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.     

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.     

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.     

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.     

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.     

Plasmaspheric hiss overview and relation to chorus

A brief overview is given of the history of plasmaspheric hiss research, particularly in the context of the recent work by Bortnik et al. (2008) indicating that chorus could be the likely source of plasmaspheric hiss. Previous suggestions given in the literature for this theory are reviewed and then the mechanism itself is outlined, focusing on the characteristic cyclical trajectories executed by typical ray paths that enter into the plasmasphere. A number of directional propagation studies performed in the past are then discussed as well as other work which bears relevance to the present mechanism.     

地球电子外辐射带的数据同化建模与分析

地球电子外辐射带对太阳与地磁活动呈现高度动态变化的响应,了解外辐射带的全球动态变化过程对于近地空间粒子辐射环境的理解认知和预测预报具有重要意义.基于卡尔曼滤波数据同化方法,本文利用范阿伦A星、B星和GOES-13和GOES-15四颗卫星的辐射带电子观测数据,分别利用三种不同维度的辐射带物理模型,将观测结果与数值结果有机融合,对2013年3月地球外辐射带电子通量的径向分布与变化进行数据同化分析.结果表明,考虑了磁层波动与辐射带电子共振作用引起的径向扩散、投掷角扩散以及能量扩散过程的三维同化模型可有效、合理地重现外辐射带电子通量的径向分布.本文进一步利用该三维同化模型对2013年一整年外辐射带电子的相空间密度分布进行重构与分析,得到了不同绝热不变量和不同地磁活动条件下电子辐射带的时空演化过程,从而为深入理解外辐射带电子的变化过程和动力学机制提供了强有力信息.通过分析同化过程中的新息矢量以及度量同化过程中观测数据在多大程度上修改了物理模型结果,还有助于定量分析现有辐射带物理模型中的源项和损失项的相对贡献以及可能忽略的物理机制或过程.     

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.     

磁暴期间辐射带电子相空间密度的多卫星联合观测

地球外辐射带是一个高度动态变化的空间环境,辐射带电子通量的变化在磁暴期间尤为明显.要分析潜在的电子动态变化机制,需要排除绝热效应产生的影响.在以三个绝热不变量组成的相空间坐标中,利用相空间密度(PSD)可以反映电子的真实加速和损失情况.本文详细分析两颗范艾伦卫星和三颗GPS导航卫星在2013年3月的同步电子通量观测数据,发现在3月17日磁暴期间,当太阳风动压增大、行星际磁场南向时,辐射带电子通量会发生骤降.进一步将电子通量转换成电子相空间密度并利用不同第一、第二绝热不变量(μ,K)组合条件下PSD径向分布的差异性,深入探究磁暴期间辐射带电子的动态变化机制.结果表明:磁暴初期由于电子的局地加速导致PSD不断上升;磁暴主相期间,由于磁层顶阴影效应以及伴随的向外径向扩散损失导致PSD快速降低;位于不同空间位置的多颗卫星观测为明晰辐射带电子动态物理过程提供了重要的便利.     

Daytime VLF emissions at the Sodankyla Observatory (L ∼ 5.3) at the front of high-speed solar wind streams

We discuss the results of an analysis of digital high-sensitivity ground-based observations of very low frequency (VLF) emissions, carried out in Northern Finland (L = 5.3) in May–June 2012. During this period of time, we found that three high-speed solar wind streams approached the Earth’s magnetosphere and at the front of these fluxes long-lasting intense daytime bursts of VLF emissions were generated in two frequency bands: above and below ～2.5 kHz. At frequencies above ～2.5–3.0 kHz, there were VLF hiss waves, the temporal structure of which consisted of a quasi-periodic sequence of separate stronger spots of noise signals. The low-frequency band was represented by chorus waves, superimposed on intense hiss emissions at frequencies below ～1.5 kHz. The high-frequency (f > 2.5 kHz) waves were elliptic and, predominately, left-hand polarized and the low-frequency waves were right-hand polarized. It was supposed that high-frequency VLF hiss waves were generated at L < 5 and VLF chorus waves were generated at L > 5. We discuss a possible scenario of the generation and propagation of the VLF emissions observed.     

Relationship of the Van Allen radiation belts to solar wind drivers

Discovery of the Van Allen radiation belts by instrumentation flown on Explorer 1 in 1958 was the first major discovery of the Space Age. A view of the belts as distinct inner and outer zones of energetic particles with different sources was modified by observations made during the Cycle 22 maximum in solar activity in 1989–1991, the first approaching the activity level of the International Geophysical Year of 1957–1958. The dynamic variability of outer zone electrons was measured by the NASA–Air Force Combined Radiation Release and Effects Satellite launched in July 1990. This variability is caused by distinct types of heliospheric structure which vary with the solar cycle. The largest fluxes averaged over a solar rotation occur during the declining phase from solar maximum, when high-speed streams and co-rotating interaction regions (CIRs) dominate the inner heliosphere, leading to recurrent storms. Intense episodic events driven by high-speed interplanetary shocks launched by coronal mass ejections (CMEs) prevail around solar maximum when CMEs occur most frequently. Only about half of moderate storms, defined by intensity of the ring current, lead to an overall flux increase, emphasizing the need to quantify loss as well as source processes; both increase when the magnetosphere is strongly driven. Three distinct types of acceleration are described in this review: prompt and diffusive radial transport, which increases energy while conserving the first invariant, and local acceleration by waves, which change the first invariant. The latter also produce pitch angle diffusion and loss, as does outward radial transport, especially when the magnetosphere is compressed. The effect of a dynamic magnetosphere boundary on radiation belt electrons is described in the context of MHD-test particle simulations driven by measured solar wind input.     

基于Van Allen Probes EMFISIS波动仪器观测的内磁层下频带哨声合声波全球分布的统计分析

基于Van Allen Probes近三年的EMFISIS仪器波动观测数据,对内磁层下频带哨声模合声波幅度的全球分布特性对地磁活动水平的依赖性进行了详细的统计分析,着重研究下频带合声波平均场强幅度随磁壳值L、磁地方时、地磁纬度的分布特征及不同强度区间的合声波的发生概率.结果表明,下频带合声波的波动强度与地磁活动密切正相关,处于强磁扰期间的合声波具有更大的振幅,其发生率与地磁活动强度具有同样的正相关特性.下频带合声波主要发生于午夜至下午的磁地方时区间,其余的磁地方时时段下频带合声波较弱.赤道面附近的下频带合声波主要分布在夜侧至黎明这一时段内,随着磁纬度的增加逐步向日侧扩展.下频带合声波在午夜侧(21-03 MLT)主要出现在15°的磁纬范围内,在晨侧(03-09 MLT)可以到达15°磁纬甚至更高纬度.下频带合声波主要发生于L=~4.5的附近区域.随着地磁活动的增加,下频带合声波所覆盖的L-shell空间区域增大,趋势为向高、低L值区域同时扩展.建立的下频带哨声合声波的全球分布模型将有助于进一步深入理解该重要磁层波动对辐射带电子的波粒作用散射效应和对辐射带动力学过程的定量贡献.     

波粒相互作用导致环电流质子沉降的卫星共轭观测

波粒相互作用是环电流损失的重要机制之一,但波粒相互作用导致的环电流离子沉降而损失迄今为止缺乏直接的观测证据.基于磁层及电离层卫星的协同观测,本文报道了发生在2015年9月7日,由电磁离子回旋波(EMIC波)导致环电流质子沉降的共轭观测事件.在等离子体层的内边界,Van Allen Probe B卫星观测到,存在EMIC波的区域和不存在EMIC波的区域相比,离子通量的投掷角分布的各向异性变弱.我们将Van Allen Probe B卫星沿着磁力线投影到电离层高度,同时在该投影区域内DMSP 16卫星在亚极光区域观测到环电流质子沉降.而且,通过从理论上计算质子弹跳平均扩散系数,我们进一步证实观测的EMIC波确实能将环电流质子散射到损失锥中.本文的研究工作为EMIC波导致环电流质子沉降提供了直接的观测证据,揭示了环电流衰减的重要物理机制:EMIC波将环电流质子散射到损失锥中,从而沉降到低高度大气层中而损失.     

基于Van Allen Probes EMFISIS波动仪器观测的内磁层上频带哨声合声波全球分布的统计分析

基于Van Allen Probes近三年的EMFISIS仪器波动观测数据,针对内磁层上频带哨声模合声波幅度的全球分布特性对地磁活动水平的依赖性进行了详细的统计分析,着重研究上频带合声波平均场强幅度随磁壳值(L)、磁地方时(MLT)、地磁纬度(MLAT)的分布特征及不同强度区间的合声波的发生概率.结果表明,上频带合声波的平均场强幅度与地磁活动条件密切相关,在强磁扰期,平均幅度可达到40 pT以上.在外辐射带中心区域(L=4~6),上频带合声波的幅度最强;在L~3的区域,上频带磁层合声波没有分布.在夜侧至晨侧(22—09MLT),上频带合声波幅度最强;在下午侧至昏侧(15-19MLT),上频带合声波幅度最弱;日侧(10-14MLT)上频带合声波在不同地磁活动条件下都存在,幅度偏小.上频带合声波主要分布在|MLAT|10°,其中21-09MLT范围内、磁纬位于|MLAT丨5°的平均场强幅度最强,磁扰期间可达约100 pT.另外,统计而言,中等幅度(10~30 pT)的上频带合声波在夜侧至晨侧(23-09MLT)靠近磁赤道区域的发生率最高,可达15%左右.强幅度(30 pT)的上频带合声波普遍分布在夜侧(01-05MLT),发生率最小.本文建立的上频带哨声模合声波的全球分布模型结合已经建立的下频带合声波的全球分布模型,将有助于进一步深入理解该重要磁层等离子体波动对地球等离子体片、辐射带、环电流动力学过程的定量贡献.     

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.     

A theoretical verification of intensity of plasmaspheric ELF hiss emissions: theory versus GEOS-1 observations

An attempt is made to confirm the generation mechanism of plasmaspheric ELF hiss emissions observed aboard GEOS-1 satellite in the equatorial region both at small and large wave normal angles by calculating their magnetic field intensities in terms of incoherent Cerenkov radiation mechanism and cyclotron resonance instability mechanism, using appropriate and suitable plasma parameters. The ELF intensities calculated by Cerenkov radiation mechanism, being 4 to 5 orders of magnitude lower than the observed intensities, rule out the possibility of their generation by this mechanism. On the other hand, the intensities calculated under electron cyclotron resonance instability mechanism are found to be large enough to account for both the observed intensity and propagation losses and hence to confirm that plasmaspheric ELF hiss emissions observed aboard GEOS-1 satellite both at small and large wave normal angles were originally generated in the equatorial region by this mechanism just near the inner edge of the plasmapause. The difference in the observed intensities of two types of the emissions has been attributed to the propagation effect rather than the generation efffect.     

Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency

Acceleration of relativistic electrons in an inhomogeneous geomagnetic field during their resonant interaction with longitudinally propagating whistler-mode waves of varying frequency has been considered. Specific features of acceleration of electrons trapped by the wave field have been studied. Previous estimates of the efficiency of such acceleration have been generalized with regard to relativistic effects, and the simple formula for energy gain in a wide range of initial energies has been obtained. It has been indicated that the energy gain during a single interaction between electron and a whistler-mode wave packet, with typical parameters of an element of chorus emissions in the Earth’s magnetosphere, can reach several keV. The conditions of this acceleration mechanism realization are discussed. Specifically, it has been found that, in the case of chorus emissions in the Earth’s magnetosphere, this mechanism can be effective for electrons with perpendicular energies several times as high as such an energy of electrons generating chorus.     

Quasi-periodic very low frequency emissions, very low frequency chorus, and geomagnetic Pc4 pulsations (Event on April 3, 2011)

The results of an analysis of ground-based observations of very low frequency (VLF) emissions in Scandinavia (L ∼ 5) in April 2011 are discussed. A detailed study is conducted of an non-typical event (April 3, 2011) of simultaneous generation of VLF chorus at frequencies below 3 kHz and quasi-periodic VLF emissions (QP) in the band of 4–6 kHz, which were not discrete emissions but consisted of separate short (about 20 s) bursts of hiss. It is shown that these emissions were mainly characterized by right-hand polarization, which indicates the location of the exit point of waves from the ionosphere near the point of ground observations. Based on an analysis of the spectral characteristics of emissions, it is concluded that the generation regions of chorus and QP emissions were located at different L shells. The appearance of QP emissions coincided with the excitation of resonance geomagnetic pulsations of the Pc4 range in the magnetosphere with a period that was close to the quasi-period of repetition of spectral forms in QP emissions. However, based on the available data, it is not possible to conclude that these geomagnetic pulsations caused the quasi-periodic generation of bursts of VLF hiss. The time shift between the peaks of QP and geomagnetic pulsations was inconsistent and varied from one burst of hiss to another. It is suggested that the discussed QP emissions were a result of the development of self-oscillations in the Earth’s radiation belts.