【作者】 郝娟；

【导师】 聂清香； 张枚；

【作者基本信息】 山东师范大学 ， 理论物理， 2007， 硕士

【摘要】 太阳磁场是研究太阳物理的关键。然而,目前对太阳磁场的精确观测只限于光球层。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。目前讨论较多的是非线性无力场模型。围绕太阳磁场理论外推方法,本文完成了如下的主要内容:1.简要回顾了太阳磁场理论外推方法的发展历史,叙述了外推方法的基本理论假设和理论方程。对无力场假设下三种模型中使用较多的外推方法进行了一一举例,介绍了它们在天文研究中的一些应用,并简要评论了各种方法的优缺点。2.对一种非线性无力场模型进行了研究。颜毅华和樱井在2000年的太阳物理杂志上发表一文,就太阳光球外围开放空间磁场建立了一个具有有限能量的非线性无力场模型。在此基础上,颜毅华和李柱恒通过第二格林定理,推导出一个直接边界积分方程。借助一个单纯形的优化数值方法,能够求解出太阳半空间中任意一点的磁场。我们在第四章,利用一个解析解,通过IDL语言中的Broyden和Newton函数反解出方程假无力因子的初始值,再将该初始值带入边界积分方程,检验其结果与解析解的差值。从而验证了直接边界积分方程解的存在性,证明了其解确实存在。3.研究了该方法方程的数值解对其中四个主要参数的依赖性。这四个主要参数为:边界区域网格的疏密程度、边界区域的大小、所选假无力因子的初始值和点源邻域的大小。我们发现,方程的数值解与假无力因子的初始值有很大关系,对程序中的其他参量的依赖性不大。4.从不同角度验证了这种最优化数值方法总体的精确性。得到的结论是用这种方法计算太阳大气较低层磁场要比计算较高层磁场效果好。更多还原

【Abstract】 Understanding solar magnetic field is the predominant factor in studying solar physics. However, precise measurements of solar magnetic fields so far are still confined to the thin layer of solar photosphere. In order to understand the nature of the coronal magnetic fields, it becomes necessary to extrapolate the coronal magnetic fields based on theoretical models using observed photospheric magnetograms as boundary conditions. Taking force-free assumptions, three kinds of models are currently being used: the potential field model, the linear force-free field model and the non-linear force-free (NLFF) field model. Enclosed in this thesis, I have completed following studies related to the extrapolation of solar magnetic field.1. The progress and development of the solar magnetic field extrapolation methods are reviewed briefly. Basic theoretical hypothesis and equations of extrapolation methods are introduced. Methods of extrapolations based on three models, that are, potential field model, linear force-free field model and nonlinear force-free field model, are introduced, with specific examples given and their astrophysical applications mentioned. Problems and related progress in the extrapolation methods are also briefly addressed.2. A specific nonlinear force-free field model is studied and examined. In 2000, Yan & Sakurai proposed a boundary integral method to extrapolate nonlinear force-free fields. Basing on this work, Yan & Li (2006) proposed a new direct boundary integral formulation. Using an optimal method, they can obtain the numerical solution at any position in semi-space. We first test the existence of the solution of the direct boundary integral equation. Using the semi-analytical solutions of NLFF magnetic field in Low & Lou (1990) as the known solution, we use the BROYDEN function and the NEWTON function in IDL to solve the inverse function of the direct boundary equation and get the values of the pseudo force-free factors. We find that we can always find pseudo force-free factors, putting which into the direct boundary equation recovers the analytical solution. So the existence of the equation is validated.3. We further test the dependence of the solution on the four main parameters used in the calculation. The results show that the solution mainly depends on the initial values of the pseudo force-free factor, and there is no strong dependence on other parameters.4. We give an overall accuracy of this method by comparing the numerical results with the exact analytical solution. We conclude that this method provides better solutions at the lower layers than those at higher ones.更多还原