Effectiveness of fast electron retention in the magnetic cavern during disturbance of the magnetic field azimuthal symmetry

The loss rate of fast electrons (with an energy much higher than the energy of the plasma electron thermal motion), when they leave a magnetic cavern during a disturbance of the magnetic field azimuthal symmetry, is studied. The cases of point and volume sources of fast particles have been considered. The plasma density in the cavern is supposed to be low, so that collisions of fast electrons with plasma particles can be neglected. The effect of the electric field on particle motion is neglected because it is assumed that the electric charge particles outgoing from the cavern is compensated by the counter current of plasma conductivity electrons. The dependence of the loss value on the harmonic number and the amplitude of the cavern boundary radius disturbance has been obtained.     

Inverse problem for the current loop model: Possibilities and restrictions

The possibilities of determining arbitrary current loop parameters based on the spatial structures of the magnetic field components generated by this loop on a sphere with a specified radius have been considered with the use of models. The model parameters were selected such that anomalies created by current loops on a sphere with a radius of 6378 km would be comparable in value with the different-scale anomalies of the observed main geomagnetic field (MGF). The least squares method was used to solve the inverse problem. Estimates close to the specified values were obtained for all current loop parameters except the current strength and radius. The radius determination error can reach ±120 km; at the same time, the magnetic moment value is determined with an accuracy of ±1%. The resolvability of the current force and radius can to a certain degree be improved by decreasing the observation sphere radius such that the ratio of the source distance to the current loop radius would be at least smaller than eight, which can be difficult to reach when modeling MGF.     

大功率长偶极与环状电流源电磁波响应特征对比

为了在深部第二成矿带找矿,需要进一步提高电磁法可控源的强度,因此,一种新的大功率固定发射源的电磁法正在孕育之中.该方法采用长偶极源或者环状电流源,为了提高发射源的强度,偶极长度L或者环状源半径R需要非常大.然而,电磁场信号的强度不仅仅依赖于发射源,当L或者R为数十公里时,接收点的位置远离发射源,电离层对电磁场的影响不可以忽略.电离层的影响既可能是增强信号,也可能是削弱信号,这依赖于不同类型源产生的电磁波.本文利用三维积分方程法对包含电离层、空气层、固体地球层(简称地-电离层模型)的线状和环状大功率电流源电磁波响应进行了三维数值模拟,对两种源的电磁波的响应特征进行了对比研究.研究表明虽然磁性源的发射效率高于电性源,但是由于发射源在波导区产生的直达波经电离层的反射波要产生相长相消干涉,波导区的场特征既和发射源的特征有关,也和电离层有关.对比研究发现对于x方向的水平长偶极源电离层对电磁场 E_x 和 H_y 的影响是使场的幅值增强,即波导场的 E_x 和 H_y 的衰减是减缓的.而对于水平环状电流源,电离层对水平方向的电磁场的影响是使场的幅值减弱,即波导场的 E_x 和 H_y 的衰减是增大的.为此,认为采用大功率固定源在波导场工作时应该采用线状电流源.     

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.     

Point source radiation in inhomogeneous anisotropic structures

The ray formulae for the radiation from point sources in unbounded inhomogeneous isotropic as well as anisotropic media consist of two factors. The first one depends fully on the type and orientation of the source and on the parameters of the medium at the source. We call this factor the directivity function. The second factor depends on the parameters of the medium surrounding the source and this factor is the well-known geometrical spreading. The displacement vector and the radiation pattern defined as a modulus of the amplitude of the displacement vector measured on a unit sphere around the source are both proportional to the ratio of the directivity function and the geometrical spreading.For several reasons it is desirable to separate the two mentioned factors. For example, there are methods in exploration seismics, which separate the effects of the geometrical spreading from the observed wave field (so-called true amplitude concept) and thus require the proposed separation. The separation also has an important impact on computer time savings in modeling seismic wave fields generated by point sources by the ray method. For a given position in a given model, it is sufficient to calculate the geometrical spreading only once. A multitude of various types of point sources with a different orientation can then be calculated at negligible additional cost.In numerical examples we show the effects of anisotropy on the geometrical spreading, the directivity and the radiation pattern. Ray synthetic seismograms due to a point source positioned in an anisotropic medium are also presented and compared with seismograms for an isotropic medium.     

Dynamics of the spatial distribution of electrons and their gyrosynchrotron emission characteristics in a collapsing magnetic trap

The dynamics of the distribution of nonthermal electrons, injected into a collapsing magnetic trap, has been considered. The electron energy and pitch angle nonstationary spatial distributions in an extensive magnetic trap have been obtained for the first time for different laws of inhomogeneous magnetic field evolution in this trap by numerically solving the Fokker-Planck kinetic equation. The gyrosynchrotron emission intensity has been calculated for the obtained electron spatial distributions. It has been indicated that energetic electrons are effectively accumulated and accelerated at the top of a collapsing trap due to the first-order Fermi and betatron acceleration mechanisms at certain rates of variations in the magnetic field and background plasma density.     

A case study of electron precipitation in the late substorm growth phase on and nearby a preonset arc

We follow the electron precipitation characteristics on and nearby a preonset arc using the high resolution Freja TESP instrument. Our data coverage extends from about 10 min before onset up to 1 min before onset. The arc is the most equatorward one (around MLAT 62°) of a system of growth phase arcs, and it was close to the radiation belt precipitation. Within the preonset arc, inverted-V type precipitation dominates. Poleward of the arc we also find some precipitation regions, and here there is systematically a cold electron population superposed with a warm population. Using single and double Maxwellian fits to the measured electron spectra we find the ionosphere-magnetosphere coupling parameters (field-aligned conductance K and the parallel potential drop V) as well as the effective source plasma properties (density and temperature) during the event. Compared to typical expansion phase features, the preonset parallel potential drop is smaller by a factor of ten, the electron temperature is smaller by a factor of at least five, and the field-aligned conductance is about the same or larger. The fact that there are two isotropic superposed electron populations on the poleward side of the preonset arc suggests that the distance between warm trapped electrons on dipolar field lines and colder electrons on open field lines has become so small near the onset that mixing e.g. due to finite electron Larmor radius effects can take place.     

Review paper: Virtual sources and their responses,Part II: data‐driven single‐sided focusing

In Part I of this paper, we defined a focusing wave field as the time reversal of an observed point‐source response. We showed that emitting a time‐reversed field from a closed boundary yields a focal spot that acts as an isotropic virtual source. However, when emitting the field from an open boundary, the virtual source is highly directional and significant artefacts occur related to multiple scattering. The aim of this paper is to discuss a focusing wave field, which, when emitted into the medium from an open boundary, yields an isotropic virtual source and does not give rise to artefacts. We start the discussion from a horizontally layered medium and introduce the single‐sided focusing wave field in an intuitive way as an inverse filter. Next, we discuss single‐sided focusing in two‐dimensional and three‐dimensional inhomogeneous media and support the discussion with mathematical derivations. The focusing functions needed for single‐sided focusing can be retrieved from the single‐sided reflection response and an estimate of the direct arrivals between the focal point and the accessible boundary. The focal spot, obtained with this single‐sided data‐driven focusing method, acts as an isotropic virtual source, similar to that obtained by emitting a time‐reversed point‐source response from a closed boundary.     

Parallel Electric Field and Electron Acceleration: an Advanced Model

A kinetic theory is necessary to explain the electron flows forming strong field-aligned currents in the auroral region. Its construction in this paper is based on the following propositions. (a) In the equatorial region, the arrival of electrons through the lateral surface of the magnetic flux tube is compensated for by their escape along the magnetic field. This is provided by action of the pitch-angle diffusion mechanism in the presence of plasma turbulence concentrated in this region. (b) Outside the equatorial region, the distribution functions of trapped and precipitating particles become “frozen.” The distributions and particle concentrations are calculated there in a model with conservation of the total energy and the magnetic moment. (c) The quasi-neutrality condition yields a large-scale parallel electric field, which contributes to the conserved total energy. In this field, the electron acceleration occurs, causing strong field-aligned currents directed upward from the ionosphere.     

Generation of auroral kilometric radiation in inhomogeneous magnetospheric plasma

The generation of auroral kilometric radiation in a narrow 3D plasma cavity, in which a weakly relativistic electron flow is propagated along the magnetic field against a low-density cold background plasma, is studied. The time dynamics of the propagation and intensification of waves are analyzed using geometric optics equations. The waves have different wave vector components and start from the cavity center at an altitude of about the Earth’s radius at plasma parameters typical for the auroral zone at this altitude. It is shown that the global inhomogeneity of the Earth’s magnetic field is of key importance in shaping the auroral kilometric radiation spectra.     

地磁学中的球面各向同性随机矢量场

从地磁场随机模拟的需要出发，研究球面各向同性随机矢量场．首先指出，与三维空间中的随机矢量场不同，在球上均匀性蕴含于各向同性；三维均匀各向同性随机矢量场一定是球上各向同性随机矢量场，反之不真．其次，以地核磁场的随机模型为例，给出了球面各向同性模型的空间两点关联张量的并矢表示，并将其在不变坐标系分解；利用核幔边界地球主磁场的球谐功率谱的幂级数拟合模型，估算空间两点关联张量．因此，即使根据地球主磁场观测认定地核场具有球面各向同性，亦不能推定地核内部磁流体运动是三维均匀各向同性的．     

A gradient‐ratio method for the semi‐automatic interpretation of gravity map data sets

The application of semi‐automatic interpretation techniques to potential field data can be of significant assistance to a geophysicist. This paper generalizes the magnetic vertical contact model tilt‐depth method to gravity data using a vertical cylinder and buried sphere models. The method computes the ratio of the vertical to the total horizontal derivative of data and then identifies circular contours within it. Given the radius of the contour and the contour value itself, the depth to the source can be determined. The method is applied both to synthetic and gravity data from South Africa. The Matlab source code can be obtained from the author upon request.     

The volcano-magnetic effect

Summary A geometrically simple volcano is considered, havig a spherical magma chamber of 2.5 km radius centred at 10 km depth. The Curie point isotherm is assumed to be a plane at 20 km depth, except for the spherical volume which is also non-magnetic. The stress pattern in the vicinity of the spherical chamber, due to regional stress of sufficient intensity to cause an eruptions, is used to calculate the change in magnetization which results from the piezomagnetic effect through the volume of solid rock. The consequent magnetic field anomaly at the surface is then obtaied by numerical integration of the dipole law of force over the stressed volume. For rocks of the type found on the volcanic island of St. Vincent (West Indies), this model gives a maximum local volcano-magnet c effect of about 7 gammas.     

On the excitation of the earth's seismic normal modes

Summary The excitation of the earth's normal modes is formulated as an initial value problem. The static state of the earth, stressed from its hydrostatic reference situation, is considered as the initial state. The initial state is relaxed, at the time of the earthquake, by the removal of the forces maintaining the departure from hydrostatic equilibrium. Expressions are derived for the coefficients giving the relative excitation of the individual modes for the cases where these forces are compensating volume forces or compensating tractions on the faces of a dislocation. It is demonstrated that a point slip dislocation has a body force equivalent in the form of a double couple with a deviatoric moment tensor. However, for a source with volume change no moment tensor equivalent can be found. The volume change, apart from an elastic effect which can be represented by an isotropic moment tensor, has a direct gravitational effect on the excitation. This effect is due to a balanced force field consisting of a point force at the source and a continuous distribution of volume forces throughout the earth. The latter distribution, if not taken into account, may give rise to artificial phases in the frequency spectrum of the normal modes.     

Generation of electromagnetic oscillations at frequencies of the lower hybrid and bounce resonance in mirror magnetic traps: Laboratory and rocket experiments

The generation of electromagnetic oscillations in the vicinity of the lower hybrid resonance and at the frequency of bounce oscillations of fast electrons in the plasma resonator of the magnetospheric type, formed by an HF discharge in a mirror magnetic trap, has been detected and studied. The results of the field rocket experiments aimed at stimulating maser effects, including such effects at frequencies of bounce oscillations of 40-keV electrons in the magnetospheric flux tube of the geomagnetic field, are discussed.     

Spatial structure of the plasma sheet boundary layer at distances greater than 180 RE as derived from energetic particle measurements on GEOTAIL

We have analyzed the onsets of energetic particle bursts detected by the ICS and STICS sensors of the EPIC instrument on board the GEOTAIL spacecraft in the deep magnetotail (i.e., at distances greater than 180 RK). Such bursts are commonly observed at the plasma-sheet boundary layer (PSBL) and are highly collimated along the magnetic field. The bursts display a normal velocity dispersion (i.e., the higher-speed particles are seen first, while the progressively lower speed particles are seen later) when observed upon entry of the spacecraft from the magnetotail lobes into the plasma sheet. Upon exit from the plasma sheet a reverse velocity dispersion is observed (i.e., lower-speed particles disappear first and higher-speed particles disappear last). Three major findings are as follows. First, the tailward-jetting energetic particle populations of the distant-tail plasma sheet display an energy layering: the energetic electrons stream along open PSBL field lines with peak fluxes at the lobes. Energetic protons occupy the next layer, and as the spacecraft moves towards the neutral sheet progressively decreasing energies are encountered systematically. These plasma-sheet layers display spatial symmetry, with the plane of symmetry the neutral sheet. Second, if we consider the same energy level of energetic particles, then the H layer is confined within that of the energetic electron, the He⁺⁺ layer is confined within that of the proton, and the oxygen layer is confined within the alpha particle layer. Third, whenever the energetic electrons show higher fluxes inside the plasma sheet as compared to those at the boundary layer, their angular distribution is isotropic irrespective of the Earthward or tailward character of fluxes, suggesting a closed field line topology.     

Flow past spheres and spheroids in the presence of a toroidal magnetic field

Summary Stewartson [1]²) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.     

Powerful nonstationary processes on the sun: Spatio-temporal structure and efficient particle acceleration

Data on high-energy processes on the Sun are summarized. We refine the classification of flares and substantiate the view that a coronal mass ejection and a flare proper are manifestations of the same common process, at least for the most powerful events. Next, we analyze data on the acceleration of electrons (RHESSI, Mars Odyssey) and protons. The existence of two peaks of hard X-ray emission spaced 10–20 min apart and the evolution of its spectra are shown to be indicative of two acceleration episodes. We have analyzed the spectra of 172 proton increases identified with the ratio of the proton fluxes at energies above 10 and 100 MeV near the Earth. These spectra turn out to be virtually the same for most of the large flares under favorable conditions for the escape of particles from the corona and their propagation in the interplanetary space. This is an argument for the invariance of the main features of efficient particle acceleration in powerful events. This process takes place at the explosive phase of a flare and its source is located low, immediately above the chromosphere, in the region adjacent to sunspots. There is a reason to believe that, in this case, a rapid simultaneous acceleration of electrons and protons takes place with the capture of some fraction of the particles into magnetic traps. However, there exist a few events in which an additional number of protons with energies as high as 10–30 MeV escape from the corona at the post-eruptive phase of flare development. Analysis of these cases with softer particle spectra more likely suggests an additional particle acceleration at coronal heights (about 30 000 km) than the facilitation of particle escape from magnetic traps. We estimate the contribution from the proton flux at an energy above 10 MeV arising at the post-eruptive phase of a flare to the total particle flux at the maximum of a proton increase and discuss possible particle acceleration mechanisms at significant coronal heights.     

磁暴主相的經度不对称性

太阳带电粒子流通过磁边界层的中性点或阻塞点,由于极化电場的漂移运动或雷萊-泰勒（Rayleish-Taylor）不稳定运动,穿透磁层而进入地磁場被輻射带所捕获。这些被捕获的电子将向东漂移而形成西向电流。在它們围繞地球一周形成封閉的电流环以前,由于地球的自轉以及这个电流弧对地球各地的相对位置的不同,电流分布以及它在地面磁赤道附近所产生的磁場分布都将是不均匀的,对經度来耕是不对称的。本文假定电子繞地球的漂移周期为两天,計算了当磁暴开始时位于地方时00,06,12及18小时的台站記录的磁場随“暴时”T_st变化的曲线。理論結果与用佘山及洪伽幼地磁台站得到的統計結果是一致的。