A high order WENO finite difference scheme for incompressible fluids and magnetohydrodynamics

We present a high order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of incompressible fluid dynamics and magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme that has been successfully applied to compressible fluids, with or without magnetic fields. A fractional time-step method is used to enforce the incompressibility condition. Two basic elements of the WENO scheme, upwinding and wave decomposition, are shown to be important in solving the incompressible systems. Numerical results demonstrate that the scheme performs well for one-dimensional Riemann problems, a two-dimensional double-shear flow problem, and the two-dimensional Orszag–Tang MHD vortex system. They establish that the WENO code is numerical stable even when there are no explicit dissipation terms. It can handle discontinuous data and attain converged results with a high order of accuracy.     

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.     

驱动重联过程中等离子体团的聚合

本文对驱动重联过程作了二维可压缩磁流体动力学模拟．对于长的计算域（１：４），在持续入流的作用下形成了双重磁岛结构，这些磁岛在向外运动的过程中不断靠近，逐渐聚合成为一个大的等离子体团，并继续向外运动．这说明在地球磁层顶和磁尾所观测到的大尺度磁结构，很可能是在驱动重联过程中，由较小的等离子体团聚合后形成的．并初步揭示了在空间等离子体中，磁岛的聚合过程难以直接观测的动力学原因．     

位于导电介质中三维导体的电磁响应

本文给出一种用积分方程法配合有限差分法计算位于导电介质中三维导体的电磁响应的新途径,在二层大地条件下给出了具体计算方法和结果。详细讨论了围岩介质的导电性对导体异常的影响。这对于开展低阻覆盖层地区的电磁法工作具有一定的指导意义。     

位于导电介质中三维导体的电磁响应

本文给出一种用积分方程法配合有限差分法计算位于导电介质中三维导体的电磁响应的新途径,在二层大地条件下给出了具体计算方法和结果。详细讨论了围岩介质的导电性对导体异常的影响。这对于开展低阻覆盖层地区的电磁法工作具有一定的指导意义。     

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．     

涡旋诱发重联模型(Ⅰ)——动力学特性

本文首先从理论上系统地研究了涡旋诱发重联的基本动力学特性.包括:涡旋诱发重联的物理机制;Kelvin—Helmholtz(K-H)不稳定性和撕裂模不稳定性耦合过程;磁流体涡管的基本特性;不同尺度涡旋间的相互作用,动能和磁能间的转化及准稳态时流线、磁力线、等涡度线和等电流密度线的相似性等.用二维MHD数值模拟方法研究了上述一些特性,并与理论分析结论进行了比较.结果表明,模拟结果证实了理论推论.涡旋诱发重联是产生局部磁场重联的重要机制之一,该模型在磁顶区的应用将另文发表.     

涡旋诱发重联模型（Ⅰ）——动力学特性

本文首先从理论上系统地研究了涡旋诱发重联的基本动力学特性.包括:涡旋诱发重联的物理机制;Kelvin-Helmholtz（K-H）不稳定性和撕裂模不稳定性耦合过程;磁流体涡管的基本特性;不同尺度涡旋间的相互作用,动能和磁能间的转化及准稳态时流线、磁力线、等涡度线和等电流密度线的相似性等.用二维MHD数值模拟方法研究了上述一些特性,并与理论分析结论进行了比较.结果表明,模拟结果证实了理论推论.涡旋诱发重联是产生局部磁场重联的重要机制之一,该模型在磁顶区的应用将另文发表.     

磁通量浮现驱动磁场重联的数值研究

应用二维时变可压缩磁流体动力学数值模拟,研究了双极－单极磁场中由于磁通量浮现驱动的磁场重联过程．结果表明,双极场与单极场间磁力线的重联形成上升的冷而密的等离子体团,磁场演变成鞭状结构．向上运动的等离子体团到达其最大高度后将回落和弥散.等离子体团最大上升速度达０．１４ＶＡ,等离子体最大上升速度达０．２７ＶＡ,ＶＡ为下边界处的Ａｌｆｖｅｎ速度．随着磁通量浮现幅度的增大,等离子体上升速度增加,重联过程发展得较快．背景等离子体β１值（β１为等离子体压力与磁压之比）越小,等离子体团中密度增量越大．磁Ｌｕｎｄｑｕｉｓｔ数Ｓ在１０３－１０６之间的改变对等离子体的速度和密度增量影响并不明显．与电阻撕裂模不稳定性引起的自发重联相比,磁通量浮现会更有效地驱动双极－单极场中的磁场重联过程,寻致日冕Ｈα冲浪和Ｘ射线喷流的形成．     

Stability of the line preserving flows

We examine the equations that are used to describe flows which preserve field lines. We study what happens if we introduce perturbations to the governing equations. The stability of the line preserving flows in the case of the magneto-fluids permeated by magnetic fields is strictly connected to the non-null magnetic reconnection processes. In most of our study we use the Euler potential representation of the external magnetic field. We provide general expressions for the perturbations of the Euler potentials that describe the magnetic field. Similarly, we provide expressions for the case of steady flow as well as we obtain certain conditions required for the stability of the flow. In addition, for steady flows we formulate conditions under which the perturbations of the external field are negligible and the field may be described by its initial unperturbed form. Then we consider the flow equation that transforms quantities from the laboratory coordinate system to the related external field coordinate system. We introduce perturbations to the equation and obtain its simplified versions for the case of a steady flow. For a given system, use of this method allows us to simplify the considerations provided that some part of the system may be described as a perturbation. Next, to study regions favourable for the magnetic reconnection to occur we introduce a deviation vector to the basic line preserving flows condition equation. We provide expressions of the vector for some simplifying cases. This method allows us to examine if given perturbations either stabilise the system or induce magnetic reconnection. To illustrate some of our results we study two examples, namely a simple laboratory plasma flow and a simple planetary magnetosphere model.     

K-H不稳定性在多电流片系统磁场重联中的效应

等离子体系统中存在两个或多个电流片时，电流片中发生的不稳定性可能会相互作用．行星际磁场北向时，背阳面碰层顶电流片与磁尾等离子体片之间可能发生相互作用，高纬边界层强烈的流场剪切可能促进磁场重联，产生磁层亚暴．本文运用二维可压缩磁流体模拟研究具有强流场剪切的多个电流片系统中磁场重联的演化．结果表明，Kelvin－Helmholtz不稳定性使多电流片系统的磁场重联过程明显加快；相邻电流片之间的距离越近，两者相互作用越强，重联增长率越大；在三电流片系统中，超Alfven速度强流场导致外侧两个电流片中出现强烈的磁场重联，并引发中心电流片的磁场重联．行星际磁场北向时，也可能发生磁层亚暴．     

A complex analysis approach to the motion of uniform vortices

A new mathematical approach to kinematics and dynamics of planar uniform vortices in an incompressible inviscid fluid is presented. It is based on an integral relation between Schwarz function of the vortex boundary and induced velocity. This relation is firstly used for investigating the kinematics of a vortex having its Schwarz function with two simple poles in a transformed plane. The vortex boundary is the image of the unit circle through the conformal map obtained by conjugating its Schwarz function. The resulting analysis is based on geometric and algebraic properties of that map. Moreover, it is shown that the steady configurations of a uniform vortex, possibly in presence of point vortices, can be also investigated by means of the integral relation. The vortex equilibria are divided in two classes, depending on the behavior of the velocity on the boundary, measured in a reference system rotating with this curve. If it vanishes, the analysis is rather simple. However, vortices having nonvanishing relative velocity are also investigated, in presence of a polygonal symmetry. In order to study the vortex dynamics, the definition of Schwarz function is then extended to a Lagrangian framework. This Lagrangian Schwarz function solves a nonlinear integrodifferential Cauchy problem, that is transformed in a singular integral equation. Its analytical solution is here approached in terms of successive approximations. The self-induced dynamics, as well as the interactions with a point vortex, or between two uniform vortices are analyzed.     

引力场中磁场重联的数值研究（Ⅱ）磁力线足点的剪切运动

本文基于二维三分量可压缩磁流体动力学模拟，数值研究由于磁力线足点在光球层的剪切运动引起日冕电流片中的磁场重联过程。结果表明，磁力线足点的剪切运动作为引起强迫磁场重联的一种触发机制，将加速磁场重联的发展和磁岛的合并过程。结合不稳定性导致等离子体急剧加速，在β_∞＝０．１的情况下其加速度达到０．３４ν_Ａ∞／τＡ，等离子体的最大下落速度可达１．９０ν_Ａ∞，大于纯电阻撕裂模情况。还讨论了β_∞值对这种磁场重联过程的影响。β_∞值越小，磁场重联和磁岛合并过程发展得越快。     

Forward plane-wave electromagnetic model in three dimensions using hybrid finite volume–integral equation scheme

We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure.     

磁岛合并研究

本文采用二维全粒子模拟来研究无碰撞等离子体中的磁岛合并过程.结果表明,磁岛合并分为两个阶段,在第一个阶段,两个磁岛因同向电流丝之间的吸引力而缓慢地相互靠近,在这个过程中,合并线附近的电子被面外电场加速,形成薄电流片,同时电流片两侧形成磁场堆积.第二个阶段为快速重联阶段,合并线附近的电磁场结构和以Harris电流片为初态的重联扩散区的电磁场结构很相似,其中最显著的特点为面外磁场的四极型结构.     

Relationship between auroral oval poleward boundary intensifications and magnetic field variations in the solar wind

As a rule, bright auroral arcs evolve near the poleward boundary of the auroral oval at the growth phase of a substorm, a phenomenon that is known to occur near the poleward edge of the auroral oval. The closeness of these arcs to the projection of the magnetic separatrix on the night side suggests that their generation is related to magnetic reconnection in the magnetospheric tail in a particular way. In this study this suggestion is confirmed by the fact that integral brightness of the auroral oval at the poleward edge correlates with magnetic field structures in the solar wind that are observed by ACE and Wind satellites at distances of 50–300 R_E upstream and are shifted towards the magnetospheric tail with time delays of ~ 10–80 min, consistent with measurements of the solar wind velocity. About 50 examples of this correlation have been found. The possible physical mechanisms of the effect observed are discussed.     

Magnetic reconnection as a possible heating mechanism of the local high temperature protons within magnetic clouds

Magnetic clouds have the outstanding observational features of low proton temperature and plasma beta value, but numerous observations show that some magnetic clouds often have local high temperature phenomena. The local high temperature protons may be heated by magnetic reconnections within magnetic clouds. Here we take the magnetic cloud on 18–20 October 1995 as an example to discuss the possible heating mechanism. There is a famous protuberance in proton temperature between the front boundary and 11: 00 UT on 19 October 1995. Eight magnetic reconnection events were identified within the magnetic cloud, whose duration was less than 31 hours, and most of these reconnection events occurred within the proton temperature enhanced part of the magnetic cloud. Hence, it is possible for the local protons in the magnetic cloud to be heated by magnetic reconnections.     

地球磁尾中不同类型磁结构的磁螺度演化特征

在二维三分量MHD数值模拟的基础上 ,对地球磁尾不同类型磁结构的形成作磁螺度分析 .研究表明 ,对于由晨昏电场产生的磁尾驱动重联过程 ,通过系统边界输运的磁螺度通量是引起系统总磁螺度变化的直接原因 .不同的初始磁螺度密度分布和磁螺度通量输运 ,可以引起中性片区域磁螺度密度分布的不同演化 ,从而导致具有不同拓扑位形磁结构的形成 .     

地球磁尾和磁层顶磁场变化的随机特性

本文讨论了平板模型下电阻不稳定性使磁力线由对称平衡状态进入随机状态的可能性;给出该模型下以（x,z）为正则坐标的哈密顿函数表达式;在Harris平衡磁场分布下分析了撕裂模不稳定性,驱动重联和涡旋诱发重联引起的磁力线随机特性;估计了两个磁岛相互作用时磁力线进入随机态的临界值.本文结果可用于讨论地球磁层顶和磁尾处磁场的性质.