The Research Of Force-free Field Models And Computational Methods For The Solar Magnetic Field

We have done the investigation about solar magnetic field in the following respects:1. We have introduced in detail main methods of solving solar linear force-free field models,discussed their advantages and disadvantages and understood fully the relations of themethods. We also made comments on some works about linear force-free field.2. A boundary integral formulation describing constant-αforce-free field with finite energycontent in the semi-infinite space above the sun was proposed(Yan,1995), this formulationcontains boundary field and its normal gradient under integral sign. We present a new directboundary integral formulation based on the formulation of Yan in term of the boundary fieldonly. Compared with Yan's formulation, to calculate field using this new formulation hasadvantages of speediness and nicety. Two examples are given for indicating non-necessity ofthe asymptotic condition of the model(Yan,1995).3. A boundary integral equation representation for the non-constant-αforce-free field inspace outside the Sun was investigated by Yan & Sakurai, who introduced a local parameterλinstead of the force-free factor αwhich should satisfy a proposed condition. Then thefield at any point in space can be represented by the boundary integral equation. In chapter 5,it is justified that, for a closed-form non-constant force-free field problem with finite energycontent in free space around the Sun, as in Low & Lou, such real λsolutions do exist.4. The property of boundary integral equation(Yan & Sakurai 2000) has been discussed(Li etal.2004),where a kind of important singularity surface integration can be found. In order tocalculate this kind of integration,we build the same distribution principle to Riemann-integraland give some important applications of it.5. A direct boundary integral formulation for force-free magnetic field with finite energycontent in the semi space above the Sun is presented. The non-linear force-free field model istranslated into a nonlinear programming problem. We have proposed an optimal method tonumerically solve the nonlinear programming problem so that non-linear force-free fieldsolution can be obtained. A test case study has been carried out to demonstrate theconvergence, accuracy and efficiency of the numerical procedures. The agreement betweennumerical and exact results validate the correctness and merits of the new formulation andcomputational procedure proposed.6. The boundary integral equation (Yan & Sakurai,2000) contains boundary magnetic fieldand its normal gradient under right integral sign. We present a new direct boundary integralequation in term of the boundary magnetic field only. While calculating magnetic field valuesat space points with the equation of Yan & Sakurai , we must first calculate normal gradient ofmagnetic field at the boundary by using boundary element method, and it must takes muchtime to calculate magnetic normal gradient;but while calculating magnetic field with newdirect equation, we need not calculate magnetic normal gradient. Compared with Yan'sequation, to calculate field using this new equation has advantage of speediness.