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

小行星9622923 这个项目的主要目标是对E.N.帕克关于太阳日冕加热。根据帕克的说法，日冕中的主要热源是由非常薄的强电流区域（电流片）组成，这些区域是日冕等离子体松弛到平衡状态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，以及磁力线在光球稠密气体中的脚点或端部的锚定，脚点被光球的湍流运动对流。在试图理解的现象，电流片形成的帕克的模型的变分方法与能量最小化将被使用依赖于磁场的分解作为一种手段的特征和处方场线拓扑结构。一个仔细的研究将作出哪些场线拓扑结构承受弱Sobolev空间限制与等离子体向最小能量的松弛。一个一般的二维理论将被开发和应用到分析的天体物理学文献中的电流片形成的众所周知的例子。一个完整的三维理论的开始将被描述，特别强调在两个维度的等离子体的通量函数表示的局部矢量位类似物。还将探讨涉及螺旋度的拓扑约束，以及测量高阶联动的场线拓扑的更精细的措施。 太阳天体物理学中一个悬而未决的问题是太阳大气层（日冕）中存在着极高的温度，大约200万华氏度，这使几代天体物理学家感到困惑。虽然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，由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，并澄清日冕加热所涉及的基本物理机制。 由于与太阳黑子和太阳耀斑（太阳日冕的剧烈破坏，将等离子体和相关的磁场推向地球）的关系，日冕加热的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。 ***

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. ***