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。     

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。     

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。     

半圆拱无力场的稳定性

本文从能量原理出发，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。     

日冕三重无力场电流片的磁场重联

采用二维三分量磁流体力学模型,对日冕三重无力场电流片的磁场重联进行了数值研究,揭示了重联过程的基本物理特征．这类重联过程将加热和加速日冕等离子体,并导致多个高温、高密度、高磁螺度的磁岛的形成和向上喷发．这表明,多重无力场电流片的重联可能在日冕磁能释放、上行等离子体团的形成和太阳磁场螺度向行星际空间的逃逸方面起重要的作用．     

日冕三重无力场电流片的磁场重联

采用二维三分量磁流体力学模型,对日冕三重无力场电流片的磁场重磁联进行了数值研究,揭示了重联过程的基本物理特征,这类重联过程将加热和加速日冕等离子体,并导致多个高温、高密度、高磁螺度的磁岛的形成和向上喷发,这表明,多重无力场电流片的重联可能在日冕磁能释放、上行等离子体的形成和太阳磁场螺度向行星际空间的逃逸方面起重要的作用。     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

A Fluid Dynamics Approach for the Computation of Non—linear Force—Free Magnetic Field

Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.     

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy re-lease mechanism. Based on observed vector magnetograms, we have determined the three-dimensional (3D) topology skeleton of the magnetic fields in the active region NOAA 10720.The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans,and null-null lines. For the first time, we have identified a spiral magnetic null in Sun's corona.The magnetic lines of force twisted around the spine of the null, forming a 'magnetic wreath'with excess of free magnetic energy and resembling observed brightening structures at extra-ultraviolet (EUV) wavebands. We found clear evidence of topology eruptions which are re-ferred to as catastrophic changes of topology skeleton associated with a coronal mass ejection(CME) and an explosive X-ray flare. These results shed new lights on the structural complex-ity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather ob-scure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.     

Magnetofrictional Extrapolations of Low and Lou’s Force-Free Equilibria

We present a careful investigation of the magnetofrictional relaxation and extrapolation technique applied to the reconstruction of two test fields. These fields are taken from the family of nonlinear force-free magnetic equilibria constructed by Low and Lou (Astrophys. J. 352, 343, 1990), which have emerged as standard tests for extrapolation techniques in recent years. For the practically relevant case that only the field values in the bottom plane of the considered volume (vector magnetogram) are used as input information (i.e., not including the knowledge about the test field at the side and top boundaries), the test field is reconstructed to a higher accuracy than obtained previously. Detailed diagnostics of the reconstruction accuracy show that the implementation of fourth-order spatial discretization was essential to reach this accuracy for the given test fields and to achieve near machine precision in satisfying the solenoidal condition. Different variants of boundary conditions are tested, which all yield comparable accuracy. In its present implementation, the technique yields a scaling of computing time with total number of grid points only slightly below N ^5/3, which is too steep for applications to large (≥1024²) magnetograms, except on supercomputers. Directions for improvement are outlined.     

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic mag-netographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss     

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates,we investigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fields that are completely closed.The background fields are produced by a dipole,a quadrupole,and an octapole,respectively,located below the photosphere at the same depth.A magnetic flux rope is then launched from below the photo-sphere,and its magnetic properties,i.e,the annular magnetic fluxφp and the axial magnetic fluxφz,are controlled by a single emergence parameter.The whole sys-tem eventually evolves into equilibrium,and the resultant flux rope is characterized by three geometrical parameters:the height of the rope axis,the half-width of the rope,and the length of the vertical current sheet below the rope.It is found that the geometrical parameters increase monotonically and continuously with increasing φp and φz:no catastrophe occurs.Moreover,there exists a steep segment in the profiles of the geometrical parameters versus either φp or φz,and the faster the background field decays with height,the larger both the gradient and the growth amplitude within the steep segment will be.     

The Number of Magnetic Null Points in the Quiet Sun Corona

The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points. These points can be found directly in a potential field extrapolation or their density can be estimated from the Fourier spectrum of the magnetogram. The spectral estimate, in which the extrapolated field is assumed to be random and homogeneous with Gaussian statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO’s MDI. The majority of null points occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null point, with altitude greater than 1.5 Mm, above every 322 Mm² patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minima shows that the null point density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete elements with mean flux 〈|φ|〉=1.0×10¹⁹ Mx distributed randomly with density n=0.007 Mm⁻².     

无力场模型黑子上空的纵向磁场梯度

本文按常α无力场模型计算了1980年10月23日Boulder 2744活动区前导黑子的纵向磁场随高度的变化,并与用CIV 1548谱线观测得到的色球一日冕过渡区的磁场资料相结合,求得CIV 1548发射区的有效高度。这些结果与文献[4]中对同一黑子用势场模型推求的结果有很大差别。从而表明,势场和无力场在某些方面导致的结果是极不相同的。鉴于观测已表明活动区上空存在电流的事实,在活动区磁场的模拟中,特别是在强扭曲活动区磁场的计算中,应当避免采用势场,而尽可能采用无力场模型。