Formation of electron beams by the interaction of a whistler wave packet with radiation belt electrons

The purpose of this paper is to discuss the properties of electron beams formed by cyclotron interactions between radiation belt electrons and a quasi-monochromatic whistler wave packet from a ground-based VLF transmitter. The beams are formed due to trapping of the electrons at the forward edge of the wave packet, their acceleration inside the wave packet, the escape of the accelerated electrons from the moving backward edge of the wave packet, and their following free motion in an inhomogeneous magnetic field. A combination of these processes provides the main features of the spatial-temporal evolution of the beams which are investigated both analytically and numerically. It is shown that one or two beams can appear at one point at the same time, and that the density of the beams increases during their expansion. Motion of the pumping wave packet in the inhomogeneous magnetic field provides the variations of the initial velocity and position of the beam injection which change the spatial and temporal gradients of the parallel velocity of the beam, in contrast with the case of the pure adiabatic motion of an individual electron. Such a behaviour can be significant for the generation of secondary emissions. Numerical calculations demonstrate a wide variety of the spatio–temporal patterns of the beam parallel velocity depending on the plasma and wave packet parameters. It is shown that the most significant parameters which determine the beam characteristics are the wave packet length about the equator, its group velocity, and the initial energy and pitch angle of the electrons.     

Proton interaction with quasi-electrostatic whistler mode waves in an inhomogeneous plasma (magnetosphere)

We study the interaction between energetic protons of the Earth’s radiation belts and quasi-electrostatic whistler mode waves. The nature of these waves is well known: whistler waves, which are excited in the magnetosphere due to cyclotron instability, enter the resonant regime of propagation and become quasielectrostatic, while their amplitude significantly increases. Far enough from the equator where proton gyrofrequency and transversal velocity increase the nonlinear interaction between these waves and energetic protons becomes possible. We show that plasma inhomogeneity may destroy cyclotron resonance between wave and proton on the time scale of the order of particle gyroperiod which in fact means the absence of cyclotron resonance; nevertheless, the interaction between waves and energetic particles remains nonlinear. In this case, particle dynamics in the phase space has the character of diffusion; however, the diffusion coefficients are determined by the averaged amplitude of the wave field, but not by its resonant harmonics. For real parameters of the waves and magnetospheric plasma, proton pitch-angle diffusion leading to their precipitation from the magnetosphere becomes essential.     

Nonlinear interaction between acoustic gravity waves

The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.     

Latest progress on interactions between VLF/ELF waves and energetic electrons in the inner magnetosphere

Interactions between very/extremely low frequency (VLF/ELF) waves and energetic electrons play a fundamental role in dynamics occurring in the inner magnetosphere. Here, we briefly discuss global properties of VLF/ELF waves, along with the variability of the electron radiation belts associated with wave-particle interactions and radial diffusion. We provide cases of electron loss and acceleration as a result of wave-particle interactions primarily due to such waves, and particularly some preliminary results...     

Soil-structure interaction with Rayleigh waves

Presented is a plane-strain method for soil-structure interaction analysis consisting of the superposition of the free field motions and the interaction motions in a generalized seismic environment. The free field is modelled as a horizontally layered viscoelastic medium and the seismic environment may consist of a combination of S, P and Rayleigh waves. The soil-structure system is modelled with viscoelastic finite elements, transmitting boundaries, viscous boundaries and a three-dimensional simulation. Comparative analyses of the same structure are conducted for an input of R waves and for vertically propagating S and P waves in a rock site and sand site. In the rock site the R waves produce higher peak horizontal spectral acceleration up to 25 per cent, and a significant rocking effect at points away from the centre of gravity of the structure. However, the S and P waves show higher peak vertical spectral acceleration by up to 15 per cent at the centre of the structure. Very similar horizontal response, but higher vertical response only at the centre of the structure for S and P waves, is obtained for the sand site.     

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.     

Effect of loss-cone distribution on the generation of whistler waves in the magnetosphere

An anisotropic kappa velocity distribution with loss-cones is used to investigate whistler wave instability occurring in the magnetosphere. The elements of the dielectric tensor and dispersion relation using modified plasma dispersion function $\text{Z}{}_{\mathrm{\kappa }}{}^1\text{(ξ)}$ with loss-cone angle have been obtained for the linear waves propagating exactly parallel to a uniform local magnetic field in a homogeneous and hot plasma. The modified plasma dispersion function and integrals have been expressed in power-series form for argument of ξ≫1. Temporal/spatial growth rates for whistler wave in the magnetosphere have been evaluated by the method of numerical techniques. The results of such a kappa loss-cone distribution function on the generation of whistler waves are compared with those obtained by Maxwellian loss-cone distribution. Calculations show that either a loss-cone or a thermal anisotropy in the hot plasma component of the magnetosphere can lead to the generation of incoherent emission of low-frequency whistler waves. This methodology could be easily extended to the study of low frequency emissions from planetary magnetospheres under suitable choice of models of density and magnetic field and other plasma parameters.     

基于智能语音技术的闪电哨声波自动识别

闪电哨声波是一种重要的电磁波动,了解其传播特征及传播过程有助于揭开圈层电磁耦合机理.从卫星观测资料识别闪电哨声波通常需要将原始电磁波形进行滤波处理再转化为时频图像,最后采用目视方法识别图像中的色散状形态,整个过程消耗大量人机时间和内存资源,不能满足张衡一号(ZH-1)卫星观测的海量电磁场数据处理的需求.针对该问题,鉴于闪电哨声波原始波形数据能够通过播放器产生降调的声音,本文打破以视觉分析为主的闪电哨声波研究惯例,首次采用语音智能技术研究其自动识别算法.首先,以张衡一号卫星感应磁力仪(SCM)的VLF波段的波形数据为研究对象,截取时间窗口为0.16 s的波形数据作为音频片段;然后对该片段进行去趋势处理;基于梅尔频率倒谱系数(MFCCs)能够刻画人耳的听觉机理,提取闪电哨声波的MFCCs特征;其次,构建长短期记忆(LSTM)神经网络并输入波形数据的MFCCs特征训练分类模型;最后利用MFCCs特征和训练得到的LSTM分类模型实现闪电哨声波自动识别.通过对10200数据集(5100段包含闪电哨声波,5100段无闪电哨声波)上开展实验发现：该方法的准确率为96.7%,召回率为84.2%,调和平均得分(F1-score)为90.0%,AUC(Area under Curve)评分为90.1%,而且消耗的时间成本是2.28 s,消耗内存资源是82.89 MB;当前最优的基于时频图的闪电哨声波识别算法在本数据集上的准确率为97.3%,内存消耗为233 MB,在CPU上处理0.16 s的片段数据所消耗的时间是6.71 s,内存消耗和时间消耗比较严重.相比而言,基于智能语音的闪电哨声波识别算法准确率略低0.6%,但能够节约66%的时间成本以及65%的内存资源.这表明该算法不仅仅适合从卫星观测的海量数据中快速准确识别出闪电哨声波,且更适合应用于星载识别.

     

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.     

Precipitation of energetic electrons and Pi3 geomagnetic pulsations at polar latitudes

Precipitation of electrons with energies of 0.3–1.5 MeV has been analyzed based on the CORONAL-F satellite data at polar latitudes of the Northern Hemisphere on December 13, 2003. The instants of electron precipitation have been compared with the ground-based observations of geomagnetic disturbances and auroras near the satellite orbit projection. It has been indicated that precipitation of energetic electrons in the high-latitude nightside sector is accompanied by the simultaneous development of bay-like magnetic field disturbances on the Earth’s surface and the appearance of riometer absorption bursts and Pi3 geomagnetic pulsations, and auroras.     

基于JUNO卫星WAVES仪器波动数据的木星磁层哨声波分析研究

等离子体波的空间分布在木星磁层高能电子动力学过程中起着重要的作用.现有大多数对木星磁层哨声波的观测仅限于|λ|≤ 15°的磁纬范围内,但是最新的JUNO卫星WAVES仪器提供的波动数据使得更高纬度、更广区域范围内的等离子体波动分布研究成为可能.本文通过对JUNO卫星WAVES仪器数据进行分析处理,详细研究了木星磁层哨声波的空间分布特性.观测表明,存在位于高L_J、高磁纬的木星磁层哨声波,它们广泛分布于距木星中心距离35~75个木星半径、磁纬为|λ|≤ 30°的空间区域.分析研究发现,WAVES仪器观测的木星磁层哨声波幅度一般为几个pT,远小于地球磁层哨声波的强度.木星磁层哨声波幅会随着L_J的增大缓慢增加,也会随着磁纬的减小趋向平缓变化.基于以上观测事实,本文利用指数幂函数分别拟合得到木星磁层哨声波幅随L_J和磁纬变化的经验模型.该模型将有助于精确理解哨声波对木星磁层高能电子动力学过程的重要影响.

     

Nonlinear waves in rotating magnetohydrodynamics

We consider an electrically conducting fluid in rotating cylindrical coordinates in which the Elsasser and magnetic Reynolds numbers are assumed to be large while the Rossby number is assumed to vanish in an appropriate limit. This may be taken as a simple model for the Earth's outer core. Fully nonlinear waves dominated by the nonlinear Lorentz forces are studied using the method of geometric optics (essentially WKB). These waves are assumed to be of the form of an asymptotic series expanded about ambient magnetic and velocity fields which vanish on the equatorial plane. They take the form of short wave, slowly varying wave trains. The first-order approximation is sinusoidal and basically the same as in the linear problem, with a dispersion relation modified by the appearance of mean terms. These mean terms, as well the undetermined amplitude functions, are found by suppressing secular terms in a “fast” variable in the second-order approximation. The interaction of the mean terms with the dispersion relation is the primary cause of behaviors which differ from the linear case. In particular, new singularities appear in the wave amplitude functions and an initial value problem results in a singularity in one of the mean terms which propagates through the fluid. The singularities corresponding to the linear ones are shown to develop when the corresponding waves propagate toward the equatorial plane.     

On the problem of quasi-electrostatic whistler mode waves: A possible interpretation of discrete plasmaspheric emissions

Summary In a number of VLF experiments with low-orbiting Intercosmos satellites, high-intensity, discrete VLF emissions at frequencies above the local LHR were observed predominantly between L=2.3 and 4.0. The frequency of their intensity maximum varies continuously with geomagnetic latitude, and approximately parallels the value of a quarter of the equatorial electron gyrofrequency. An attempt is made to interprete these emissions in terms of quasi-electrostatic whistler-mode waves, generated in the near-equatorial region and propagating downward in the quasi-resonance mode. The generating mechanism is supposed to be the kinetic instability connected with the loss-cone and temperature anisotropy of the distribution function of energetic electrons. Some features of the discrete plasmaspheric emissions are discussed on the basis of theoretical considerations.

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On the interaction of rayleigh surface waves with structures

A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the [frequency filtering] effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical motions and for vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves.     

Nonlinear aspects of long shelf waves

Abstract

Continental shelf waves are examined in the long wavelength limit, and the effects of weak topographic dispersion calculated. These dispersive effects are then balanced against nonlinear terms and a Korteweg-de Vries equation is derived to describe the evolution of the wave amplitude. Two particular cases are worked in detail.     

伴随等离子体密度下降的磁声波与辐射带电子的波粒相互作用及其散射效应

利用范阿伦卫星的高质量观测数据,我们报道了伴随等离子体密度下降的磁声波现象.通过选取分别发生于2013年7月26日（事件A）和2013年9月19日（事件B）的两个相应事件进行细致分析,我们开展试验粒子模拟计算了磁声波对辐射带电子的散射系数,并求解二维福克-普朗克扩散方程量化了磁声波散射导致的辐射带电子动态变化.结果表明,事件A中的磁声波的散射作用主要发生于投掷角范围为60°~80°、能量范围为20~200 keV的辐射带电子,而事件B中的磁声波的散射作用主要发生于投掷角范围为50°~80°、能量范围为20~400 keV的辐射带电子;两个事件中的磁声波均能导致辐射带电子的蝴蝶状投掷角分布,但是由于事件B的磁声波幅度更强,形成的电子蝴蝶状分布更明显.

     

Nonlinear waves on a coupled density front

Abstract

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.     

Nonlinear interactions between gravity waves and tides

In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.