Two-spacecraft observations of reconnection at the magnetopause: Model results and data comparison

We revisit an example of “quasi-steady” magnetic reconnection at the dayside magnetopause on February 11, 1998, observed by Equator-S and Geotail at the dawnside magnetopause. Phan et al. [Phan, T.D. et al., 2000. Extended magnetic reconnection at the Earth’s magnetopause from detection of bi-directional jets. Nature 404, 848–850.] reported oppositely directed jets at these spacecrafts and inferred a length of the reconnection line of about 38R_E. Pinnock et al. [Pinnock, M., Chisham, G., Coleman, I.J., Freeman, M.P., Hairston, M., Villain, J.-P., 2003. The location and rate of dayside reconnection during an interval of southward interplanetary magnetic field. Ann. Geophys. 21, 1467–1482.] used measurements from SuperDARN radars to show that the reconnection electric field was variable. Here we complement this work by obtaining snapshots of the reconnection electric field from the in situ observations. To do this, we apply a reconstruction method based on a model of compressible Petschek-type magnetic reconnection. This independent method uses magnetic field observations as input data to calculate the reconnection electric field. We obtain average values of E_rec in the range of 0.4–2.4 mV/m. Further we infer a distance perpendicular to the reconnection line of 0.4–0.6R_E. The model results are compared with the two studies mentioned above. It thus appears that while the transfer of momentum for this event is indeed large-scale, the actual rate depends on the time it is measured.     

Theoretical model of steady-state magnetic reconnection in collisionless incompressible plasma based on the Grad–Shafranov equation solution

The problem of steady-state magnetic reconnection in an infinite current layer in collisionless, incompressible, nonresistive plasma, except of the electron diffusion region, is examined analytically using the electron Hall magnetohydrodynamics approach. It is found that this approach allows reducing the problem to the magnetic field potential finding, while last one has to satisfy the Grad–Shafranov equation. The obtained solution demonstrates all essential Hall reconnection features, namely proton acceleration up to Alfvén velocities, the forming of Hall current systems and the magnetic field structure expected. It turns out that the necessary condition of steady-state reconnection to exist is an electric field potential jump across the electron diffusion region and the separatrices. Besides, the powerful mechanism of electron acceleration in X-line direction is required. It must accelerate electrons up to the electron Alfvén velocity inside the diffusion region and on the separatrixes. This is a necessary condition for steady-state reconnection as well.     

Magnetic reconnection on the Sun: ESPD Senior Prize Lecture

Magnetic reconnection is a fundamental process for changing the magnetic topology and converting magnetic energy into other forms on the Sun, such as heat, flow energy and fast particle energy. In two dimensions it is fairly well understood, although some aspects still need to be developed. In three dimensions, it behaves very differently and a substantial body of theory and numerical experiment has now been built up, including reconnection at null points, separators and quasi-separators.Some aspects of solar flares can be understood with 2D reconnection models, but other aspects such as the shapes of flare ribbons, the acceleration of particles and the creation of twist in erupting flux ropes need a 3D understanding. A paradigm shift in our understanding of coronal heating by reconnection has been stimulated by dramatic new observations of photospheric flux cancellation from SUNRISE and from SST together with the realisation that it may well be driving nanoflare heating events and possibly campfires.     

Converging motion of conjugate flaring kernels during two large solar flares

In this paper, we analyze the footpoint motion of two large solar flares using observations made by the Transition Region and Coronal Explorer (TRACE) and Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The two flares are the M5.7 flare of March 14, 2002 and the X10 flare of October 29, 2003. They are both classical two-ribbon flares as observed in TRACE 1600 or 171 Å images and have long-duration conjugate hard X-ray (HXR) footpoint emission. We use the ‘center-of-mass’ method to locate the centroids of the UV/EUV flare ribbons. The results are: (1) The conjugate UV/EUV ribbons and HXR footpoints of the two flares show a converging (inward) motion during the impulsive phase. For the two flares, the converging motion lasts about 3 and 10 min, respectively. The usual separation (outward) motion for the flare ribbons and footpoints take place only after the converging motion. (2) During the inward and the outward motion, the conjugate ribbons and footpoints of the two events exhibit a strong unshear motion. In obtaining above results, TRACE UV/EUV and RHESSI HXR data show an overall agreement. The two events demonstrate that the magnetic reconnection for the flares occurs in highly sheared magnetic field. Furthermore, the results support the magnetic model constructed by Ji et al. [Ji, H., Huang, G., Wang, H. Astrophys. J. 660, 893–900, 2007], who proposed that the contracting motion of flaring loops is the signature of the relaxation of sheared magnetic fields.     

Modeling the (upper) solar atmosphere including the magnetic field

The atmosphere of the Sun is highly structured and dynamic in nature. From the photosphere and chromosphere into the transition region and the corona plasma-β changes from above to below one, i.e., while in the lower atmosphere the energy density of the plasma dominates, in the upper atmosphere the magnetic field plays the governing role – one might speak of a “magnetic transition”. Therefore the dynamics of the overshooting convection in the photosphere, the granulation, is shuffling the magnetic field around in the photosphere. This leads not only to a (re-)structuring of the magnetic field in the upper atmosphere, but induces also the dynamic reaction of the coronal plasma, e.g., due to reconnection events. Therefore the (complex) structure and the interaction of various magnetic patches is crucial to understand the structure, dynamics and heating of coronal plasma as well as its acceleration into the solar wind.

The present article will emphasize the need for three-dimensional modeling accounting for the complexity of the solar atmosphere to understand these processes. Some advances on 3D modeling of the upper solar atmosphere in magnetically closed as well as open regions will be presented together with diagnostic tools to compare these models to observations. This highlights the recent success of these models which in many respects closely match the observations.     

Statistical study of electrostatic solitary waves associated with reconnection: Geotail observations

The role of waves in the dynamics of the magnetotail has long been a topic of interest in magnetospheric physics. The characteristics of Electrostatic Solitary Waves (ESWs) associated with reconnection have been studied statistically in the magnetotail by surveying the large amounts data obtained from Waveform Capture (WFC) which is an important component of Plasma Wave Instrument (PWI) on the Geotail spacecraft. About 150 reconnection events with WFC data available are selected, and approximately 10 thousands of ESW waveforms are picked up by hands for statistical study. The ESWs are observed near diffusion region and near the plasma sheet boundary layer (PSBL). Two kinds of waveforms of ESWs are observed: bi-polar and tri-polar pulses. It is found that the pulse width of the ESWs is in the order of 1–5 ms and the peak-to-peak amplitude is in the order of 0.1–5 mV/m. The amplitudes of ESWs are larger in the near-earth tail region than that in deep tail region. ESWs have been observed with or without guide magnetic field 〈By〉. The characteristics of ESWs in different reconnection region and under different strength of guild magnetic field, their possible generation mechanism will be discussed.     

三维非线性撕裂模耦合和快速磁场重联

基于三维不可压缩电阻性ＭＨＤ方程，在长柱形位型下，数值研究了电阻撕裂模不稳定性所引起的磁场重联过程。研究结果表明，撕裂模的非线性相互作用和耦合，将产生许多模式的强裂解稳和导致快速的磁场重联。这一过程的进一步发展，导致具有螺旋形结构，不同模式的磁岛磁力线重叠，从而引起较大区域内的磁场各态经历和磁力线随机走向，形成撕裂模端动。     

Combining MHD and kinetic modelling of solar flares

Solar flares are explosive events in the solar corona, representing fast conversion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely difficult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging the gap between fluid and kinetic modelling of solar flares. Two types of approaches are discussed: combined MHD/test-particle (MHDTP) models, which can be used for modelling the flaring corona with relatively small numbers of energetic particles, and hybrid fluid-kinetic methods, which can be used for modelling stronger events with higher numbers of energetic particles. Two specific examples are discussed in more detail: MHDTP models of magnetic reconnection and particle acceleration in kink-unstable twisted coronal loops, and a novel reduced-kinetic model of particle transport in converging magnetic fields.     

Coronal heating by reconnection

The outermost atmosphere of the Sun, called the corona, is some 200 times hotter than the surface of the Sun. The main source of energy for heating the corona is believed to be the magnetic field which dominates the corona. Magnetic reconnection is probably the most important mechanism for releasing magnetic energy and may, therefore, be important for coronal heating or micro-flaring. The best observational examples of reconnection in the corona are thought to be X-ray bright points, which are small-scale brightenings seen randomly throughout the whole corona. Theoretical models can not only explain the key observations relating to bright points, but they can also explain the complex three-dimensional structures often seen in bright points. In these models magnetic neutral points play a significant role as the centres for reconnection both in two and three dimensions.     

Acceleration of charged particles by fluctuating and steady electric fields in a X-type magnetic field

Release of stored magnetic energy via particle acceleration is a characteristic feature of astrophysical plasmas. Magnetic reconnection is one of the mechanisms for releasing energy from magnetized plasmas. Collisionless magnetic reconnection could provide both the energy release mechanism and the particle accelerator in space plasmas. Here we studied particle acceleration when fluctuating (in-time) electric fields are superposed on an static X-type magnetic field in collisionless hot solar plasma. This system is chosen to mimic the reconnective dissipation of a linear MHD disturbance. Our results are compared to particle acceleration from constant electric field superposed on an X-type magnetic field. The constant electric field configuration represents the effects of steady state magnetic reconnection. Time evolution of ion and electron distributions are obtained by numerically integrating particle trajectories. The frequencies of the electric field represent a turbulent range of waves. Depending on the frequency and amplitude of the electric field, electrons and ions are accelerated to different degrees and have energy distributions of bimodal form consisting of a lower energy part and a high energy tail. For frequencies (ω in dimensioless units) in the range 0.5 ? ω ? 1.0 a substantial fraction (20%–30%) of the proton distribution is accelerated to gamma-ray producing energies. For frequencies in the range 1 ? ω ? 100.0 the bulk of the electron distribution is accelerated to hard X-ray producing energies. The acceleration mechanism is important for solar flares and solar noise storms but it could be applicable to all collisionless astrophysical plasmas.     

Global MHD simulations for southward IMF: a pair of wings in the flanks

Global magnetohydrodynamic (MHD) simulations have shown that for southward interplanetary magnetic field nightside reconnection takes place only in a limited spatial scale in the cross-tail direction. Between the end of the nightside reconnection line and the flank magnetopause are regions of closed magnetic field lines which move relatively slowly tailward, compared with the magnetosheath flow on the far side and the jet flow produced by nightside reconnection on the side closer to the midnight. The magetosphere appears to have a pair of extended wings on the nightside. Further refinement of the simulations shows that the wings are not produced by the numerical effects. Similar features have been observed previously and also shown in different simulation models. The existence of the wings in the simulations indicates that the solar wind momentum is transferred to the closed magnetosphere if the simulations are relevant to reality.     

2.5维自适应磁场重联MHD模式

磁雷诺数(R_m)是影响磁场重联的重要因素. 真实的物理环境中R_m往往很高, 例如, 在行星际空间和太阳日冕中R_m通常大于104量级. 高R_m条件下的磁重联表现出很多异常特性, 然而高R_m条件下的磁场重联数值模拟需要很高的时空分辨率, 否则很难分辨出重联过程中形成的薄电流片. 本文基于自适应软件包PARAMESH将并行自适应网格技术引入磁场重联数值模拟, 建立了一个2.5维自适应磁场重联MHD模式, 研究高磁雷诺数条件下重联的动态演化过程, 进而将不同磁雷诺数的参数进行对比研究. 结果表明, 该模式可以自动捕捉到磁场重联产生的奇性电流片, 高磁雷诺数条件下产生的慢激波结构可提供一种快速磁能释放机制.      

Two sources of magnetosheath ions observed by Cluster in the mid-altitude polar cusp

Double cusps have been observed on a few occasions by polar orbiting spacecraft and ground-based observatories. The four Cluster spacecraft observed two distinct regions, showing characteristics of a double cusp, during a mid-altitude cusp pass on 7 August 2004. The Wind spacecraft detected a southward turning of the Interplanetary Magnetic Field (IMF) at the beginning of the cusp crossings and IMF–Bz stayed negative throughout. Cluster 4 observed a high energy step in the ion precipitation around 1 keV on the equatorward side of the cusp and a dense ion population in the cusp centre. Cluster 1, entering the cusp around 1 min later, observed only a partial ion dispersion with a low energy cutoff reaching 100 eV, together with the dense ion population in the cusp centre. About 9 min later, Cluster 3 entered the cusp and observed full ion dispersion from a few keV down to around 50 eV, together with the dense ion population in the centre of the cusp. The ion flow was directed poleward and eastward in the step/dispersion, whereas in the centre of the cusp the flow was directed poleward and westward. In addition the altitude of the source region of ion injection in the step/dispersion was found 50% larger than in the cusp centre. This event could be explained by the onset of dayside reconnection when the IMF turned southward. The step would be the first signature of component reconnection near the subsolar point, and the injection in the centre of the cusp a result of anti-parallel reconnection in the northern dusk side of the cusp. A three-dimensional magnetohydrodynamic (MHD) simulation is used to display the topology of the magnetic field and locate the sources of the ions during the event.     

太阳表面水平运动驱动的磁圈与开放磁场重联的模拟研究

太阳大气的诸多观测事件(如耀斑、喷流等)均被归因于磁重联产生的能量转换. 近年来, 关于太阳风起源, 有研究提出了磁重联使闭合磁圈开放为太阳风供应物质的新模式. 在该模式中, 闭合磁圈被光球超米粒组织对流携带, 向超米粒边界运动, 与位于边界的开放磁场相碰撞进而发生磁重联. 该模式中磁重联的驱动及其效应是本文的研究目标. 磁流体力学(MHD)数值模拟是研究太阳大气磁重联物理过程的重要途径. 本文建立了一个二维MHD数值模型, 结合太阳大气温度和密度的分层分布, 在超米粒组织尺度上模拟了水平流动驱动的闭合磁圈与开放磁场的重联过程. 通过对模拟结果的定量分析, 认为磁重联确实能够将闭合磁圈的物质释放, 进而供应给新的开放磁结构并产生向上流动. 该结果为进一步模拟研究太阳风初始外流奠定了基础.      

Theory of magnetic reconnection in three dimensions

Magnetic reconnection in traditional, two-dimensional theory can be closely associated with topological properties of the magnetic field, separatrices, neutral lines, or separators. Such well-defined topological properties may no longer exist, or become hopelessly complicated, in more general three-dimensional configurations, that otherwise behave physically quite similarly to the two-dimensional configurations. We discuss generalized definitions of reconnection applied to such situations and illustrate typical properties with simulations of three-dimensional reconnection in the magnetotail.     

Numerical study of magnetic reconnection possibly occurring near heliospheric current sheet

The third-order accurate upwind compact difference scheme has been applied for the numerical study of the magnetic reconnection driven by a plasma blob impacting the heliospheric current sheet, under the framework of the two-dimensional compressible magnetohydrodynamics. The results show that the driven reconnection near the current sheet could occur in about 10–30 min for the interplanetary high magnetic Reynolds number, R_M = 2000–10,000, a stable magnetic reconnection structure can be formed in hour order of magnitude, and there appear some basic properties such as the multiple X-line reconnections, vortex structures, filament current systems, splitting and collapse of the high-density plasma blob. These results are helpful in understanding and identifying the magnetic reconnection phenomena possibly occurring near the heliospheric current sheets.     

On the universality of asymptotic limits in the theory of field line diffusion and perpendicular transport of energetic particles

We discuss the random walk of magnetic field lines in astrophysical plasmas. Based on the standard theory of field line diffusion we show that there are two asymptotic limits. In these limits field line wandering is universal because in both regimes the field line diffusion coefficient depends only on fundamental length scales and absolute magnetic field strengths. As examples we discuss the field line diffusion coefficient for different prominent turbulence models namely the slab model, the two-dimensional model, and the Goldreich–Sridhar model. We show that the field line diffusion coefficient for the latter model agrees with the results obtained for slab and two-dimensional turbulence in limiting cases. We also discuss the transport of energetic particles perpendicular with respect to the mean magnetic field. Based on the unified nonlinear transport theory we consider again asymptotic limits. It is shown that one can identify four different regimes in which the transport is again universal. In all four cases perpendicular transport only depends on fundamental length scales of turbulence, magnetic field values, and the parallel diffusion coefficient.     

日冕冲浪形成的磁流体动力学模拟

应用二维时变可压缩磁流体动力学模拟,数值研究了双极-单极磁场中电阻撕裂模不稳定性引起的磁场重联过程,用于模拟日冕冲浪的形成.结果表明,在包含有三区——双极场、电流片和单极场的磁静力平衡初态下,双极场和单极场中的磁力线将会直接重联,磁场演变成鞭状(whip)结构.由弯曲磁力线支撑的等离子体团向上运动到最高位置后,逐渐下落和弥散.等离子体团上升速度可达到0.10v_A(v_A为双极场中的Alfv'én速度).模拟结果证实日冕冲浪的形成可能与双极-单极场中的磁场重联密切相关.      

Determination of reconnected flux via remote sensing

Magnetic reconnection is one of the most fundamental processes in the magnetosphere. We present here a simple method to determine the essential parameters of reconnection such as reconnected flux and location of the reconnection site out of single spacecraft data via remote sensing. On the basis of a time-dependent reconnection model, the dependence of the reconnected flux on the magnetic field z-component B_z is shown. The integral of B_z over time is proportional to the reconnected flux and depends on the distance between the reconnection site and the actual position where B_z is measured. This distance can be estimated from analysis of magnetic field B_z data. We apply our method to Cluster measurements in the Earth’s magnetotail.