半圆拱无力场的稳定性

本从能量原理出发，导出了半圆拱无力场的能量积分的普遍形式，并证明所有半圆拱无力场都是稳定的。     

磁拱脚点缓慢运动引起的磁场演化和日冕加热

Heyvaerts和Priest最近提出了一个线性无力场演化的简化模型来定量计算磁拱脚点做缓慢的剪切运动所引起的日冕加热。由于他们在能量的计算中漏掉了一些二阶项,并且保留了导致位移无界的磁场的线性演化项,本文对他们的工作进行了修正,同时还对脚点运动引起的磁拱无力场演化进行了进一步探讨。本文主要结果如下:(1)得到的加热效率(即耗散能量在光球供给能量中所占比例)比Heyvaerts和Priest所得结果大。(2)磁拱无力场的无耗散线性演化是不可能的。(3)由磁场位形具体说明了非线性无力场发生磁力线重联的可能性,并指出最容易发生磁力线重联的高度大约为一个磁拱宽度。     

无力场准静演化中的等离子体运动

在研究磁力线脚点缓慢运动引起的无力场的准静演化时,考虑等离子体运动对演化的影响是非常重要的。本文以基本的MHD方程为依据,给出一种二维无力场进行小扰动准静演化时求等离子体位移的方法,并对一个二维无力磁拱模型的脚点运动引起的无力场演化和等离子体运动进行了具体的研究。     

非对称四极无力场的磁能释放

本文采用二维三分量耗散ＭＨＤ模型，对带高电流层的局地非对称的四极无力场的磁能释放过程进行数值模拟，结果表明，磁能释放过程大体可以分为两个阶段：高电流层引起的异常电阻耗散使该层等离子体加热至３×１０６Ｋ的高温，形成一高温环；在高电流层耗散的触发下，磁分隔面的电流急剧增长并爆发异常电阻耗散和磁场重联，导致耀斑发生，主要的能量释放发生在磁分隔线和高剪切无力场中的磁分隔面上，等离子体温度可以达到１．９×１０７Ｋ。上述无力场的触发释能过程可能是太阳耀斑的一种重要的释能机制。     

太阳活动区的磁场观测

我们利用北京天文台太阳磁场望远镜在1983年投入试观测期间取得的资料,对该年6月份的一群黑子的磁场以及耀斑作了综合分析,得到一些结论。以光球纵场为边界条件,计算了常α无力场。根据挤压无力场耀斑模式,我们认为耀斑爆发的能量,来自异极性黑子的相互靠近。磁中性线的扭曲程度,反映了无力场的状态。     

具奇异电流密度面的一维无力场的稳定性

从Ｎｅｗｃｏｍｂ（１９６０） 给出的直线箍缩等离子体的一维能量积分和稳定性定理出发,证明Ｌｏｗ（１９９３） 在圆柱坐标系下找到的具奇异电流密度面的一维无力场是稳定的     

太阳耀斑可能的储能过程

一般看法是,太阳耀斑的能量源于对流层和光球层,然后逐步堆积到外层的色球和日冕活动区中。所以,分析太阳大气中能量是如何从低层转移到上层的过程,以及分析太阳活动区中无力场能量是怎样堆积起来的机制,显然是讨论耀斑储能过程的中心问题之一。本文从冻结型无力场的基本方程组出发,不仅仅考虑旋转的环形流场,更考虑子午流场之间的相互作用,并具体推算了非定常的时间演化过程。     

无力场的运动学特征

无力场在太阳物理中是常遇到的,特别是色球和日冕活动区中,那里的磁场位形都应该是无力场。通常认为,磁力线的扭绞过程可以将势场变为有电流的无力场,从而在活动区中储存能量。在我们碰到的太阳大气活动的实际问题中,磁雷诺数R_m≈10~3>>1,所以对这种条件下的无力场必须作专门讨论。本文利用冻结型无力场的一般结果,讨论了太阳大气中等离子体的运动状况及无力场的运动学特征。     

质子耀斑活动区特征与无力磁场

本文在综合分析质子耀斑活动区观测特点的基础上,指出在密集的多极黑子构成的局部区域中,同极黑子分裂,互相排斥,异极黑子相互靠近,向异极区中场强较弱部分的挤压和渗入,是一大批质子耀斑活动区的共同特点.这种黑子间的相对运动,使中性线严重扭曲,呈现出质子耀斑活动区特有的“S”型。根据这些观测特点,寻找到了一种定量估计无力因子的方法。对三个典型的质子耀斑活动区估计了无力因子的变化,并在常无力因子的假定下进行了无力场结构和势场磁能的计算。计算表明质子耀斑发生前无力因子逐渐增加,而势场磁能逐渐减小,减少的势场能量可能正是无力场得到发展的能源,足够质子耀斑的需要。     

太阳单极黑子的无力磁场理论和耀斑能量

太阳活动区中无作用力磁场偏离势场而积累了能量,对势场的偏离表现为磁场的切变。只要磁场松开扭转,就会释放能量而产生耀斑。本文根据这一基本思想,在无力因子α=常数的假定下,求出了无力磁场方程的分析解,并求出了扭转场磁能M_势场磁能M_p,可释放的自由磁能△M,磁通量Φ,总电流I,α和磁场衰减因子k等7个重要参量。这些量可表为场强B、扭转角和半影半径b的函数,后3个量可以测出,△M的公式可供太阳预报工作参考使用。将上述公式应用于1972年10月太阳活动区,算出各参量,其中△M的量级为10~(32)尔格,足够供给该活动区耀斑等活动现象的能量。与用Alfvén和Carlqvist的一维理论算出的结果比较,本文结果与观测结果更为符合。     

无力磁场的稳定性

无力场被广泛用来模拟太阳活动区的强磁场,本文从Bernstein能量原理出发,导出了无力场能量原理的普遍形式,并给出了若干稳定性的充分条件,它们可方便而有效地对无力场进行稳定性判断。     

非线性无力场模型的线性稳定性

本文从能量原理出发，对无力场稳定性进行了研究，给出了一般情形下无力场稳定性的充要判据。它可以把线性无力场稳定性判据作为特例包括在内。还对Ｋｒｕｇｅｒ给出的一个充分判据作了进一步的探讨，对无力场稳定性的物理图象也作了讨论。     

Magnetic field configurations associated with polarity intrusion in a solar active region

The theoretical force-free magnetic fields in the first paper of this series, modeling magnetic configurations associated with polarity intrusion in active regions, are established to be all stable to linear ideal hydromagnetic perturbations under the boundary condition that anchors the lines of force rigidly to the photosphere. It is shown first that these force-free fields belong to an even larger class found by Chang and Carovillano (1981). A proof by the energy principle is then given to establish that all force-free magnetic fields in the larger class are absolutely stable. The physical implications of this result are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Force-free magnetic fields and flares of August 1972

On the basis of observations (Zirin and Tanaka, 1973) inferring the presence of shear in magnetic fields, the amount of extractable energy stored in a class of force-free magnetic fields is evaluated for the flares of August 1972, using the formulations developed by Nakagawa and Raadu (1972). It is shown that the evaluated energy storage could be built up by the proper motions of sunspots in the active region McMath 11976 during July 31 and August 7. Then for the flare of August 7, a detailed analysis is made of the manner of energy release in the post maximum phases deduced from the configuration of flare loops. It is shown that the observed flare loops could be represented closely by the force-free magnetic fields and that the evaluated rate of energy release is consistent with observed rate given by the soft X-ray emission. The results of analysis suggest that the flare of August 1972 could be identified with the relaxation of an energetic force-free magnetic field towards lower energy states. The limitations and possible future extension of this type of analysis are discussed.Visiting scientist from the Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

Force-free magnetic fields with singular current density surfaces and their stability

Starting from Bernstein's principle of magnetohydrodynamic energy, a general analysis is presented for the stability of a kind of 1-D force-free magnetic fields with singular current density surfaces and a single parameter in cylindrical coordinates. It is found that in the parameter space of this kind of force-free magnetic fields there simultaneously exist stable and unstable regions. Their stability is solely determined by the radial distribution of the magnetic pitch in the neighborhood of the cylinder axis, and is independent of the presence of singular current density surface at the boundary of the field.     

The stability of force-free magnetic fields with cylindrical symmetry in the context of solar flares

The problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of the chromosphere and corona. The consequences of a large ratio of magnetic pressure to gas pressure are investigated. In this case the field must be approximately force-free. The only suitable force-free fields which allow an analytical treatment are those of cylindrical symmetry. The stability of these fields is studied with the energy principle. It is shown that they are always unstable due to kink type instabilities. The shape of the unstable perturbations is described in detail and an upper limit for their amplitude is estimated. The consequences for the proposed mechanism of energy storage are briefly discussed.     

A class of force-free magnetic fields for modeling pre-flare coronal magnetic configurations

Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 10³⁰ ergs to several 10³¹ ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Non-ideal evolution of non-axisymmetric, force-free magnetic fields in a magnetar

Recent numerical magnetohydrodynamic calculations by Braithwaite and collaborators support the 'fossil field' hypothesis regarding the origin of magnetic fields in compact stars and suggest that the resistive evolution of the fossil field can explain the reorganization and decay of magnetar magnetic fields. Here, these findings are modelled analytically by allowing the stellar magnetic field to relax through a quasi-static sequence of non-axisymmetric, force-free states, by analogy with spheromak relaxation experiments, starting from a random field. Under the hypothesis that the force-free modes approach energy equipartition in the absence of resistivity, the output of the numerical calculations is semiquantitatively recovered: the field settles down to a linked poloidal–toroidal configuration, which inflates and becomes more toroidal as time passes. A qualitatively similar (but not identical) end state is reached if the magnetic field evolves by exchanging helicity between small and large scales according to an α-dynamo-like, mean-field mechanism, arising from the fluctuating electromotive force produced by the initial random field. The impossibility of matching a force-free internal field to a potential exterior field is discussed in the magnetar context.     

Magnetic field configurations associated with polarity intrusion in a solar active region

This paper presents a new class of exact solutions describing the non-linear force-free field above a spatially localized photospheric bipolar magnetic region. An essential feature is the variation in all three Cartesian directions and this could not be modelled adequately with previously known symmetric force-free fields. Sequences of force-free fields are constructed and analyzed to simulate the slow growth of a pair of spots on the photosphere. The axis connecting the spots executes rotational motion, distorting the photospheric neutral line separating fluxes of opposite signs. We show directly from the analytic solutions that the resulting reversal of the positions of the spots relative to the background field is associated with (i) the creation of magnetic free energy, (ii) the severe shearing of localized low-lying loops in the vicinity where the photospheric transverse field aligns with the photospheric neutral line, and (iii) the emergence and disappearance of flux from the photosphere at these highly stressed regions. The model relates theoretically for the first time these different magnetic field features that have been suggested by observation and theoretical considerations to be flare precursors. A general formula, based on the virial theorem, is also given for the free energy of a force-free field, strictly in terms of the field value at the photosphere. This formula has obvious practical application.The National Center for Atmospheric Research is sponsored by the National Science Foundation.