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. ***

9622923 Stredulinsky这个项目的主要目标是对E.N.引起的理论进行仔细的数学分析。帕克在太阳能冠状加热上。根据帕克的说法，太阳电晕的主要热源由非常薄的电流（电流片）组成，这些区域是冠状血浆趋势放松至平衡的趋势与某些拓扑约束之间的介导。 这种约束是由于冠状血浆的几乎完美的电导率而产生的，并且磁场线在其脚尖或末端的锚定在光球的致密气体中，脚尖是通过光球的湍流运动所吸引的。在尝试了解帕克模型中当前纸的现象时，将使用与能量最小化相关的变异方法，这些方法依赖于磁场的分解，作为表征和规定场线拓扑的一种手段。仔细研究将对哪种场线拓扑承受与血浆对最小能量的松弛相关的弱Sobolev空间限制。一般的二维理论将被开发，并应用于天体物理学文献中当前纸构成的众所周知的示例。完全三维理论的开始，将特别强调在两个维度中等离子体的通量函数表示的局部矢量电位类似物。还将探索涉及螺旋性的拓扑约束，以及测量更高阶段链接的现场线拓扑测量的衡量标准。 %% %%太阳天体物理学中最关注的开放问题是在太阳大气中（Corona）的高温存在，达到了200万华氏度的秩序，这几代人都有令人困惑的天体物理学家。尽管已经探讨了许多合理的冠状供暖模型，但该问题仍引起激烈的辩论。在该项目中，由于E.N. Parker，将在严格的数学层面上分析冠状加热的主要模型之一。希望这将有助于解决不确定性，并阐明冠状加热所涉及的基本物理机制。 由于与太阳斑和太阳耀斑的关系（太阳电晕中的剧烈破坏将等离子体和相关的磁场向地球推向地球），因此冠状加热问题直接与地球气候和电磁干扰中变化的实际问题直接相关。 ***