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Abstract
In this thesis a consistent theoretical framework is built for understanding magnetic reconnection, a fundamental physical process important in many space and laboratory plasmas.
As a basis for the theory, the so-called double spheromak configuration is considered, which provides a typical example of a generic reconnecting system. The model is restricted to two-dimensional (2D) resistive magnetohydrodynamics (MHD).
In the limit of large Lundquist numbers, the whole problem is broken into the global and the local problems. The global ideal MHD problem describes the system on the large (global) scale, while treating the reconnection and separatrix layers as singular current sheets. The local problem requires resistive MHD to resolve the inner local-scale structure of these layers. The reconnection rate can be determined only after the local problem is solved.
The global solution is represented by a sequence of magnetostatic equilibria, which are independent of the local physics and which provide the boundary conditions for the local reconnection layer problem. In particular, a cusp-like configuration is found near the end of the reconnection layer.
The local problem with these boundary conditions is considered assuming incompressibility and uniform resistivity. A system of rescaled MHD equations is derived and used to develop a computer code that follows the time evolution to approach a steady state. Independent of the initial conditions, the system always evolves towards a stationary Sweet-Parker reconnection layer, indicating that Petschek's fast reconnection mechanism does not work in this model. Particular steady state magnetic field and velocity profiles are obtained. It is conjectured that anomalous resistivity must be included to explain fast reconnection in solar flares.
Finally, a viscous boundary layer near the X point is investigated in the limit of small viscosity. When the viscosity goes to zero, the system exhibits nonanalytic behavior. In particular it is found that, contrary to the common belief, the separatrices cross at a nonzero angle at the X point instead of osculating.
The strategy and methods developed in this thesis can be used for a broader class of magnetic reconnection problems.
