Magnetohydrodynamic Wave Behaviour in the Vicinity of Proper and Improper Magnetic Null Points

Context: Both MHD waves and magnetic null points are prevalent in many astrophysical plasmas, including the solar corona, and as such their interaction is inevitable. Current theory implicates coronal null points as locations of localised heating events due to MHD waves propagating in their vicinity. However, previous work on the topic of wave-null interactions has almost exclusively been based on treatments of two-dimensional (2D) magnetic null point models. The surrounding magnetic field configuration of three-dimensional (3D) magnetic null points is, topologically, significantly different. Since MHD wave behaviour is highly dependent on the magnetic structure of the medium in which it propagates, it is not clear whether these existing 2D results apply to realistic magnetic null points, which are necessarily 3D. Aims: To investigate the nature of MHD wave propagation about 3D null points, with a specific interest in their transient behaviour and interaction with other modes of oscillation. This thesis evaluates the extent to which 2D theory carries over to the 3D case, and determines whether realistic 3D null points are also likely locations for localised heating events. Methods: This thesis primarily considers simulations of wave propagation in the vicinity of 3D null points by numerically solving the MHD equations using the LARE3D code. The isolation of different modes of oscillation in the vicinity of 3D null points is facilitated by the construction of a special fieldline and flux-based coordinate system. The coordinate system permits the introduction of pure-mode waves in driving conditions, and the tracking of subsequent excitation of different modes of oscillation. Results: It is found at � = 0 potential 3D null points that the linear, transient behaviour of the different modes are as follows: (i) Fast waves propagate according to the Alfv´en-speed profile along and across the fieldlines, refracting and accumulating at the null point where ohmic heating occurs; (ii) Alfv´en waves, which are necessarily torsional, are confined to fieldlines which diverge on the approach to the null, thus pulses exhibit a ‘spreading’ effect (dilation) and typically accumulate near the fan plane. Different degrees of fieldline eccentricity at the null simply alter the rate of refraction/dilation, i.e. the qualitative behaviour of waves is the same for proper and improper null points. These modes are found to be linearly decoupled in all cases considered, although there is some evidence for nonlinear Alfv´en to fast mode conversion due to the action of the ponderomotive force. In a treatment of the ponderomotive force, it is found that in general inhomogeneous MHD Alfv´en waves sustain longitudinal and transverse compressive daughter disturbances, and that excitation of magnetoacoustic modes can occur as they undergo dispersion or phase mixing. Conclusions: The main results from existing 2D work do indeed carry over to 3D magnetic null points and so this thesis concludes that 3D nulls are likely locations for preferential heating in the corona by interaction with MHD waves