Mathematical Sciences: "RUI: Magnetohydrostatic Problems Relevant to Current Sheets and Heating of the Solar Corona"

数学科学：“RUI：与电流片和日冕加热相关的磁流体静力问题”

• 批准号: 9622923
• 负责人: Edward Stredulinsky
• 金额: $ 6.75万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622923&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Magnetohydrostatic; Problems

9622923 Stredulinsky The main goal of this project is to give a careful mathematical analysis of a theory due to E.N. Parker on solar coronal heating. According to Parker the main source of heat in the solar corona consists of very thin regions of intense current (current sheets) which arise as a mediation between the tendency of coronal plasma to relax to equilibrium, and certain topological constraints. Such constraints arise due to the near perfect conductivity of the coronal plasma, and the anchoring of magnetic field lines at their footpoints or ends in the dense gas of the photosphere, the footpoints being convected by the turbulent motion of the photosphere. In attempting to understand the phenomenon of current sheet formation in Parker's model a variational approach associated with energy minimization will be used which relies on decompositions of magnetic fields as a means of characterizing and prescribing field line topology. A careful study will be made of which field line topologies withstand the weak Sobolev space limits associated with the relaxation of a plasma towards minimum energy. A general two-dimensional theory will be developed and applied to the analysis of well known examples of current sheet formation in the astrophysics literature. Beginnings of a fully three-dimensional theory will be described with special emphasis on localized vector potential analogs of the flux function representation of plasmas in two dimensions. Also topological constraints involving helicity, and more refined measures of field line topology measuring higher order linkage will be explored. %%% One of the outstanding open problems in solar astrophysics is the existence of enormously high temperatures in the sun's atmosphere (corona), on the order of two million degrees Fahrenheit, which have baffled astrophysicists for generations. Though a number of reasonable models of coronal heating have been explored the issue still engenders intense debate. In this project one of the leading models of coronal heating, due to E.N.Parker, will be analyzed on a rigorous mathematical level. It is hoped that this will help resolve uncertainties, and clarify the basic physical mechanism involved in coronal heating. Due to the relationship with sun spots and solar flares(violent disruptions in the solar corona which propel plasma and associated magnetic fields toward the earth), the issue of coronal heating is directly tied to practical issues of variations in the earth's climate and electromagnetic interference. ***

这个项目的主要目标是对E.N.帕克关于太阳日冕加热的理论进行仔细的数学分析。根据帕克的说法，太阳日冕的主要热源是由非常薄的强电流区域（电流片）组成的，这些区域是日冕等离子体趋于松弛到平衡的趋势和某些拓扑约束之间的中介。这种限制是由于日冕等离子体近乎完美的导电性，以及磁力线在它们的脚点或末端锚定在光球的致密气体中，脚点被光球的湍流运动所对流。在试图理解帕克模型中的电流片形成现象时，将使用与能量最小化相关的变分方法，该方法依赖于磁场分解，作为表征和规定场线拓扑结构的手段。将仔细研究哪些场线拓扑能够承受与等离子体向最小能量松弛相关的弱索博列夫空间限制。将发展一个一般的二维理论，并将其应用于天体物理学文献中关于当前薄片形成的众所周知的例子的分析。一个完全三维理论的开端将被描述，特别强调在二维等离子体的通量函数表示的局域向量势类似物。此外，涉及螺旋度的拓扑约束，以及测量高阶连杆的更精细的场线拓扑措施将被探索。太阳天体物理学中一个悬而未决的突出问题是，太阳大气（日冕）中存在着高达200万华氏度的极高温度，这一问题世世代代困扰着天体物理学家。尽管已经探索了一些合理的日冕加热模型，但这个问题仍然引起了激烈的争论。在这个项目中，e.n.帕克提出的日冕加热的主要模型之一将在严格的数学水平上进行分析。希望这将有助于解决不确定性，并澄清涉及日冕加热的基本物理机制。由于与太阳黑子和太阳耀斑（太阳日冕的剧烈破坏，推动等离子体和相关磁场向地球移动）的关系，日冕加热问题直接与地球气候变化和电磁干扰的实际问题联系在一起。＊＊＊