessary to understand the space environments of bodies other than Earth. This is the background for an emerging aspect of the space weather discipline: planetary space weather. In this article, we explore what characterizes planetary space weather, using some examples throughout the solar system. We consider energy sources and timescales, the characteristics of solar system objects and interaction processes. We discuss several developments of space weather interactions including the effects on planetary radiation belts, atmospheric escape, habitability and effects on space systems. We discuss future considerations and conclude that planetary space weather will be of increasing importance for future planetary missions.

Limiting energy spectrum of an electron radiation belt

AbstractTo determine the Kennel‐Petschek limiting particle flux in a planetary radiation belt in a fully relativistic regime, without assuming a predetermined form for the particle energy distribution, has been a long‐standing challenge in space physics. In this paper, for the case of whistler mode wave‐electron interaction, we meet this challenge. The limiting flux is determined by a steady state marginal stability criterion in which a convective wave gain condition is applied over all frequencies for which wave growth occurs. This condition produces an integral equation for the trapped flux. We find that in the relativistic regime the limiting electron energy spectrum varies asymptotically as 1/E, for large energy E, just as in the nonrelativistic case. However, the scaling coefficient in the relativistic case is twice that in the nonrelativistic result. We compare numerical solutions for the limiting spectra with measured energetic electron spectra at Jupiter.

Megavolt Parallel Potentials Arising from Double-Layer Streams in the Earth’s Outer Radiation Belt

Huge numbers of double layers carrying electric fields parallel to the local magnetic field line have been observed on the Van Allen probes in connection with in situ relativistic electron acceleration in the Earth's outer radiation belt. For one case with adequate high time resolution data, 7000 double layers were observed in an interval of 1 min to produce a 230,000 V net parallel potential drop crossing the spacecraft. Lower resolution data show that this event lasted for 6 min and that more than 1,000,000 volts of net parallel potential crossed the spacecraft during this time. A double layer traverses the length of a magnetic field line in about 15 s and the orbital motion of the spacecraft perpendicular to the magnetic field was about 700 km during this 6 min interval. Thus, the instantaneous parallel potential along a single magnetic field line was the order of tens of kilovolts. Electrons on the field line might experience many such potential steps in their lifetimes to accelerate them to energies where they serve as the seed population for relativistic acceleration by coherent, large amplitude whistler mode waves. Because the double-layer speed of 3100 km/s is the order of the electron acoustic speed (and not the ion acoustic speed) of a 25 eV plasma, the double layers may result from a new electron acoustic mode. Acceleration mechanisms involving double layers may also be important in planetary radiation belts such as Jupiter, Saturn, Uranus, and Neptune, in the solar corona during flares, and in astrophysical objects.

MAGNETIC SHIELDING OF EXOMOONS BEYOND THE CIRCUMPLANETARY HABITABLE EDGE

With most planets and planetary candidates detected in the stellar habitable zone (HZ) being super-Earths and gas giants, rather than Earth-like planets, we naturally wonder if their moons could be habitable. The first detection of such an exomoon has now become feasible, and due to observational biases it will be at least twice as massive as Mars. But formation models predict moons can hardly be as massive as Earth. Hence, a giant planet's magnetosphere could be the only possibility for such a moon to be shielded from cosmic and stellar high-energy radiation. Yet, the planetary radiation belt could also have detrimental effects on exomoon habitability. We here synthesize models for the evolution of the magnetic environment of giant planets with thresholds from the runaway greenhouse (RG) effect to assess the habitability of exomoons. For modest eccentricities, we find that satellites around Neptune-sized planets in the center of the HZ around K dwarf stars will either be in an RG state and not be habitable, or they will be in wide orbits where they will not be affected by the planetary magnetosphere. Saturn-like planets have stronger fields, and Jupiter-like planets could coat close-in habitable moons soon after formation. Moons at distances between about 5 and 20 planetary radii from a giant planet can be habitable from an illumination and tidal heating point of view, but still the planetary magnetosphere would critically influence their habitability.

Science Objectives and Rationale for the Radiation Belt Storm Probes Mission

The NASA Radiation Belt Storm Probes (RBSP) mission addresses how populations of high energy charged particles are created, vary, and evolve in space environments, and specifically within Earth’s magnetically trapped radiation belts. RBSP, with a nominal launch date of August 2012, comprises two spacecraft making in situ measurements for at least 2 years in nearly the same highly elliptical, low inclination orbits (1.1×5.8 RE, 10∘). The orbits are slightly different so that 1 spacecraft laps the other spacecraft about every 2.5 months, allowing separation of spatial from temporal effects over spatial scales ranging from ∼0.1 to 5 RE. The uniquely comprehensive suite of instruments, identical on the two spacecraft, measures all of the particle (electrons, ions, ion composition), fields (E and B), and wave distributions (d E and d B) that are needed to resolve the most critical science questions. Here we summarize the high level science objectives for the RBSP mission, provide historical background on studies of Earth and planetary radiation belts, present examples of the most compelling scientific mysteries of the radiation belts, present the mission design of the RBSP mission that targets these mysteries and objectives, present the observation and measurement requirements for the mission, and introduce the instrumentation that will deliver these measurements. This paper references and is followed by a number of companion papers that describe the details of the RBSP mission, spacecraft, and instruments.