The Earth's Dynamic Magnetotail

Geomagnetic field lines that are stretched on the nightside of the Earth due to reconnection with the interplanetary magnetic field constitute the Earth's magnetotail. The magnetotail is a dynamic entity where energy imparted from the solar wind is stored and then released to generate disturbance phenomena such as substorms. This paper gives an updated overview on the physics of the magnetotail by drawing heavily from recent research conducted with the GEOTAIL satellite. It summarizes firstly the basic properties of the magnetotail such as shape, size and magnetic flux content, internal motion and plasma regimes. Then it describes characteristics of tail plasmas of the solar-wind and the ionosphere origins. Thirdly it addresses acceleration and heating of plasmas in the magnetotail, where reconnection between the stretched field lines is the main driver but the site of the acceleration is not limited to the immediate vicinity of the neutral line. In the collisionless regime of the plasma sheet kinetic behaviors of ions and electrons control the acceleration process. The paper closes by enumerating the problems posed for future studies.     

MHD ANALYSIS OF PETSCHEK-TYPE RECONNECTION IN NON-UNIFORM FIELD AND FLOW GEOMETRIES

Analytical studies of reconnection have, for the most part, been confined to steady and uniform current sheet geometries. In contrast to these implifications, natural phenomena associated with the presence of current sheets indicate highly non-uniform structure and time-varying behaviour. Examples include the violent outbursts of energy on the Sun known as solar flares, and magnetospheric phenomena such as flux transfer events, plasmoids, and auroral activity. Unlike the theoretical models, reconnection therefore occurs in a highly dynamic and structured plasma environment. In this article we review the mathematical tools and techniques which are available to formulate models capable of describing the effects of reconnection in such situations. We confine attention to variants of the reconnection model first discussed by Petschek in the 1960s, in view of its successful application in predicting and interpreting phenomena in the terrestrial magnetosphere. The analysis of Petschek-type reconnection is based on the equations of ideal magnetohydrodynamics (MHD), which describe the large-scale behaviour of the magnetic field and plasma flow outside the diffusion region, which we determine as a localised part of the current sheet in which reconnection is initiated. The approach we adopt here is to transform the MHD equations into a Lagrangian or so-called 'frozen-in' coordinate system. In this coordinate system, the equation of motion transforms into a set of coupled nonlinear equations, in which the presence of inhomogeneous magnetic fields and/or plasma flows gives rise to a term similar to that which appears in the study of the ordinary string equation in a non-homogeneous medium. As demonstrated here, this approach not only clarifies and highlights the effects of such non-uniformities, it also simplifies the solution of the original set of MHD equations. In particular, this is true for those types of problem in which the total pressure can be considered as a known quantity from the outset. To illustrate the method, we solve several 2D problems involving magnetic field and flow non-uniformities: reconnection in a stagnation-point flow geometry with antiparallel magnetic fields; reconnection in a Y-type magnetic field geometry with and without velocity shear across the current sheet; and reconnection in a force-free magnetic field geometry with field lines of the form xy = const. These case examples, chosen for their tractability, each incorporate some aspects of the field and flow geomtries encountered in solar-terrestrial applications, and they provide a starting point for further analytical as well as numerical studies of reconnection.     

Modeling coronal streamers and their eruption

Numerical solutions of the time-dependent MHD equations are used to generate ambient coronal streamer structures in a corona characteristic of that near solar minimum. The streamers are then disrupted by slow photospheric shear motion at the base of magnetic field lines within the closed field region, which is currently believed to be responsible for producing at least some CMEs. In contrast to several other simulations of this phenomena, the polytropic index is maintained at a value of 5/3 through the addition of coronal heating. Observations are used as a guide in determining the thermodynamic structure and plasma beta in the ambient corona. For a shear speed of 2.5 km/sec, the streamer configuration evolves slowly for about 65 hours before erupting outward with the formation of a CME. The bright CME leading edge travels outward at a speed of about 240 km/sec, and the sheared field lines follow at a somewhat slower speed. A closed magnetic field region is ejected as the magnetic field lines that were opened by the CME reconnect and reform the streamer.     

Origin of the Solar Wind: Theory

A theory is presented for the origin of the solar wind, which is based on the behavior of the magnetic field of the Sun. The magnetic field of the Sun can be considered as having two distinct components: Open magnetic flux in which the field lines remain attached to the Sun and are dragged outward into the heliosphere with the solar wind. Closed magnetic flux in which the field remains entirely attached to the Sun, and forms loops and active regions in the solar corona. It is argued that the total open flux should tend to be constant in time, since it can be destroyed only if open flux of opposite polarity reconnect, a process that may be unlikely since the open flux is ordered into large-scale regions of uniform polarity. The behavior of open flux is thus governed by its motion on the solar surface. The motion may be due primarily to a diffusive process that results from open field lines reconnecting with randomly oriented closed loops, and also due to the usual convective motions on the solar surface such as differential rotation. The diffusion process needs to be described by a diffusion equation appropriate for transport by an external medium, which is different from the usual diffusion coefficient used in energetic particle transport. The loops required for the diffusion have been identified in recent observations of the Sun, and have properties, both in size and composition, consistent with their use in the model. The diffusive process, in which reconnection occurs between open field lines and loops, is responsible for the input of mass and energy into the solar wind. This revised version was published online in August 2006 with corrections to the Cover Date.     

Neutral points on the boundary of the closed magnetosphere

Theoretical studies of a field-free plasma incident upon a magnetic dipole lead to a closed magnetosphere with two neutral points in the noon magnetic meridian, at a latitude of ± 70°–75° and a geocentric distance of approximately 10 R_E. The position of the neutral points with respect to the dipole axis is not greatly affected by the angle of incidence of the solar wind. Although the field magnitude near the neutral points is only a fraction of the dipole field, the direction is seen to reverse on opposite sides of the neutral point. Near the boundary the field direction is parallel to the boundary and tends to point towards the neutral point in the Northern hemisphere.     

Dynamics of the earth's ring current: Theory and observation

The development of currents within an arbitrary distribution of particles trapped in the geomagnetic field is described. These currents combine to form the earth's ring current and thus are responsible for the worldwide depressions of surface magnetic field strength during periods of magnetic activity known as magnetic storms. Following a brief review of trapped particle motion in magnetic fields, ring current development is described and presented in terms of basic field and particle distribution parameters. Experimental observations then are presented and discussed within the theoretical framework developed earlier. New results are presented which, in the area of composition and charge state observations, hold high promise in solving many long standing ring current problems. Finally, available experimental results will be used to assess our present understanding as to ring current sources, generation, and dissipation.     

含间隙运动控制系统中的定位抖动和 速率波动原因分析及解决措施

针对一类含间隙大惯量非直驱转动系统中出现的速率波动现象,利用描述函数法和计算仿真的方法进行了原因分析.在通常的解决措施如双电机消隙、机械消隙方法之外,针对一类间隙可测量的运动控制系统,提出了解决该类问题的新思路,即通过间隙的间接测量,利用反馈机制进行间隙补偿,并用小增益定理证明了其稳定性.实现了部分电气消隙的作用,在适当降低跟踪精度的情况下,消除了定位抖动,提高了速率平稳性.     

Plasma populations in a simple open model magnetosphere

The acceleration of charged particles in the magnetic current sheets downstream from magnetic neutral lines is discussed and related to the plasma populations expected to be formed in a simple open model magnetosphere. A simple model of plasma acceleration in the dayside current sheet is set up, and it is shown that magnetospheric particles may take up a considerable fraction of the electromagnetic energy dissipated in the sheet even though they may represent only a small fraction of the total particle influx. The process should result in energetic ring current and ionospheric particles being found in boundary layers on either side of the magnetopause, and accelerated ionospheric particles in the plasma mantle. Acceleration of magnetosheath plasma in the dayside current sheet should result in enhanced flow speeds in these boundary layers, but the process may amount to little more than a return to the sheath plasma of energy previously extracted from it during its inflow on the dayside and stored in the compressed sheath field, due to the appreciable energy take-up from the current sheet by magnetospheric particles. The energy separation between ionospheric plasma and magnetosheath plasma on cusp field lines is shown to result in a spatial separation of polar wind and plasma mantle populations in the tail, the polar wind ions usually reaching out to only a few tens of R _E down-tail such that they usually remain on closed field lines, forming a wedge-shaped region within the mantle shadow-zone. Polar wind ions are then convected back towards the Earth and thus their major sink is via the dayside current sheet rather than outflow into the tail. The major source for the plasmasheet depends upon the location of the neutral line, but mantle ions may usually be dominant. However, with a near-Earth neutral line during disturbed periods ionospheric plasma will be the sole ring-current source. Under usual conditions with a more distant neutral line the spatial separation of the two plasma sources in the tail may result in an energy separation in the inner ring current, with ionospheric particles dominant up to 2 to 20 keV and mantle ions dominant at higher energies. Formation of the plasmasheet is discussed, and it is shown that a layer of ions unidirectionally streaming towards the Earth should be formed on its outer boundary, due to current sheet acceleration of lobe particles and inward convection of the field lines. A similar process leads to earthward flows on the inner layer of the dayside cusp. Finally, the region tailward of the nightside neutral line is discussed and it is shown that a thin tailward flowing two-stream plasma band should be formed across the centre plane of the tail. The slow-speed stream corresponds to incoming lobe ions, the faster stream to the current sheet accelerated ions.     

Mechanisms for the discrete aurora — A review

The V-shock is identified as the primary mechanism for the acceleration of electrons responsible for the discrete aurora. A brief review of the evidence supporting the V-shock model is given, including the dynamics of auroral striations, anomalous motion of barium plasma at high altitudes and in-situ observations of large electric fields. The V-shock is a nonlinear, n = 0 ion cyclotron mode soliton, Doppler shifted to zero frequency. The V-shock is also shown to be a generalization of the one-dimensional double layer model, which is an ion acoustic soliton Doppler shifted to zero frequency. The essential difference between the double layer theory and the theory for the oblique, current-driven, laminar electrostatic shock is that the plasma dielectric constant in directions perpendicular to the magnetic field is c ²/V _a ^/2 , where V _a is the Alfvén velocity; but the plasma dielectric constant parallel to the magnetic field is unity. Otherwise, in the limit that the shock thickness perpendicular to the magnetic field is much larger than an ion gyroradius, the equations describing the double layer and the oblique shock are the same. The V-shock, while accounting for the acceleration of auroral electrons, requires an energy source and mechanism for generating large potential differences perpendicular to the magnetic field. An energy source is the earthward streaming protons coming from the distant magnetospheric tail. It is shown how these protons can be energized by the cross-tail electric field, which is the tailward extension of the polar cap dawn-to-dusk electric field. The local, large cross-field potential differences associated with the V-shock are seen to be the result of a non-linear, E × B drift turbulent cascade which transfers energy from small- to large-scale sizes. Energy at the smallest scale sizes comes from the kinetic energy in the ion cyclotron motion of the earthward streaming protons, which are unstable against the zero-frequency flute-mode instability. The review points out the gaps in our understanding of the mechanism of the diffuse aurora and the mechanism of the auroral substorm.     

Inductive electric fields in the magnetotail and their relation to auroral and substorm phenomena

The paper reviews the importance of inductive electric fields in explaining different magnetospheric and auroral phenomena during moderately and highly disturbed conditions. Quiet-time particle energization and temporal development of the tail structure during the substorm growth phase are explained by the presence of a large-scale electrostatic field directed from dawn to dusk over the magnetotail. Conservation of the first adiabatic invariant in the neutral sheet with a small value of the gradient in the magnetic field implies that the longitudinal energy increases at each crossing of the neutral sheet. At a certain moment, this may result in a rapid local growth of the current and in an instability that triggers the onset. During the growth phase energy is stored mainly in the magnetic field, since the energy density in the electric field is negligible compared to that of the magnetic field (ratio 1: 10⁷). An analytical model is described in which the characteristic observations of a substorm onset are taken into account. One major feature is that the triggering is confined to a small local time sector. During moderate disturbances, the induction fields in the magnetotail are stronger by at least one order of magnitude than the average cross-tail field. Temporal development of the disturbed area results in X- and O-type neutral lines. Particles near to these neutral lines are energized to over 1 MeV energies within a few seconds, due to an effective combination of linear and betatron acceleration. The rotational property of the induction field promotes energization in a restricted area with dimensions equivalent to a few Earth's radii. The model also predicts the existence of highly localized cable-type field-aligned currents appearing on the eastern and western edges of the expanding auroral bulge. It is shown that the predictions agree with satellite observations and with the data obtained from the two-dimensional instrument networks operated in Northern Europe during the International Magnetospheric Study (IMS, 1976–79).     

Some early results of the keV plasma experiment on GEOS-1

Some preliminary new results are presented of the keV plasma experiment on GEOS-1. Electrons and ions have been observed to stream along the magnetic field lines in the dayside magnetosphere from the ionospheric side of the satellite towards the equatorial plane during magnetic storms, with streaming velocities corresponding to a kinetic energy of the order of a keV. The opposite streaming velocity has also been seen, but primarily in the ions only and with a smaller flux ratio for the two opposite directions along the field lines. The transition between the two opposite streaming directions, as seen by the satellite, has been found to occur even in a fraction of a second.In magnetic storm conditions azimuthal asymmetries in ion fluxes corresponding to electric field intensities of several tens of millivolts per meter have been observed.     

Development of solar energetic particle sources within the background magnetic fields

The greatest coronal and interplanetary disturbances are considered consequences of complex processes accompanying development of large-flare regions. Such regions not only possess a specific magnetic field configuration, but their magnetic topology develops following certain rules within the frame of slowly changing large-scale distribution of the background magnetic field patterns as a result of the mutual influences of new magnetic flux appearance as well as old field weakening and dissipation. In this paper we try to demonstrate the individual phases of the large-scale long lasting magnetic field pattern formation with their morphological characteristics and magnetic field configurations. The time scale of the whole process is shown, and the possible reasons of such development are discussed. The proton flare regions of August 1972 and July 1974 are used as examples of the successive magnetic field complication and strengthening, the result of which is the appearance of still more complicated magnetic and velocity fields that produces proton flares and then the fast disintegration of the whole magnetic situation occupying more than one half of the visible solar surface following the occurrence of the proton flares. The consequences which may be used for the proton flare prediction are discussed.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

Small-scale solar magnetic fields: An overview

An overview is given of the observational and the theoretical methods used to investigate solar magnetic fields. It includes an introduction to the Stokes parameters, their radiative transfer in the presence of a magnetic field, and empirical techniques used to measure various properties of solar magnetic features, such as the strength and direction of the magnetic field, magnetic flux, temperature, velocity, size and lifetime. The MHD equations are introduced and some of the most common simplifications used to describe solar magnetic features are outlined.The application of these techniques to small-scale magnetic features is surveyed. The results of empirical and theoretical investigations of small-scale solar magnetic features are reviewed. Current views on their magnetic structure, thermal stratification, velocity field, size, distribution and evolution are presented. Finally, some open questions concerning small-scale solar magnetic fields are listed.     

Hydrodynamic atmosphere models for hot luminous stars II. Method and improvements over unified models

In a paper submitted to A&A we present the first line blanketed hydrodynamic models of spherically expanding atmospheres of hot stars. This paper is complementary to the submitted paper. Here, we emphasize the advantages and the weak points of our approach and we present additional technical aspects.The models are characterised by a simultaneous solution of the equation of motion, the non-LTE populations of H and He, and radiation transfer in a line blanketed atmosphere. The entire domain from the optically thick photosphere out to the terminal velocity of the wind is treated. The radiative forces are evaluated consistently with the depth-dependent radiation field, taking into account multiple scattering by metal lines and line overlap.     

Spectrum of global ideal-magnetohydrodynamic three-dimensional ballooning modes

The class of pressure-driven plasma instabilities known as ballooning modes may be responsible for such diverse phenomena as high-beta disruptions in tokamaks, solar flares and magnetospheric substorms. In this paper the theory of the spectrum of unstable eigenvalues of the linearized ideal magnetohydrodynamic (MHD) equations of motion in non-axisymmetric toroidal equilibria is sketched, comparing and contrasting systems with open field lines and systems with toroidally confined field lines. The need to regularize ideal MHD to keep the wavenumber finite, and the relevance of quantum chaos theory to understand the structure of the spectrum, is pointed out. This revised version was published online in August 2006 with corrections to the Cover Date.     

梯度磁场推进扩散火焰燃烧的实验研究

用数字粒子图像测速技术(DPIV)测量了扩散火焰周围气流在梯度磁场作用下的速度分布,并与无磁场作用下的速度分布比较。结果表明当梯度磁场作用于扩散火焰时,火焰周围气体运动被加速,火焰的形状变得尖锐,亮度增加。实验定量地验证了梯度磁场可以诱导气体对流的发生,从而进一步推进扩散火焰燃烧反应。     

任意形状平面载流线圈在远点处的磁场计算

在电磁场中,经常计算圆环、矩形、三角形等规则平面载流线圈特殊点（如中心轴线上）的磁场分布规律,而复杂一些的问题,例如规则平面载流线圈的远点和任意点的磁场分布规律由于数学处理繁杂一般不加以计算.实践中通过对规则平面载流线圈中心轴线上任意一点和与该线圈共面的对称线上的任意一点的磁场分布规律的整理分析,用二者合成的方法,经推广得出一般性规律,可以解决任意形状的平面载流线圈在远点处这一类的磁场计算问题.     

Ionosphere-magnetosphere coupling

The large-scale electrical coupling between the ionosphere and magnetosphere is reviewed, particularly with respect to behavior on time scales of hours or more. The following circuit elements are included: (1) the magnetopause boundary layer, which serves as the generator for the magnetospheric-convection circuit; (2) magnetic field lines, usually good conductors but sometimes subject to anomalous resistivity; (3) the ionosphere, which can conduct current across magnetic field lines; (4) the magnetospheric particle distributions, including tail current and partial-ring currents. Magnetic merging and a viscous interaction are considered as possible generating mechanisms, but merging seems the most likely alternative. Several mechanisms have been proposed for causing large potential drops along magnetic field lines in the upper ionosphere, and many isolated measurements of parallel electric fields have been reported, but the global pattern and significance of these electric fields are unknown. Ionospheric conductivities are now thoroughly measured, but are highly variable. Simple self-consistent theoretical models of the magnetospheric-convection system imply that the magnetospheric particles should shield the inner magnetosphere and low-latitude ionosphere from most of the time-average convection electric field.     

The magnetotail and substorms

The tail plays a very active and important role in substorms. Magnetic flux eroded from the dayside magnetosphere is stored here. As more and more flux is transported to the magnetotail and stored, the boundary of the tail flares more, the field strength in the tail increases, and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the magnetic flux crossing the neutral sheet lessens. At the onset of the expansion phase, the stored magnetic flux is returned from the tail and energy is deposited in the magnetosphere and ionosphere. During the expansion phase of isolated substorms, the flaring angle and the lobe field strength decrease, the plasma sheet thickens and more magnetic flux crosses the neutral sheet.In this review, we discuss the experimental evidence for these processes and present a phenomenological or qualitative model of the substorm sequence. In this model, the flux transport is driven by the merging of the magnetospheric and interplanetary magnetic fields. During the growth phase of substorms the merging rate on the dayside magnetosphere exceeds the reconnection rate in the neutral sheet. In order to remove the oversupply of magnetic flux in the tail, a neutral point forms in the near earth portion of the tail. If the new reconnection rate exceeds the dayside merging rate, then an isolated substorm results. However, a situation can occur in which dayside merging and tail reconnection are in equilibrium. The observed polar cap electric field and its correlation with the interplanetary magnetic field is found to be in accord with open magnetospheric models.