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，给出了一般情形下地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殊包括在内，还对Ｋｒｕｇｅｒ给出的一个充分判据作了进一步探计，对无力场稳定的物理图象也作用了讨论。     

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。     

太阳线性无力场评注和快速傅氏分析法的应用

首先对30年来用无力场计算太阳活动区磁场方法作了一些评注，特别研究了线性无力场解中的几个误区，提出了准线性无力场方法并探讨了快速傅氏变换在线性无力场计算中的应用，以2000年9月15日NOAA 9165活动区磁场为例，应用3种不同的方法计算出磁力线走向，然后同紫金山天文台赣榆观测站观测的精细Hα图形对比。     

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。     

黑洞吸积盘的演化及温度分布的热不稳定性

本文在Ｔｈｏｒｎｅ工作的基础上讨论了吸积盘中黑洞的有关参量的演化，以及由Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞吸积盘向Ｋｅｒｒ黑洞吸积盘演化过程中对吸积盘辐射通量的影响，最后针对几个典型的辐射过程，分别讨论了黑洞吸积盘在牛顿框架中的温度分布方程与广义相对论的温度分布方程的热不稳定性，并给出此类问题的热不稳定性的判据。     

太阳活动区常α无力场数值计算及其在耀斑预报中的可能应用

本文综述作者及其合作者近年来在太阳活动区无力场数值计算及其应用方面的研究概况。文中简要评价了现有几种太阳活动区常α无力场数值计算表达式,并且叙述了把常α无力场数值计算应用于耀斑研究的结果。得到的主要结论为:(1)现有几种活动区常α无力场数值计算表达式中,Chiu的公式比较好;(2)用Chiu公式外推得到的活动区磁场结构,能够较好地解释观测到的许多现象,表明常α无力场近似仍不失为一种可以接受的活动区磁场模型;(3)活动区无力场的某些参数,如无力因子α和自由磁场能ΔE(定义为无力场能与势场能之差),与耀斑发生率密切相关,可以作为耀斑预报的判据。     

对"文[1,2]"评论的答复

对“关于太阳线性无力场评注和快速傅氏分析法的应用的评论”一文,提出一些看法和补充,以增进对无力场计算太阳磁场问题的进一步的认识．     

黑洞吸积盘的演化及温度分布的热不稳定性

本文在Ｔｈｏｒｎｅ工作基础上讨论了吸积盘中黑洞的有关参量的演化，以及由Ｓｃｈｗａ－ｒｚｓｃｈｉｌｄ黑洞吸积盘向Ｋｅｒｒ黑洞吸积盘演化过程中对吸积盘辐射通量的影响，最后针对几个典型的辐射过程，分别讨论了黑洞吸积盘在牛顿框架中的温度分布方程与广义相对论的温度分布方程的热不稳定性，并给出此类问题的热不稳定性的判据。     

太阳磁场理论外推研究进展

太阳磁场是研究太阳物理的关键。目前对太阳磁场的精确测量只限于光球层。对日冕磁场结构的了解,则多是以观测的光球磁场作为边界条件,在某种理论模型下进行外推。势场模型、线性无力场模型和非线性无力场模型是无力场假设下的三种理论外推模型。文章介绍了太阳磁场理论外推的基本方法和最新进展,和对三种模型中使用较多的外推方法,列举了它们在天文研究中的一些应用,同时也简略讨论了外推方法中存在的一些问题。     

GEOSAT GM的精密轨道确定及精度估计

对最近公开的ＧＥＯＳＡＴ ＧＭ期间的ＴＲＡＮＥＴ Ｄｏｐｐｌｅｒ数据作了分析,利用这些数据和新的ＪＧＭ３重力场模型,计算了ＧＥＯＳＡＴ在ＧＭ期间的精密历元．９１个６天弧解给出的平均的Ｄｏｐｐｌｅｒ残差为４．３ｍｍ／ｓ,估计出所计算的轨道径向精度约为１０ｃｍ。     

Calculating and Testing Nonlinear Force-Free Fields

Improvements to an existing method for calculating nonlinear force-free magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In particular a solution of the 3-D Poisson equation using 2-D Fourier transforms is presented. The improved nonlinear force-free method is demonstrated in application to linear force-free test cases with localized nonzero values of the normal component of the field in the boundary. These fields provide suitable test cases for nonlinear force-free calculations because the boundary conditions involve localized nonzero values of the normal components of the field and of the current density, and because (being linear force-free fields) they have more direct numerical solutions. Despite their simplicity, fields of this kind have not been recognized as test cases for nonlinear methods before. The examples illustrate the treatment of the boundary conditions on current in the nonlinear force-free method, and in particular the limitations imposed by field lines that connect outside of the boundary region.     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Topological differences and similarities between force-free and potential models of coronal magnetic fields

Potential fields and linear force-free fields are often used as models for the magnetic field of the Sun's corona. They can be written as analytical expressions in terms of boundary values at the photosphere. Because of their relative simplicity compared with nonlinear force-free fields, these two models are of particular importance in topological analysis of solar phenomena. However, it has been suggested by Hudson and Wheatland (1999) that the topologies of potential and force-free models are in general not even qualitatively equivalent. In this paper, their example is re-examined and it is found that the opposite conclusions hold. In general, potential and force-free fields are topologically similar sufficiently close to localized sources. The exception to this are structurally unstable states, such as bifurcation states, where a small change of current can produce a significant change of topology.     

Equilibrium and stability of the force-free magnetic field

The exact limit of stability of force-free fields for the case α=const and spherical region of the disturbances is obtained. The stable fields of active regions must be close to the harmonical ones for length scales which are less than the linear dimensions of spots.     

Topological Differences Between Force-Free Field Models

The potential and linear force-free field models for the magnetic field in the solar corona are often used in the analysis of flares. The field is calculated using boundary values measured in the low solar atmosphere. The topology of the field calculated using these models is then compared to the position of flare emissions. We demonstrate that the topology of the field according to each of these models, with the same boundary conditions in place, is not in general even qualitatively equivalent. An argument is given for a similar discrepancy between a linear force-free field solution and a nonlinear force-free field solution.     

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 on curvilinear coordinate surfaces

To seek nonlinear solutions of force-free magnetic fields, some symmetries or approximations are usually invoked. We consider magnetic fields lying on coordinate surfaces of an orthogonal curvilinear coordinate system. We conclude that only fields on parallel planes or spherical shells can be expressed in the form provided by Low in 1980s. These force-free fields are stable against small perturbations with rigid boundaries. Fields on cylindrical shells are also considered.     

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.