Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves

The efficiency of energetic electron cyclotron acceleration in the Earth’s magnetosphere in different regimes of electron resonant interaction with parallel propagating whistler mode waves of variable frequency, specifically, with chorus ELF-VLF emissions, is considered. The regime of stochastic acceleration, typical of the interaction between particles and noise-like emissions, and particle acceleration in the regime of nonlinear trapping by a quasimonochromatic wave field are discussed. The specific feature of the latter regime consists in its non-diffuse character, i.e., the definite sign of the energy variation depending on the frequency variation in the wave packet. The trapped electron energy becomes higher if frequency increases within an element, which is typical of chorus emissions. For the parameters typical of chorus emissions (the amplitude of a wave magnetic field B _～ = 10² nT, the initial frequency ω ～ 0.3ω _H , and the frequency variation &;Dω ～ 0.15ω _H , where ω _H is the electron gyrofrequency), the energy increase during one act of such an interaction at L = 4?5 exceeds the rms variation in the energy of untrapped electron (during stochastic acceleration) by one-two orders of magnitude. The estimates indicate that a considerable fraction (several tens of percent) of the chorus element energy can be absorbed by electrons accelerated in the trapping regime during a single hop.     

Polar PWI and CEPPAD observations of chorus emissions and radiation belt electron acceleration: Four case studies

We investigated the role of whistler-mode chorus in accelerating outer radiation belt electrons during four moderate geomagnetic storms when data from the Polar Plasma Wave Investigation (PWI) were available. The storm time periods we examined included two storms associated with coronal mass ejections (CMEs), the well-studied January 10–13, 1997 International Solar Terrestrial Physics event and the May 12–15, 1997 event. We compared these two storms with two geomagnetically active periods that were not associated with CMEs. Although strong chorus emissions were observed during all four events, the association of electron acceleration with chorus emissions is not clear. During all four events, the Polar Comprehensive Energetic Particle and Pitch Angle Distribution (CEPPAD) experiment observed increases in the fluxes of energetic electrons (0.8<E<6.4 MeV). The two events associated with CMEs featured a sudden increase in the electron fluxes above 0.8 MeV that may have been related to the impact of the CME shock wave upon the magnetosphere. The other two events featured more gradual increases in the electron fluxes over a period of several days. The data from these events indicate that the role played by resonant interactions with chorus in accelerating electrons may depend on the upstream solar wind conditions driving the storm.     

哨声模波对高能电子槽区和外辐射带的调节作用

本文利用磁层哨声模嘶声和合声波的幅度分布模型、近赤道背景电子(能量在eV量级)的数密度分布模型和IGRF10磁场模型建立了一个高能电子(能量大于50 keV)准线性扩散模型.模型的数值结果表明,在不同的地磁条件下,等离子体层顶位置的变化改变了磁层背景电子数密度的空间分布,从而改变了哨声模嘶声对高能电子有效的投掷角扩散（损失）区域,同时也改变了哨声模合声波对高能电子有效的动量扩散（加速）区域.哨声模嘶声对电子投掷角扩散区域的变化和RRES卫星探测到的高能电子的槽区变化是一致的,而合声波对电子的动量扩散区域的变化和卫星探测到外辐射带的变化相同.这种对应关系说明：在不同的地磁条件下,哨声模波对高能电子扩散区域的变化是造成高能电子槽区和外辐射带的空间位置和大小变化的一个重要因素.在一些强磁暴期间,由于嘶声对部分能量范围电子的投掷角扩散作用消失,这些电子的槽区也随之消失,从而使内外辐射带连接在一起.     

Whistler–electron interactions in the magnetosphere: new results and novel approaches

Attention is focused here on the quasilinear and nonlinear physics of cyclotron interactions between magnetospheric whistler mode waves and energetic electrons on dipolar geomagnetic flux tubes. These interactions can lead to the generation of noise-like emissions or phase-coherent discrete signals in the frequency-time domain. In the magnetosphere noise-like emissions called hiss are accompanied by a smooth electron precipitation pattern. Examples of discrete emissions are ELF/VLF chorus or VLF emissions triggered by whistlers from lightning or by radio transmitters on the ground. The rapid temporal variations of these signals are associated with fine structure of the distribution function of the radiation belt electrons, such as a transient step-like deformation or a well-organized beam, which are prepared by initial noise-like emissions or by a quasimonochromatic whistler–wave packet, respectively. These cause the properties of the electrons, which may be observed on a satellite, to evolve rapidly in time and on relatively short spatial scales. Bursts of precipitating electrons occur, and can contribute significantly to depleting the radiation belts. Recent results on improvements in the theoretical understanding of such processes and on new observations of magnetospheric electrons and whistler-mode waves are presented.     

Effects of energy and pitch angle mixed diffusion on radiation belt electrons

Understanding the dynamics of the Earth’s radiation belts is important for modeling and forecasting the intensities of energetic electrons in space. Wave diffusion processes are known to be responsible for loss and acceleration of electrons in the radiation belts. Several recent studies indicate pitch angle and energy mixed-diffusion are also important when considering the total diffusive effects. In this study, a two-dimensional Fokker Planck equation is solved numerically using the Alternating Direction Implicit method. Mixed diffusion due to whistler-mode chorus waves tends to slow down the total diffusion in the energy-pitch angle space, particularly at smaller equatorial pitch angles. We then incorporate the electron energy and pitch angle mixed diffusions due to whistler-model chorus waves into the 4-dimensional Radiation Belt Environment (RBE) model and study the effect of mixed diffusion during a storm in October 2002. The 4-D simulation results show that energy and pitch angle mixed diffusion decrease the electron fluxes in the outer belt while electron fluxes in the slot region are enhanced (up to a factor of 2) during storm time.     

Resonant enhancement of relativistic electron fluxes during geomagnetically active periods

The strong increase in the flux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced significantly due to injection of 10–100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic field generate the rising tones of VLF whistler chorus. The seed population of relativistic electrons which bounce along the inhomogeneous magnetic field, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic field can interact with energetic electrons through Landau, cyclotron, and higher harmonic resonant interactions when the Doppler-shifted wave frequency equals any (positive or negative) integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process diffuses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10–100 fold increase of the relativistic electron flux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and enhancements in fluxes of relativistic electrons during geomagnetic storms and other active periods.     

The dual role of ELF/VLF chorus waves in the acceleration and precipitation of radiation belt electrons

This paper provides a brief review of the role that chorus waves play in controlling the dynamics of the Earth's outer radiation belt. Three major topics are discussed: (i) the morphology, characteristics, and properties of chorus waves themselves, with special emphasis on more recent results, (ii) the role that chorus waves play in the loss of radiation belt particles, showing initial results from modeling of relativistic electron microbursts, and estimated lifetimes based on microburst occurrence rates during the main phase of storms, and (iii) the role that chorus waves play in the acceleration of electrons to relativistic energies in the recovery phase of storms, based on a new quasilinear diffusion based calculation.     

ULF wave indices to characterize the solar wind-magnetosphere interaction and relativistic electron dynamics

To quantify the level of low-frequency wave activity of the magnetosphere and IMF, a set of the ULF wave power indices has been introduced. We demonstrate that the ULF activity global level can be very useful in space weather related problems. The application of the interplanetary index to an analysis of auroral activity driving has shown that a turbulent IMF drives auroral activity more strongly than the laminar solar wind does. The enhancements of relativistic electrons at the geosynchronous orbit are known not to be directly related to the intensity of magnetic storms. We found that the electron dynamics correlated well with long-lasting intervals of elevated ground ULF wave index. This fact confirms the importance of magnetospheric ULF turbulence in energizing electrons up to relativistic energies. The time-integrated ULF index demonstrates a significantly higher correlation with electron fluxes, which implies the occurrence of a cumulative effect in the electron energization.     

Responses of geostationary orbit energetic electron fluxes to chorus waves under different geomagnetic conditions

We investigate the flux evolution of geostationary orbit energetic electrons during a strong storm on 24 August 2005(event A,the storm index Dst<200 nT,the average substorm index AE=436 nT)and a weak storm on 28 October 2006(event B,Dst>50 nT,average AE=320 nT).Data collected by LANL and GOES-12 satellites show that energetic electron fluxes increase by a factor of 10 during the recovery phase compared to the prestorm level for both events A and B.As the substorm continued,the Cluster C4 satellite observed strong whistler-mode chorus waves(with spectral density approaching 10 5nT2/Hz).The wave amplitude correlates with the substorm AE index,but is less correlated with the storm Dst index.Using a Gaussian distribution fitting method,we solve the Fokker-Planck diffusion equation governing the wave-particle interaction.Numerical results demonstrate that chorus waves efficiently accelerate~1 MeV energetic electrons,particularly at high pitch angles.The calculated acceleration time scale and amplitude are comparable to observations.Our results provide new observational support for chorus-driven acceleration of radiation belt energetic electrons.     

Alfven行波涌浪携带的场向电场──极光粒子加速机制

提出一个剪切Ａｌｆｖｅｎ波加速极光粒子的新模式。频率远小于离子回旋频率的Ａｌｆｖｅｎ波由磁层向电离层传播会演化成孤波，当场向电流超过离子声不稳定性的临界电流时，激发离子声不稳定性，波与粒子的相互作用产生反常阻尼使Ａｌｆｖｅｎ波演化成行波涌浪。它携带一个方向向上的平行电场，加速极光电子形成分立极光。对等离子体密度、电场及其对应的电势进行了数值计算，结果发现满足磁层加速区条件形成Ａｌｆｖｎ行波涌浪，提供足够强的加速粒子的电场。     

Eigenmode analysis of pitch-angle diffusion of energetic electrons in the outer zone

We demonstrate a new method of analyzing observed storm-time pitch-angle distributions to obtain information regarding the appropriate choice of the pitch-angle diffusion coefficients. We apply this method to MeV electrons in the outer zone as a diagnostic of the relative contribution of electromagnetic ion-cyclotron (EMIC) waves and whistler-mode hiss and chorus. We assume EMIC and hiss are confined to a plasmaspheric plume (hence, “plume waves”), with chorus prevalent over large portions of the day and night side. First, we determine the eigenmodes and eigenvalues of the pitch-angle diffusion operator predicted by quasilinear diffusion theory and approximate chorus, hiss, or EMIC plasma wave parameters for energetic electrons in the outer zone. Then, by projecting pitch-angle distributions observed by CRRES into the eigenmodes, we determine whether the pitch-angle distributions are consistent with the assumed diffusion process for various relative weighting of chorus and plume waves. Eigenmodes with shorter decay times (i.e., larger negative eigenvalues) ought to represent a comparatively smaller portion of the total flux in the pitch-angle distribution. We show that several observed pitch-angle distributions are consistent with predominantly chorus-driven pitch-angle diffusion, with at most a minor contribution from plume waves.     

Relativistic electron losses related to EMIC waves during CIR and CME storms

The losses of radiation belt electrons to the atmosphere due to wave–particle interactions with electromagnetic ion-cyclotron (EMIC) waves during corotating interaction region (CIR) storms compared to coronal mass ejections (CME) storms is investigated. Geomagnetic storms with extended ‘recovery’ phases due to large-amplitude Alfvén waves in the solar wind are associated with relativistic electron flux enhancements in the outer radiation belt. The corotating solar wind streams following a CIR in the solar wind contain large-amplitude Alfvén waves, but also some CME storms with high-speed solar wind can have large-amplitude Alfvén waves and extended ‘recovery’ phases. During both CIR and CME storms the ring current protons are enhanced. In the anisotropic proton zone the protons are unstable for EMIC wave growth. Atmospheric losses of relativistic electrons due to weak to moderate pitch angle scattering by EMIC waves is observed inside the whole anisotropic proton zone. During storms with extended ‘recovery’ phases we observe higher atmospheric loss of relativistic electrons than in storms with fast recovery phases. As the EMIC waves exist in storms with both extended and short recovery phases, the increased loss of relativistic electrons reflects the enhanced source of relativistic electrons in the radiation belt during extended recovery phase storms. The region with the most unstable protons and intense EMIC wave generation, seen as a narrow spike in the proton precipitation, is spatially coincident with the largest loss of relativistic electrons. This region can be observed at all MLTs and is closely connected with the spatial shape of the plasmapause as revealed by simultaneous observations by the IMAGE and the NOAA spacecraft. The observations in and near the atmospheric loss cone show that the CIR and CME storms with extended ‘recovery’ phases produce high atmospheric losses of relativistic electrons, as these storms accelerate electrons to relativistic energies. The CME storm with short recovery phase gives low losses of relativistic electrons due to a reduced level of relativistic electrons in the radiation belt.     

Chung Park,pioneer of magnetosphere–ionosphere coupling research

Chung Park (1938–2003) was a true pioneer of magnetosphere–ionosphere coupling research. During a short career at Stanford University that began in 1970 and ended in 1981, he wrote seminal papers on several topics. Using ground-based whistler data, he was the first to demonstrate experimentally that day-side upward ion flow from the mid-latitude ionosphere was sufficient to maintain the night-time ionosphere. He made the only measurements to date of longitudinally localized drainage of significant quantities of plasmaspheric plasma into the underlying ionosphere during a period of enhanced convection activity. He pioneered in demonstrating the presence at ionospheric heights of geophysically important electric fields that originate in the troposphere in thunderstorm centers. He cooperated in a unique study of the guidance of whistler-mode waves by field-aligned density irregularities (ducts) in the magnetosphere. Park provided unique observational data on nonlinear wave–particle interaction processes such as: (i) the development of sidebands during the injection of whistler-mode waves from Siple, Antarctica, and (ii) the mysterious whistler precursor phenomenon. Today, in spite of the several decades that have elapsed since his work, Park's early findings remain cornerstones of our understanding of magnetosphere–ionosphere coupling processes. Some of his later studies of non-linear magnetospheric wave–particle interaction phenomena have stirred lively debate, and today remain relevant to a number of topics in space plasma wave research.     

Precipitation of energetic magnetospheric electrons and accompanying solar wind characteristics

From 1957 up to the present time, the Lebedev Physical Institute (LPI) has performed regular monitoring of ionizing radiation in the Earth’s atmosphere. There are cases when the X-ray radiation generated by energetic magnetospheric electrons penetrates the atmosphere and is observed at polar latitudes. The vast majority of these events occurs against the background of high-velocity solar wind streams, while magnetospheric perturbations related to interplanetary coronal mass ejections (ICMEs) are noneffective for precipitation. It is shown in the paper that ICMEs do not cause acceleration of a sufficient amount of electrons in the magnetosphere. Favorable conditions for acceleration and subsequent scattering of electrons into the loss cone are created by magnetic storms with an extended recovery phase and with sufficiently frequent periods of negative Bz component of the interplanetary magnetic field (IMF). Such geomagnetic perturbations are typical for storms associated with high-velocity solar wind streams.     

Characteristics of the Energetic Electron Precipitation and Magnetospheric Conditions in 1994

The problem of the rapid depletion and saturation of the Earth’s outer radiation belt with energetic electrons is one of the central problems in the physics of the magnetosphere. The precipitation into the atmosphere and the escape of electrons from the magnetosphere are competing reasons for the depletion of the radiation belt. Long-term measurements of energetic electron precipitation (EEP) in the atmosphere in the experiment of the Lebedev Physical Institute (LPI) can be used to study the relative role of these phenomena. High fluence values of relativistic electrons in the outer belt is a necessary condition for EEP observation; however, the relation of the EEP rate to the condition of the belt is ambiguous, which is shown by the example of observations in 1994.     

Source of runaway electrons in a thundercloud field caused by cosmic radiation

The volumetric generation rate of secondary electrons, produced by cosmic radiation in the Earth’s atmosphere and able to accelerate in a thundercloud electric field, has been calculated as a function of height above sea level. It is recommended to use the obtained function as a source when modeling atmospheric breakdown in thunderstorm fields with the participation of relativistic runaway electron avalanches. It has been indicated that ionization of the atmosphere by a cosmic particle with an energy of 10¹⁶ eV cannot initiate lightning.     

Exact solutions of magnetohydrodynamics for describing different structural disturbances in solar wind

We use analytical methods of magnetohydrodynamics to describe the behavior of cosmic plasma. This approach makes it possible to describe different structural fields of disturbances in solar wind: shock waves, direction discontinuities, magnetic clouds and magnetic holes, and their interaction with each other and with the Earth’s magnetosphere. We note that the wave problems of solar–terrestrial physics can be efficiently solved by the methods designed for solving classical problems of mathematical physics. We find that the generalized Riemann solution particularly simplifies the consideration of secondary waves in the magnetosheath and makes it possible to describe in detail the classical solutions of boundary value problems. We consider the appearance of a fast compression wave in the Earth’s magnetosheath, which is reflected from the magnetosphere and can nonlinearly overturn to generate a back shock wave. We propose a new mechanism for the formation of a plateau with protons of increased density and a magnetic field trough in the magnetosheath due to slow secondary shock waves. Most of our findings are confirmed by direct observations conducted on spacecrafts (WIND, ACE, Geotail, Voyager-2, SDO and others).     

Solar-wind–magnetosphere coupling,including relativistic electron energization,during high-speed streams

High geomagnetic activity occurs continuously during high-speed solar wind streams, and fluxes of relativistic electrons observed at geosynchronous orbit enhance significantly. High-speed streams are preceded by solar wind compression regions, during which time there are large losses of relativistic electrons from geosynchronous orbit. Weak to moderate geomagnetic storms often occur during the passage of these compression regions; however, we find that the phenomena that occur during the ensuing high-speed streams do not depend on whether or not a preceding storm develops. Large-amplitude Alfvén waves occur within the high-speed solar wind streams, which are expected to lead to intermittent intervals of significantly enhanced magnetospheric convection and to thus also lead to repetitive substorms due to repetitively occurring reductions in the strength of convection. We find that such repetitive substorms are clearly discernible in the LANL geosynchronous energetic particle data during high-speed stream intervals. Global auroral images are found to show unambiguously that these events are indeed classical substorms, leading us to conclude that substorms are an important contributor to the enhanced geomagnetic activity during high-speed streams. We used the onsets of these substorms as indicators of preceding periods of enhanced convection and of reductions in convection, and we have used ground-based chorus observations from the VELOX instrument at Halley station as an indicator of magnetospheric chorus intensities. These data show evidence that it is the periods of enhanced convection that precede substorm expansions, and not the expansions themselves, that lead to the enhanced dawn-side chorus wave intensity that has been postulated to cause the energization of relativistic electrons. If this inference is correct, and if it is chorus that energizes the relativistic electrons, then high-speed solar wind streams lead to relativistic electron flux enhancements because the embedded large-amplitude Alfvén waves give multi-day periods of intermittent significantly enhanced convection.     

Oblique Whistler-Mode Waves in the Inhomogeneous Magnetospheric Plasma: Resonant Interactions with Energetic Charged Particles

A consistent account is given of the theory of resonant interactions between energetic charged particles and a whistler-mode wave propagating obliquely to the non-uniform geomagnetic field in the inhomogeneous magnetospheric plasma. The basic equations for the wave field and charged particle dynamics are presented, with the emphasis being placed on the parameters governing the problem. A Hamiltonian approach is consistently used in the analysis of the particle equations of motion which are discussed in detail and solved analytically in various cases. Two applications of the theory are considered. First, we calculate the growth (or damping) rate for a whistler-mode wave propagating obliquely to geomagnetic field in the magnetosphere. Secondly, we estimate the proton precipitation into the upper atmosphere induced by a VLF transmitter signal.