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Abstract
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 different
from early 2D models.
The magnetic field in many astrophysical types of plasma, for example in the solar
corona, is known to have a highly complex – and clearly three-dimensional –structure.
Turbulent plasma motions in high-β regions where field lines are anchored, are as the
solar interior, can store large amounts of energy in the magnetic field. This energy can
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 location 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 3D
null point. One key focus will be to understand the dependence of the process of 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 we first consider the spine-fan reconnection mode. It is found that
the basic structure of the mode of magnetic reconnection considered is unaffected to
cross both the spine and fan of the null. However the peak intensity and dimensions of
the current sheet are dependent of 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 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 spastically localised around the spine or fan of the
null. The principles 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-genetic radically symmetric null. Analytical solutions
are derived for the steady kinematic equations at a three dimensional null points. In
these models the electric current lies parallel to either the fan or spine. In order to
confirm 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 elliptical crosssection when the fan eigenvalues are different. The eccentricity of the ellipse increase
as a 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 is along the weak field direction, with the current being peaked in these
weak field regions. The peak current and peak connection 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.