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Steady and unsteady visco-resistive reconnection in the presence of the Hall effect McMahon, Liam Litvinenko, Yuri E. Oughton, Sean In this thesis we investigate the effects of viscosity and the Hall effect on magnetic reconnection. Magnetic reconnection is a process of releasing large amounts of magnetic energy as observed in solar flares. In the first two chapters, we describe the basic mathematics and early models of reconnection. In Chapter 3, we search for a visco-resistive length scale in reconnection solutions. This is demonstrated in reconnective annihilation and a quasi-one-dimensional series expansion. We find that the visco-resistive length scale appears organically unless a specific geometry is chosen. Upon adding small scale perturbations, the visco-resistive length scale always appears. In Chapter 4, we build on Litvinenko’s (2007) self-similar solution that showed singularities appear with a Hall MHD X-point geometry for a certain set of initial conditions. These singularities signal current sheet formation. We consider a general set of initial conditions and find that the singularities will form in this self-similar solution unless the axial field is many orders of magnitude larger than the planar field. In Chapter 5, we review the Craig and McClymont (1991) linear, oscillatory model of reconnection. In Chapter 6, we attempt to quantify a general model that includes viscosity, pressure and axial effects, the Hall effect and electron inertia. We perform a dimensional analysis to find order-of magnitude estimates for how the aforementioned effects perturb the Craig and McClymont (1991) solution. We verify these estimates with numerical simulations. In Chapter 7, we give an overview of the thesis and make suggestions for future work. The University of Waikato 2021 Thesis en https://hdl.handle.net/10289/14067 https://researchcommons.waikato.ac.nz/bitstreams/f7ccbd23-80ca-4733-80c2-99544d0c39b1/download d2b8cf58c025c805954b68fa8b8d4955 https://researchcommons.waikato.ac.nz/bitstreams/9cdb9c0b-2104-4f1d-873c-d075dedf7644/download e14202ab27e47ddb00d33097327ba050 https://researchcommons.waikato.ac.nz/bitstreams/7607cec6-8d92-4b3a-80a7-9f53cca8a23e/download 0684389afc24eaf2b2ce534cf0fe37b3 All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated. Magnetic Reconnection Mathematics Plasma Physics Applied Mathematics Magnetohydrodynamics MHD Fluid Mechanics Differential Equations