Magnetic flux emergence is the subject of how magnetic fields fromthe solar interior can rise and expand into the atmosphere to produceactive regions. It is the link that joins dynamics in the convectionzone with dynamics in the atmosphere. In this thesis, we study manyaspects of magnetic flux emergence through mathematical modellingand computer simulations. Our primary aim is to understand the keyphysical processes that lie behind emergence.The first chapter introduces flux emergence and the theoretical framework,magnetohydrodynamics (MHD), that describes it. In the secondchapter, we discuss the numerical techniques used to solve thehighly non-linear problems that arise from flux emergence. The thirdchapter summarizes the current literature. In the fourth chapter, weconsider how changing the geometry and parameter values of the initialmagnetic field can affect the dynamic evolution of the emergingmagnetic field. For an initial toroidal magnetic field, it is found thatits axis can emerge to the corona if the tube’s initial field strength islarge enough. The fifth chapter describes how flux emergence modelscan produce large-scale solar eruptions. A 2.5D model of the breakoutmodel, using only dynamic flux emergence, fails to produce any large scaleeruptions. A 3D model of toroidal emergence with an overlyingmagnetic field does, however, produce multiple large-scale eruptionsand the form of these is related to the breakout model. The sixthchapter is concerned with signatures of flux emergence and how toidentify emerging twisted magnetic structures correctly. Here, a fluxemergence model produces signatures found in observations. The signaturesfrom the model, however, have different underlying physicalmechanisms to the original interpretations of the observations. Thethesis concludes with some final thoughts on current trends in theoreticalmagnetic flux emergence and possible future directions.
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