Electrostatic Steepening of Whistler Waves.

We present surprising observations by the NASA Van Allen Probes spacecraft of whistler waves with substantial electric field power at harmonics of the whistler wave fundamental frequency. The wave power at harmonics is due to a nonlinearly steepened whistler electrostatic field that becomes possible in the two-temperature electron plasma due to the whistler wave coupling to the electron-acoustic mode. The simulation and analytical estimates show that the steepening takes a few tens of milliseconds. The hydrodynamic energy cascade to higher frequencies facilitates efficient energy transfer from cyclotron resonant electrons, driving the whistler waves, to lower energy electrons.

Nonresonant Charged-Particle Acceleration by Electrostatic Waves Propagating across Fluctuating Magnetic Field.

In this Letter, we demonstrate the effect of nonresonant charged-particle acceleration by an electrostatic wave propagating across the background magnetic field. We show that in the absence of resonance (i.e., when particle velocities are much smaller than the wave phase velocity) particles can be accelerated by electrostatic waves provided that the adiabaticity of particle motion is destroyed by magnetic field fluctuations. Thus, in a system with stochastic particle dynamics the electrostatic wave should be damped even in the absence of Landau resonance. The proposed mechanism is responsible for the acceleration of particles that cannot be accelerated via resonant wave-particle interactions. Simplicity of this straightforward acceleration scenario indicates a wide range of possible applications.

Sympatric divergence and clinal variation in multiple coloration traits of Ficedula flycatchers.

Geographic variation in phenotypes plays a key role in fundamental evolutionary processes such as local adaptation, population differentiation and speciation, but the selective forces behind it are rarely known. We found support for the hypothesis that geographic variation in plumage traits of the pied flycatcher Ficedula hypoleuca is explained by character displacement with the collared flycatcher Ficedula albicollis in the contact zone. The plumage traits of the pied flycatcher differed strongly from the more conspicuous collared flycatcher in a sympatric area but increased in conspicuousness with increasing distance to there. Phenotypic differentiation (PST ) was higher than that in neutral genetic markers (FST ), and the effect of geographic distance remained when statistically controlling for neutral genetic differentiation. This suggests that a cline created by character displacement and gene flow explains phenotypic variation across the distribution of this species. The different plumage traits of the pied flycatcher are strongly to moderately correlated, indicating that they evolve non-independently from each other. The flycatchers provide an example of plumage patterns diverging in two species that differ in several aspects of appearance. The divergence in sympatry and convergence in allopatry in these birds provide a possibility to study the evolutionary mechanisms behind the highly divergent avian plumage patterns.

Violation of adiabaticity in magnetic billiards due to separatrix crossings.

We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of the adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance.

Intermediate regime of charged particle scattering in the field-reversal configuration.

In this paper, we investigate the charged particle scattering in the magnetic field configuration with stretched magnetic field lines. This scattering results from the violation of the adiabaticity of charged particle motion in the region with the strong gradient of the magnetic field. We consider the intermediate regime of charged particle dynamics, when the violation of the adiabaticity is significant enough, but particle motion is not chaotic. We demonstrate and describe the significant scattering of particles with large adiabatic invariants (magnetic moment). We discuss a possible application of obtained results for description of the peculiarities of pitch-angle diffusion of relativistic electrons in the Earth radiation belts.

Energetic Electron Precipitation Driven by Electromagnetic Ion Cyclotron Waves from ELFIN's Low Altitude Perspective.

We review comprehensive observations of electromagnetic ion cyclotron (EMIC) wave-driven energetic electron precipitation using data collected by the energetic electron detector on the Electron Losses and Fields InvestigatioN (ELFIN) mission, two polar-orbiting low-altitude spinning CubeSats, measuring 50-5000 keV electrons with good pitch-angle and energy resolution. EMIC wave-driven precipitation exhibits a distinct signature in energy-spectrograms of the precipitating-to-trapped flux ratio: peaks at >0.5 MeV which are abrupt (bursty) (lasting ∼17 s, or ΔL∼0.56) with significant substructure (occasionally down to sub-second timescale). We attribute the bursty nature of the precipitation to the spatial extent and structuredness of the wave field at the equator. Multiple ELFIN passes over the same MLT sector allow us to study the spatial and temporal evolution of the EMIC wave - electron interaction region. Case studies employing conjugate ground-based or equatorial observations of the EMIC waves reveal that the energy of moderate and strong precipitation at ELFIN approximately agrees with theoretical expectations for cyclotron resonant interactions in a cold plasma. Using multiple years of ELFIN data uniformly distributed in local time, we assemble a statistical database of ∼50 events of strong EMIC wave-driven precipitation. Most reside at L∼5-7 at dusk, while a smaller subset exists at L∼8-12 at post-midnight. The energies of the peak-precipitation ratio and of the half-peak precipitation ratio (our proxy for the minimum resonance energy) exhibit an L-shell dependence in good agreement with theoretical estimates based on prior statistical observations of EMIC wave power spectra. The precipitation ratio's spectral shape for the most intense events has an exponential falloff away from the peak (i.e., on either side of ∼1.45 MeV). It too agrees well with quasi-linear diffusion theory based on prior statistics of wave spectra. It should be noted though that this diffusive treatment likely includes effects from nonlinear resonant interactions (especially at high energies) and nonresonant effects from sharp wave packet edges (at low energies). Sub-MeV electron precipitation observed concurrently with strong EMIC wave-driven >1 MeV precipitation has a spectral shape that is consistent with efficient pitch-angle scattering down to ∼ 200-300 keV by much less intense higher frequency EMIC waves at dusk (where such waves are most frequent). At ∼100 keV, whistler-mode chorus may be implicated in concurrent precipitation. These results confirm the critical role of EMIC waves in driving relativistic electron losses. Nonlinear effects may abound and require further investigation.

Destruction of adiabatic invariance for billiards in a strong nonuniform magnetic field.

We study a classical billiard of charged particles in a strong nonuniform magnetic field. We provide an adiabatic description for skipping motion along the boundary of the billiard. We show that a sequence of many changes of regimes of motion from skipping to motion without collisions with the boundary and back to skipping leads to destruction of the adiabatic invariance and chaotic dynamics in a large domain in the phase space. This is a new mechanism of the origin of chaotic dynamics for systems with impacts.

Candidate genes for colour and vision exhibit signals of selection across the pied flycatcher (Ficedula hypoleuca) breeding range.

The role of natural selection in shaping adaptive trait differentiation in natural populations has long been recognized. Determining its molecular basis, however, remains a challenge. Here, we search for signals of selection in candidate genes for colour and its perception in a passerine bird. Pied flycatcher plumage varies geographically in both its structural and pigment-based properties. Both characteristics appear to be shaped by selection. A single-locus outlier test revealed 2 of 14 loci to show significantly elevated signals of divergence. The first of these, the follistatin gene, is expressed in the developing feather bud and is found in pathways with genes that determine the structure of feathers and may thus be important in generating variation in structural colouration. The second is a gene potentially underlying the ability to detect this variation: SWS1 opsin. These two loci were most differentiated in two Spanish pied flycatcher populations, which are also among the populations that have the highest UV reflectance. The follistatin and SWS1 opsin genes thus provide strong candidates for future investigations on the molecular basis of adaptively significant traits and their co-evolution.

A Climatology of Long-Duration High 2-MeV Electron Flux Periods in the Outer Radiation Belt.

Since the advent of the Space Age, the importance of understanding and forecasting relativistic electron fluxes in the Earth's radiation belts has been steadily growing due to the threat that such particles pose to satellite electronics. Here, we provide a model of long-duration periods of high time-integrated 2-MeV electron flux deep inside the outer radiation belt, based on the significant correlation obtained in 2001-2017 between time-integrated electron flux measured by satellites and a measure of the preceding time-integrated homogenized aa H geomagnetic index. We show that this correlation is likely due to a stronger cumulative chorus wave-driven acceleration of relativistic electrons and a stronger cumulative inward radial diffusion of such electrons during periods of higher time-integrated geomagnetic activity. Return levels of 2-MeV electron flux are provided based on Extreme Value analysis of time-integrated geomagnetic activity over 1868-2017, in rough agreement with estimates based on 20-year data sets of measured flux. A high correlation is also found between our measure of time-integrated geomagnetic activity averaged over each solar cycle and averaged sunspot numbers, potentially paving the way for forecasts of time-integrated relativistic electron flux during future solar cycles based on predictions of solar activity.

Extreme Energy Spectra of Relativistic Electron Flux in the Outer Radiation Belt.

Electron diffusion by whistler-mode chorus waves is one of the key processes controlling the dynamics of relativistic electron fluxes in the Earth's radiation belts. It is responsible for the acceleration of sub-relativistic electrons injected from the plasma sheet to relativistic energies as well as for their precipitation and loss into the atmosphere. Based on analytical estimates of chorus wave-driven quasi-linear electron energy and pitch-angle diffusion rates, we provide analytical steady-state solutions to the corresponding Fokker-Planck equation for the relativistic electron distribution and flux. The impact on these steady-state solutions of additional electromagnetic ion cyclotron waves, and of ultralow frequency waves are examined. Such steady-state solutions correspond to hard energy spectra at 1-4 MeV, dangerous for satellite electronics, and represent attractors for the system dynamics in the presence of sufficiently strong driving by continuous injections of 10-300 keV electrons. Therefore, these analytical steady-state solutions provide a simple means for estimating the most extreme electron energy spectra potentially encountered in the outer radiation belt, despite the great variability of injections and plasma conditions. These analytical steady-state solutions are compared with numerical simulations based on the full Fokker-Planck equation and with relativistic electron flux spectra measured by satellites during one extreme event and three strong events of high time-integrated geomagnetic activity, demonstrating a good agreement.

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation.

Short and intense lower-band chorus wave packets are ubiquitous in the Earth's outer radiation belt. In this article, we perform various Vlasov hybrid simulations, with one or two triggering waves, to study the generation of short chorus packets/subpackets inside long rising tone elements. We show that the length of the generated short wave packets is consistent with a criterion of resonance non-overlap for two independent superposed waves, and that these chorus packets have similar characteristics as in Van Allen Probes observations. We find that short wave packets are mainly formed near the middle/end of long rising tones for moderate linear growth rates, and everywhere for stronger linear growth rates. Finally, we analyze an event characterized by Time History of Events and Macroscale Interactions during Substorms spacecraft measurements of chorus rising tones near the equator and simultaneous measurements by low altitude ELFIN CubeSats of precipitating and trapped electron fluxes in the same sector. The measured precipitating electron fluxes are well recovered by test particle simulations performed using measured plasma and wave properties. We show that short chorus wave packets of moderate amplitudes (160-250 pT) essentially lead to a more diffusive-like transport of 50-200 keV electrons toward the loss cone than long packets. In contrast, long chorus packets are found to produce important nonlinear effects via anomalous trapping, which significantly reduces electron precipitation below 150 keV, especially for higher wave amplitudes.

Regimes of ion dynamics in current sheets: The machine learning approach.

Current sheets are spatially localized almost-one-dimensional (1D) structures with intense plasma currents. They play a key role in storing the magnetic field energy and they separate different plasma populations in planetary magnetospheres, the solar wind, and the solar corona. Current sheets are primary regions for the magnetic field line reconnection responsible for plasma heating and charged particle acceleration. One of the most interesting and widely observed types of 1D current sheets is the rotational discontinuity, which can be force-free or include plasma compression. Theoretical models of such 1D current sheets are based on the assumption of adiabatic motion of ions, i.e., ion adiabatic invariants are conserved. We focus on three current sheet configurations, widely observed in the Earth magnetopause and magnetotail and in the near-Earth solar wind. The magnetic field in such current sheets is supported by currents carried by transient ions, which exist only when there is a sufficient number of invariants. In this paper, we apply a machine learning approach, AI Poincaré, to determine parametrical domains where adiabatic invariants are conserved. For all three current sheet configurations, these domains are quite narrow and do not cover the entire parametrical range of observed current sheets. We discuss possible interpretation of obtained results indicating that 1D current sheets are dynamical rather than static plasma equilibria.

Jumps of adiabatic invariant at the separatrix of a degenerate saddle point.

We consider a slow-fast Hamiltonian system with two degrees of freedom. One degree of freedom corresponds to slow variables, and the other one corresponds to fast variables. A characteristic ratio of the rates of change of slow and fast variables is a small parameter κ. For every fixed value of the slow variables, in the phase portrait of the fast variables there are a saddle point and separatrices passing through it. When the slow variables change, phase points may cross the separatrices. The action variable of the fast motion is an adiabatic invariant of the full system as long as a trajectory is far from the separatrices: value of the adiabatic invariant is conserved with an accuracy of order of κ on time intervals of order of 1/κ. A passage through a narrow neighborhood of the separatrices results in a jump of the adiabatic invariant. We consider a case when the saddle point is degenerate. We derive an asymptotic formula for the jump of the adiabatic invariant which turns out to be a value of order of κ(3/4) (in the case of a non-degenarate saddle point a similar jump is known to be a value of order of κ). Accumulation of these jumps after many consecutive separatrix crossings leads to the "diffusion" of the adiabatic invariant and chaotic dynamics. We verify the analytical expression for the jump of the adiabatic invariant by numerical simulations. We discuss application of the obtained results to the description of charged particle dynamics in the Earth magnetosphere.

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.

Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves.

We present an analytical and numerical study of the surfatron acceleration of nonrelativistic charged particles by electromagnetic waves. The acceleration is caused by capture of particles into resonance with one of the waves. We investigate capture for systems with one or two waves and provide conditions under which the obtained results can be applied to systems with more than two waves. In the case of a single wave, the once captured particles never leave the resonance and their velocity grows linearly with time. However, if there are two waves in the system, the upper bound of the energy gain may exist and we find the analytical value of that bound. We discuss several generalizations including the relativistic limit, different wave amplitudes, and a wide range of the waves' wavenumbers. The obtained results are used for qualitative description of some phenomena observed in the Earth's magnetosphere.

Juno Observations of Heavy Ion Energization During Transient Dipolarizations in Jupiter Magnetotail.

Transient magnetic reconnection and associated fast plasma flows led by dipolarization fronts play a crucial role in energetic particle acceleration in planetary magnetospheres. Despite large statistical observations on this phenomenon in the Earth's magnetotail, many important characteristics (e.g., mass or charge dependence of acceleration efficiency and acceleration scaling with the spatial scale of the system) of transient reconnection cannot be fully investigated with the limited parameter range of the Earth's magnetotail. The much larger Jovian magnetodisk, filled by a mixture of various heavy ions and protons, provides a unique opportunity for such investigations. In this study, we use recent Juno observations in Jupiter's magnetosphere to examine the properties of reconnection associated dipolarization fronts and charged particle acceleration. High-energy fluxes of sulfur, oxygen, and hydrogen ions show clear mass-dependent acceleration with energy ~ m 1/3. We compare Juno observations with similar observations in the Earth's magnetotail and discuss possible mechanism for the observed ion acceleration.

Superfast ion scattering by solar wind discontinuities.

Large-amplitude fluctuations of the solar wind magnetic field can scatter energetic ions. One of the main contributions to these fluctuations is provided by solar wind discontinuities, i.e., rapid rotations of the magnetic field. This study shows that the internal configuration of such discontinuities plays a crucial role in energetic ion scattering in pitch angles. Kinetic-scale discontinuities accomplish very fast ion pitch-angle scattering. The main mechanism of such pitch-angle scattering is the adiabatic invariant destruction due to separatrix crossings in the phase space. We demonstrate that efficiency of this scattering does not depend on the magnetic field component across the discontinuity surface, i.e., both rotational and almost tangential discontinuities scatter energetic ions with the same efficiency. We also examine how the strong scattering effect depends on the deviations of the discontinuity magnetic field from the force-free one.

Magnetotail reconnection onset caused by electron kinetics with a strong external driver.

Magnetotail reconnection plays a crucial role in explosive energy conversion in geospace. Because of the lack of in-situ spacecraft observations, the onset mechanism of magnetotail reconnection, however, has been controversial for decades. The key question is whether magnetotail reconnection is externally driven to occur first on electron scales or spontaneously arising from an unstable configuration on ion scales. Here, we show, using spacecraft observations and particle-in-cell (PIC) simulations, that magnetotail reconnection starts from electron reconnection in the presence of a strong external driver. Our PIC simulations show that this electron reconnection then develops into ion reconnection. These results provide direct evidence for magnetotail reconnection onset caused by electron kinetics with a strong external driver.

The ELFIN Mission.

The Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving option (ELFIN-STAR, or heretoforth simply: ELFIN) mission comprises two identical 3-Unit (3U) CubeSats on a polar (∼93∘ inclination), nearly circular, low-Earth (∼450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of storm-time relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitch-angle-resolving capability to determine whether measured relativistic electron pitch-angle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowly-variable along-track separation allows disambiguation of spatial and temporal evolution of the precipitation over minutes-to-tens-of-minutes timescales, faster than the orbit period of a single low-altitude satellite (Torbit ∼ 90 min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50 keV to 5 MeV electrons with Δ E/E < 40% and a fluxgate magnetometer (FGM) on a ∼72 cm boom that measures magnetic field waves (e.g., EMIC waves) in the range from DC to 5 Hz Nyquist (nominally) with <0.3 nT/sqrt(Hz) noise at 1 Hz. The spinning satellites (Tspin ∼ 3 s) are equipped with magnetorquers (air coils) that permit spin-up or -down and reorientation maneuvers. Using those, the spin axis is placed normal to the orbit plane (nominally), allowing full pitch-angle resolution twice per spin. An energetic particle detector for ions (EPDI) measures 250 keV - 5 MeV ions, addressing secondary science. Funded initially by CalSpace and the University Nanosat Program, ELFIN was selected for flight with joint support from NSF and NASA between 2014 and 2018 and launched by the ELaNa XVIII program on a Delta II rocket (with IceSatII as the primary). Mission operations are currently funded by NASA. Working under experienced UCLA mentors, with advice from The Aerospace Corporation and NASA personnel, more than 250 undergraduates have matured the ELFIN implementation strategy; developed the instruments, satellite, and ground systems and operate the two satellites. ELFIN's already high potential for cutting-edge science return is compounded by concurrent equatorial Heliophysics missions (THEMIS, Arase, Van Allen Probes, MMS) and ground stations. ELFIN's integrated data analysis approach, rapid dissemination strategies via the SPace Environment Data Analysis System (SPEDAS), and data coordination with the Heliophysics/Geospace System Observatory (H/GSO) optimize science yield, enabling the widest community benefits. Several storm-time events have already been captured and are presented herein to demonstrate ELFIN's data analysis methods and potential. These form the basis of on-going studies to resolve the primary mission science objective. Broad energy precipitation events, precipitation bands, and microbursts, clearly seen both at dawn and dusk, extend from tens of keV to >1 MeV. This broad energy range of precipitation indicates that multiple waves are providing scattering concurrently. Many observed events show significant backscattered fluxes, which in the past were hard to resolve by equatorial spacecraft or non-pitch-angle-resolving ionospheric missions. These observations suggest that the ionosphere plays a significant role in modifying magnetospheric electron fluxes and wave-particle interactions. Routine data captures starting in February 2020 and lasting for at least another year, approximately the remainder of the mission lifetime, are expected to provide a very rich dataset to address questions even beyond the primary mission science objective.

Publisher Correction: Wave energy budget analysis in the Earth's radiation belts uncovers a missing energy.

This corrects the article DOI: 10.1038/ncomms8143.