Reconstruction of reconnection: Theoretical considerations and application to cluster data

摘要

The thesis was accepted at the University of Graz, Austria, in May 2006. The thesis was accepted by Professor H.K. Biernat. This thesis gives a detailed analysis of the reconstruction of reconnection features from satellite observations of flux transfer events (FTEs) in the Earth's magnetosphere. For the mathematical treatment of FTEs, the ideal MHD equations are utilized. After linearization and the introduction of a displacement vector, a Fourier-Laplace transformation is applied in order to get a solution for the displacement vector in Fourier-Laplace space. To establish a solution in time-coordinate space, the so-called Cagniard-deHoop method is used, allowing an analytical solution of the inverse Fourier transformation. The inverse Laplace transformation can be rewritten in a way that the solution for the displacement vector in time-coordinate space is given in form of a convolution integral. All necessary MHD quantities can be found easily from the definition of the displacement vector. They have the form of a convolution integral of the integration kernel and the reconnection electric field. The calculation of the MHD quantities for a given reconnection electric field is called the direct problem.