Plasmas occur in many technical, laboratory and space environments, and often behave in a highly ideal manner. This means that advection of the plasma can store large amounts of energy in the magnetic field. This energy is released when a sudden change in the magnetic topology of the field occurs-facilitated by the process of `magnetic reconnection'. A great deal of research has been focussed on understanding the reconnection process and we now appreciate that the 3D process is critically di erent from early 2D models. The magnetic field in many astrophysical plasmas, for example in the solar corona, is known to have a highly complex { and clearly three-dimensional { structure. Turbulent plasma motions in high-ß regions where field lines are anchored, such as the solar interior, can store large amounts of energy in the magnetic field. This energy can only be released when magnetic reconnection occurs. Reconnection may only occur in locations where huge gradients of the magnetic field develop, and one candidate for such locations are magnetic null points, known to be abundant for example in the solar atmosphere. Reconnection leads to changes in the topology of the magnetic field, and energy being released as heat, kinetic energy and acceleration of particles. Thus reconnection is responsible for many dynamic processes, for instance solar flares and jets in the solar atmosphere.The aim of this thesis is to investigate the properties of magnetic reconnection at a 3D null point. One key focus will be to understand the dependence of the process on the symmetry of the magnetic field around the null. In particular we examine the rate of reconnection of magnetic flux at the null point, as well as how the current sheet forms and its properties. According to our present understanding, there are three main modes of magnetic reconnection that may occur at 3D nulls, spine-fan reconnection, torsional spine reconnection and torsional fan reconnection. We first consider the spine-fan reconnection mode. It is found that the basic structure of the mode of magnetic reconnection considered is una ected by varying the magnetic field symmetry, that is, the plasma flow is found to cross both the spine and fan of the null. However the peak intensity and dimensions of the current sheet are dependent on the symmetry/asymmetry of the field lines. As a result, the reconnection rate is also found to be strongly dependent on the field asymmetry. In addition, the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed which for the first time include a current layer that is fully spatially localised around the spine or fan of the null. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process { where previous studies always considered a non-generic radially symmetric null. Analytical solutions are derived for the steady kinematic equations at a three dimensional null point. In these models the electric current lies parallel to either the fan or spine. In order to conform the results of kinematic models, numerical simulations are performed in which the full set of resistive MHD equations are solved. It is found that the geometry of the current layers within which torsional spine and torsional fan reconnection occur is strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with ellipticalcross-section when the fan eigenvalues are dfferent. The eccentricity of the ellipse increases as the degree of asymmetry increases, with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased.
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