| 摘要: | Grad-Shafranov (GS)重建方法是一資料分析的應用模式，用來重建電漿與磁場的二維結構。此重建方法是藉由單一人造衛星穿越太空電漿中之薄電流片所收集的電漿與磁場資料，當作一個空間初始值的問題去解二維磁流體力學(magnetohydrodynamics; MHD)之GS equation。在magnetohydrostatic (MS)之近似下， Hau and Sonnerup [1999] 已發展出完整之一套GS重建方法，用於建立地球磁層頂電流片的二維結構。此MS GS重建方法並被應用到不同的太空環境，如太陽風的磁繩與磁雲。之前，應用MS GS重建方法於AMPTE/IRM和Cluster的衛星資料發現，切線不連續面型的磁層頂電流片包含著一連串的磁島，且以Alfvén速度往地球磁尾方向移動。在本論文中，我們利用此重建方法於一罕見的AMPTE/IRM磁層頂多次穿越事件，並第一次發現，其中三次磁層頂穿越有相似的二維磁島由單一人造衛星所觀測到。從磁層頂法線方向，deHoffmann-Teller (HT)速度和二維結構不變軸的分析顯示，此三次磁層頂穿越所觀測到的磁島是屬於同一個磁層頂大結構中的一部份。在論文中，我們並使用最近Sonnerup et al. [2006]所提出的field-aligned-flow GS理論，發展一新的field-aligned-flow GS重建方法，可應用於建立旋轉不連續面型的二維磁層頂電流片結構。我們利用一解析解來驗證此新的重建方法之準確性，然後應用到由AMPTE/IRM和Cluster分別在September 15, 1984和July 5, 2001所觀測到的磁層頂穿越事件上。在AMPTE/IRM事件中，重建的磁場結構顯示磁層頂的厚度比MS GS重建的來得薄，這是由於有field-aligned flow的效應 [Hau, 1996]。Cluster事件的重建結果顯示，估算的和量測的field-line invariants之間有些微誤差，而此誤差可能是由於發展中的磁重連所造成的時變效應。另一個重要結果是，在HT參考座標上，磁層頂附近看到的field-aligned flow是超音速且流體在磁管裡遵循流體力學理論所預測之行為。此外，我們也估算了磁重連的電場為0.47 mV/m。 Grad-Shafranov (GS) reconstruction technique is a data analysis tool for reconstruction of two-dimensional (2D) coherent field structures from data taken by single satellite traversing a current layer by solving the GS equation as a spatial initial value problem. For magnetohydrostatic approximation, the GS reconstruction technique has been developed by Hau and Sonnerup [1999] and successfully applied to the Earth’s magnetopause, to the magnetic cloud in the solar wind, and to the flux rope by various authors. In previous studies based on the analysis of AMPTE/IRM and Cluster data, the magnetopause current layers of tangential-discontinuity type are found to be imbedded with a string of magnetic islands moving down the magnetotail. In this thesis, we first present a rare event of triple magnetopause crossings encountered by AMPTE/IRM using the similar magnetohydrostatic GS construction method that shows similar features of magnetic islands embedded within the overall tangential discontinuity-like current layer. Detailed analyses of the magnetopause normal orientation, the deHoffmann-Teller (HT) velocity, and the invariant axis indicate that these are likely to be part of the same magnetopause structures moving inward and outward seen by the same spacecraft. The thesis also presents the first new results from a recently developed version of GS reconstruction in the presence of field-aligned flow based on the formulation of Sonnerup et al. [2006] that can be applied to rotational discontinuity-like magnetopause current layer structures. A new GS solver that incorporates the field-aligned flow is benchmarked with an exact analytical solution to demonstrate the accuracy of the new GS reconstruction scheme. It is then applied to the magnetopause crossings by the AMPTE/IRM on September 15, 1984, and by the Cluster 1 (C1) and the Cluster 3 (C3) on July 5, 2001. In the AMPTE/IRM event, the reconstructed magnetic field map shows that the magnetopause current layer becomes thinner than that recovered from the magnetohydrostatic reconstruction, an effect due to the presence of field-aligned flow [Hau, 1996]. For the Cluster event, the agreement between map-predicted and measured values of the field-line invariants along the trajectory of the spacecraft not used in generating the map is less than perfect but most of the differences are accounted by the time evolutionary effect due to developing reconnection at a site close to the spacecraft. An important new feature is that the field-aligned flow, as seen in the HT frame, is supersonic in the magnetopause region and is qualitatively and quantitatively as expected for supersonic flow in a duct (a flux tube). We provide an estimate of 0.47 mV/m for the reconnection electric field. |
