Dynamic non-null magnetic reconnection in three dimensions–II: composite solutions

In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space so that the reconnection is fully three dimensional. In a previous paper we presented a technique for obtaining analytical solutions to the full set of stationary resistive MHD equations and examined specific examples of non-ideal reconnective solutions. Here we further develop the model, noting that certain ideal solutions may be superimposed onto the fundamental non-ideal solutions. This provides the first analytical demonstration of a lack of coupling between reconnective and non-reconnective flows. We examine the effect of imposing various such ideal flows. Significant implications are found for the evolution of magnetic flux in the reconnection process so that several reconnection solutions may have the same reconnection rate, as defined by the integral of the parallel electric field along the reconnection line, but each appear quite different in terms of their global effect. It is shown that, in contrast to the two-dimensional case, in three dimensions there is a very wide variety of physically different steady reconnection solutions.     

Kinematic reconnection at a magnetic null point: spine-aligned current

Magnetic reconnection at a three-dimensional null point is the natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a spiral null point, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. A steady magnetic field is assumed, as well as the existence of a localised diffusion region surrounding the null point. Outside the diffusion region the plasma and magnetic field move ideally. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flows are found to be rotational in nature, as is the change in connections of the magnetic field lines.     

非均匀动压冲击和停止后产生的瞬时重联过程

在非均匀动压冲击期间和冲击突然停止,可引起等离子体边界层的局部瞬时重联过程．本文用二维可压缩ＭＨＤ数值模拟方法研究了这两个过程．结果表明：当大尺度的均匀横向流从一侧边冲击边界层时,磁力线不弯曲,也不发生磁场重联,只是边界层被推着向下游运动;当局部的非均匀动压（特别是横向剪切流）冲击边界层时,被冲击的同向磁场区磁力线逐渐弯曲,在弯曲的反磁场区,出现磁岛,然后在电流片区发生磁场重联,且逐渐形成准稳态的“反Ｋ型”重联结构;当横向剪切流冲击停止后,边界层区变为非常不稳定的系统,产生多种流体涡旋和流型,并相应地产生多种类型的磁场重联结构,直到涡旋消失变为湍动状态时,磁场拓扑才逐渐恢复到未扰动状态。我们提出,外力作用的突然停止,可能是驱动重联的一种新机制,并对这种重联过程在磁层物理中可能的应用进行了讨论．     

Kinematic reconnection at a magnetic null point: fan-aligned current

Magnetic reconnection at a three-dimensional null point is a natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a null point with current directed parallel to the fan plane, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. The magnetic field is assumed to be steady, and a localised diffusion region surrounding the null point is also assumed, outside which the plasma is ideal. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flow is found to cross the spine and fan of the null, and thus transfer magnetic flux between topologically distinct regions. Solutions are also found in which the flow crosses either the spine or fan only.     

Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry

Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are parameterised by D, representing a differential rotation, M, a meridional circulation, and C, a component characterising convective rolls. The dynamo action of all solutions with fixed parameters (steady flows) is known from earlier studies. Dynamo action is sensitive to these flow parameters and fails spectacularly for much of the parameter space where magnetic flux is concentrated into small regions, leading to high diffusion. In addition, steady flows generate only steady or regularly reversing oscillatory fields and cannot therefore reproduce irregular geomagnetic-type reversal behaviour. Oscillations of the flow are introduced by varying the flow parameters in time, defining a closed orbit in the space ( D,?M ). When the frequency of the oscillation is small, the net growth rate of the magnetic field over one period approaches the average of the growth rates for steady flows along the orbit. At increased frequency time-dependence appears to smooth out flux concentrations, often enhancing dynamo action. Dynamo action can be impaired, however, when flux concentrations of opposite signs occur close together as smoothing destroys the flux by cancellation. It is possible to produce geomagnetic-type reversals by making the orbit stray into a region where the steady flows generate oscillatory fields. In this case, however, dynamo action was not found to be enhanced by the time-dependence. A novel approach is being taken to solve the time-dependent eigenvalue problem where, by combining Floquet theory with a matrix-free Krylov-subspace method, we can avoid large memory requirements for storing the matrix required by the standard approach.     

Variational principles for topological barotropic fluid dynamics

Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested (vortex line foliation) with the topology of cylinders, toroids or a combination of both, we show how a Clebsch representation of the flow velocity can be introduced. This is then used to reduce the number of functions to be varied in the variational principles for such flows. We introduce a three function variational formalism for steady and non-steady barotropic flows.     

近尾无碰撞多重X线重联的观测

利用Cluster星簇sc3卫星2001年10月1日09:46~09:50UT时段磁场和等离子数据,探测到近尾尾向传播的两个磁通量绳,时间间隔为26 s.通量绳结构的尾侧存在高速地向流,地侧有高速的尾向流.同时观测到了尾向流的重联X线源区和地向流的重联出流区,直接地观测到了近尾无碰撞多重X线重联.     

Reconnection driven lobe convection: Interball tail probe observations and global simulations

We present Interball Tail Probe observations from the high latitude mid-tail magnetopause which provide evidence of reconnection between the interplanetary magnetic field (IMF) and lobe field lines during a 6 h interval of stable northward and dawnward IMF on October 19, 1995. Results from a global magnetohydrodynamic simulation for this interval compare well with the Interball observations. With the simulations, we provide an extended global view of this event which gives us insight into the reconnection and convection dynamics of the magnetosphere. We find that reconnection occurs in a region of limited spatial extent near the terminator and where the IMF and the lobe field are anti-parallel. Reconnected IMF field lines drape over the dayside magnetosphere, convect along the flanks into the nightside, and enter the magnetotail through a small entry window that is located in the flank opposite to the reconnection site. Ionospheric convection is consistent with previous observations under similar IMF conditions and exhibits a two cell pattern with a dominant lobe cell over the pole. The magnetic mapping between the ionosphere and the lobe boundary is characterized by two singularities: the narrow entry window in the tail maps to a 6 h wide section of the ionospheric lobe cell. A singular mapping line cuts the lobe cell open and maps to almost the entire tail magnetopause. By this singularity the magnetosphere avoids having a stagnation point, i.e., the lobe cell center maps to a tailward convecting field line. The existence of singularities in the magnetic mapping between the ionosphere and the tail has important implications for the study of tail–ionosphere coupling via empirical magnetic field models. Because the lobe–IMF reconnection cuts away old lobe flux and replaces it with flux tubes of magnetosheath origin, solar wind plasma enters the lobes in a process that is similar to the one that operates during southward IMF.     

Specific features of magnetic barrier formation near the magnetopause

The numerical three-dimensional MHD model is used to study the formation of the magnetic barrier in the inner part of the magnetosheath near the magnetopause. The set of the quasistationary solutions for several characteristic directions of the interplanetary magnetic field (IMF) has been obtained: for northward and southward IMF, for the direction along the Parker helix (at an angle of 45° with respect to the Sun-Earth line), and for the predominantly radial direction (at an angle of 20° with respect to the Sun-Earth line). The mechanism used to take into account the effect of magnetic reconnection at the magnetopause on a flow in the magnetosheath is introduced in the case of southward IMF. The results of the calculations indicate that the magnetic field absolute value in the magnetic barrier reaches its maximal value when IMF is northward. The introduction of magnetic reconnection at southward IMF can result in an insignificant decrease in the field value. However, the model predicts that a decrease in the magnetic field is much more substantial when the IMF direction is close to radial.     

2008年1月5日磁层亚暴期间磁尾近地重联事件的THEMIS观测与分析

本文主要应用THEMIS卫星的磁场和等离子体流观测数据,分析了2008年1月5日08∶51~08∶57 UT亚暴膨胀相期间磁尾的一个近地重联事件.在亚暴膨胀相期间,地面的全天空成像仪清楚地记录到了极光的极向扩展,THEMIS的P5卫星在地球同步轨道附近观测到了磁场的偶极化现象.在亚暴膨胀相末期的08∶51~08∶57 UT期间,P3(X_GSM~-9.12R_E) 和P4 (X_GSM ~-9.40R_E) 同时观测到了一对方向相反的高速等离子体流.这对方向相反的高速等离子体流是由磁尾的重联现象所引起.重联的位置被估计位于X_GSM ~-9.12R_E 和X_GSM~-9.40R_E之间较小的空间范围内.并且,在重联位置的两侧,重联的Hall效应被P3和P4两颗卫星观测到.因此,这一磁尾重联事件发生在距离地球非常近的空间范围内.     

球坐标系中图形单元应变与旋转张量及其误差解算

利用泰勒级数展开和弹性力学的几何方程,推导了球坐标系中由GPS位移数据解算图形单元应变和旋转张量的解析公式. 通过线性化处理,并利用误差传播定律,详细推导了图形单元应变和旋转张量的误差公式. 利用川滇地区最新的GPS测站位移速率数据,采用图形单元法解算了该区的面应变率及最大剪切应变率分布,并对其进行了初步的分析. 同时阐述了图形单元应变数学模型的局限性,讨论了图形单元法计算应变的意义以及图形单元的选择问题,进一步分析了应变计算的定权方法,还讨论了GPS观测网图形单元的地心半径差异与应变的关系问题.      

Automatic Interpretation of Magnetic Data Using Euler Deconvolution with Nonlinear Background

The voluminous gravity and magnetic data sets demand automatic interpretation techniques like Naudy, Euler and Werner deconvolution. Of these techniques, the Euler deconvolution has become a popular choice because the method assumes no particular geological model. However, the conventional approach to solving Euler equation requires tentative values of the structural index preventing it from being fully automatic and assumes a constant background that can be easily violated if the singular points are close to each other. We propose a possible solution to these problems by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization technique like conjugate gradient. This technique is applied to a published synthetic data set where the magnetic anomalies were modeled for a complex assemblage of simple magnetic bodies. The results for close by singular points are superior to those obtained by assuming linear background. We also applied the technique to a magnetic data set collected along the western continental margin of India. The results are in agreement with the regional magnetic interpretation and the bathymetric expressions.     

Simulation Studies of High-Latitude Magnetospheric Boundary Dynamics

Magnetic reconnection at the high-latitude magnetopause is studied using 2–1/2-dimensional (2−1/2-D) Hall-MHD simulation. Concentric flow vortices and magnetic islands appear when both Hall effect and sheared flow are considered. Plasma mixing across the magnetopause occurs in the presence of the flow vortices. Reconnected structure generated in the vicinity of the subsolar point changes its geometry with increasing flow shear while moving to high latitudes. In the presence of flow shear, with the Hall-MHD reconnection a higher reconnection rate than with the traditional MHD is obtained. The out-of-plane components of flow and magnetic field produced by the Hall current are redistributed under the action of the flow shear, which makes the plasma transport across the boundaries more complicated. The simulation results provide some help in understanding the dynamic processes at the high-latitude magnetopause.     

磁场重联中的电子加速机制的数值模拟研究

在应用2.5维混合模拟方法研究Petschek模型磁场重联的基础上,考察了试验电子被加速的特征. 模拟结果表明,稳态的低频重联场能将少量试验电子加速到高能,电子的能谱为幂律谱,但总体分布函数未发生显著变化. 电子在整个加速过程中被束缚在低磁场的加速区内,由重联产生的感应电场Ey分量对其直接加速,根据加速时间和加速区域可以将这些电子分为两种情况：初始位于加速区和漂移到加速区被加速.     

准周期性磁结构的形成过程及其特征的数值分析

在入流马赫数ＭＡ为０．１－０．４范围内，选取不同的入流，逐一考察在可压缩导电介质中磁场重联的类型随磁雷诺数Ｒｍ的变化．大量的数值结果表明：在不同入流驱动下，磁雷诺数（Ｒｍ）均有临界值存在，如果等离子体系统逐渐趋于稳定的单Ｘ线重联；若间歇性的次级撕裂产生了重复出现的磁结构，而且Ｍａ越大产生间歇性次级撕裂的临界值越高，与ＭＡ之间基本上符合线性关系．此外还发现，当多重Ｘ线重联间歇性地出现时，有关物理量发生准周期性地振荡．     

Predicted signatures of pulsed reconnection in ESR data

Early in 1996, the latest of the European inco-herent-scatter (EISCAT) radars came into operation on the Svalbard islands. The EISCAT Svalbard Radar (ESR) has been built in order to study the ionosphere in the northern polar cap and in particular, the dayside cusp. Conditions in the upper atmosphere in the cusp region are complex, with magnetosheath plasma cascading freely into the atmosphere along open magnetic field lines as a result of magnetic reconnection at the dayside magnetopause. A model has been developed to predict the effects of pulsed reconnection and the subsequent cusp precipitation in the ionosphere. Using this model we have successfully recreated some of the major features seen in photometer and satellite data within the cusp. In this paper, the work is extended to predict the signatures of pulsed reconnection in ESR data when the radar is pointed along the magnetic field. It is expected that enhancements in both electron concentration and electron temperature will be observed. Whether these enhancements are continuous in time or occur as a series of separate events is shown to depend critically on where the open/closed field-line boundary is with respect to the radar. This is shown to be particularly true when reconnection pulses are superposed on a steady background rate.     

The stabilizing effect of viscosity on magnetic wind flows from accretion discs

Magnetically channelled winds are believed to be a feature of most accretion discs. It has been shown that such flows can remove significant amounts of angular momentum from the disc and make a major contribution to driving the inflow. For a suitable range of poloidal magnetic field bending, only a small fraction of the disc mass is lost in the wind flow, so most material reaches the inner region of the disc. However, discs driven purely by such a process are prone to a field-bending instability which can lead to runaway mass loss. It is shown here that a small amount of disc viscosity can quench such an instability and allow steady disc-wind models to be constructed. The effects of perturbations to the coupling between the radial and vertical structures are allowed for, with the thermal balance having particular relevance. Runaway increases in field bending are prevented by increases in the disc temperature and magnetic diffusivity mainly caused by viscous dissipation.     

磁场重联中离子轨道的混合模拟研究

在使用2.5维混合模拟方法研究了Petschek模型稳态驱动磁场 重联演化的基础上， 本文考察了计算域内各典型区域中粒子分布函数的变化，描绘了重联区不同位置几种类型的 非Maxwell分布函数. 结果表明，磁场重联会将重联区少部分粒子加速到很高的能量，不同 加速程度的粒子将形成球壳状的速度分布. 粒子的轨道特征表明，在重联区中出流的粒子， 有一部分被磁镜捕获，其回旋半径大于重联区宽度，并构成整个流体速度的低速部分. 另外 ，在X中性点附近进入重联区的粒子沿磁力线向出流区以三种形式漂移，分别为：沿磁力线 逃逸、捕获在磁镜中随流体运动、横越磁力线漂移，其比例分别约为70%，20%和10%。     

A Route to Magnetic Field Reversals: An Example of an ABC-Forced Nonlinear Dynamo

We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system.