| Magnetic reconnection is a fundamental and important phenomenon in space and laboratory plasmas. Double resonant surfaces (or current sheets) can exist in many plasma systems, such as the solar wind, corona, and advanced tokamaks with nonmonotonic safety factor. Due to the mutual interaction between the two resonant surfaces, the double tearing mode (DTM) becomes a much stronger instability than the single tearing mode.In this thesis, the nonlinear evolution of the DTM is investigated by using MHD simulations. The contents are arranged as follows:In chapter 1, the review on magnetic reconnection, tearing mode and double tearing mode are introduced.In chapter 2, the nonlinear dynamic evolution of DTM is systematically investigated for different guiding fields and separation distances of the two resonant surfaces. It is found that the weaker driving plasma flow for the stronger guiding field decreases the coupling of the two resonant surfaces, or slows down the development of the DTMs. The maximum reconnection rate during the nonlinear growth phase decreases with increase of the guiding magnetic field. The distance between two current sheets is an important parameter. For the cases with a small distance, a nonlinear explosive phase of magnetic reconnection is not observed. The growth rate of kinetic energy decreases with increase of the guiding field for different separations of the current sheets.In chapter 3, the secondary magnetic islands are observed in the final stage of the explosive phase in the cases with low resistivities. The current sheets will be thinner as the resistivity becomes smaller. A bigger aspect ratio and the strong drive force will lead to the reconnection region becoming more unstable and the formation of secondary islands. The formation of secondary islands will alter the dynamic evolution of magnetic reconnection in the late phase. A strong core magnetic field in a flux tube was observed. The simulation results indicate that the aspect ratio has to exceed a critical value in order to form of the secondary island. The critical value varies aroundαcr= 20. A strong guiding magnetic field can stop the onset of the secondary tearing mode instability, since the aspect ratio of the reconnection diffusion region decreases with increase of the guiding field.The dynamic evolution of a DTM is also dependent on the separation distance of the current sheets. For a small separation, there is no explosive phase because the free magnetic energy contained in the initial current sheet is too small. With increase of the current sheet separation, the early nonlinear phase takes longer because the magnetic islands in the two resonant surfaces have to grow sufficiently large to interact with each other. When the separation distance of the two current sheets increases, larger magnetic islands or a longer duration of the early nonlinear growth phase are required for the system to evolve into the DTM stage from the single tearing mode stage. The larger magnetic island at the upper (lower) resonance surface leads to more reconnection magnetic flux pile-up on the lower (upper) resonance surface. The dynamic evolution in the late nonlinear growth phase becomes of a more explosive nature, which leads no formation of the secondary island for larger current sheet separation. In chapter 4, the nonlinear evolution of the DTM in Hall magnetohy-drodynamics (MHD) is carefully studied. It is found that Hall effects on DTM can be ignorable in the early nonlinear growth and transition phases because the thickness of the current sheet△is still larger than the ion inertial length di. With further development of the DTM, the thickness of the current sheet decreases and falls in the range of de <<△ |
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