Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 197-198).

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 188-205). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 121-129). Also available in electronic version.

Thesis (M.S.)--Naval Postgraduate School, 1978. / AD A059693. Bibliography: leaves 64-65.

Thesis (Ph. D.)--University of Florida, 1987. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 164-167).

This thesis presents several analytical models of magnetic annihilation and reconnection and studies their properties. The models investigated are 1. Steady-state magnetic annihilation. The assumption of straight field lines reduces the resistive, viscous MHD equations to two ordinary differential equations, one for the flow and one for the magnetic field. These equations can be solved exactly (for the case of a simple stagnation-point flow) and asymptotically (for a more general stagnation-point flow). In both cases the reconnection rates can be fast due to advection effects which create large magnetic gradients. 2. Time-dependent magnetic annihilation. The assumption of straight field lines whose strength can vary with time reduces the MHD equations to two partial differential equations, one for the flow and one for the magnetic field. The time-modulated simple stagnation-point flow is shown to be an exact solution and the equation for the magnetic field is then solved on infinite and finite intervals. For the infinite interval the reconnection rates are shown to be dependent on the nature of the advected initial field. Also examined are self-similar solutions and the effect of variation of diffusivity with time. 3. Annihilation in a compressible, inviscid plasma. Here, the assumption of straight field lines and an inviscid, compressible flow reduce the MHD equations to a pair of non-linear coupled partial differential equations. Further assuming that the density only varies in one direction and the flow is of a stagnation-point type allow these equations to be solved approximately analytically and exactly numerically. It is shown that the magnetic field and reconnection rates are the same in both the compressible and incompressible cases and that the density of the plasma is greatest within the current sheet. 4. Steady-state magnetic reconnection. For an incompressible flow the MHD equations can be reduced to two coupled non-linear partial differential equations. These two equations are studied by seeking asymptotic solutions around the annihilation solution and then looking for series solutions to the first-order equations. It is found that the magnetic field always has a magnetic cusp and never possesses an x-type neutral point. 5. Reconnection in a viscous plasma. Assuming that the viscous forces dominate, the induction equation and equation of motion decouple and become linear. The magnetic field is obtained for the case of a simple stagnation-point flow. It is shown that if the inflow magnetic field is taken to be straight then the magnetic field within the region tends towards the annihilation solution as the magnetic Reynolds number increases. 6. Magnetic flipping. A previous ideal model of magnetic flipping is refined so that it becomes an exact solution of the MHD equations. In the refined model the streamlines are straight rather than curved. Assuming straight streamlines, the MHD equations reduce to two linear ordinary differential equations, one for the flow and one for the magnetic field. These are then solved exactly analytically to find a flow containing a viscous boundary layer and a magnetic field that contains an x-type neutral point. The angle between the separatrices of the field is determined by the Reynolds and magnetic Reynolds numbers. It is shown that most of the ohmic heating occurs within the viscous boundary layer.

This thesis will deal with certain problems of parametric instabilities in the inhomogeneous plasma. A large amplitude, 'pump' wave can deposit some of its energy into the plasma through resonance with two lower frequency waves (which may be damped). This type of process is a parametric decay of the pump wave and has applications in many fields. We consider, predominantly, that of laser fusion, in which the pump wave is electromagnetic and incident on the plasma. The objective is to deposit as much energy as possible within the plasma. Instabilities reducing this energy input are therefore of importance and it is, mostly, to these that this thesis will turn. They are mostly scattering processes in which one of the decay modes is electromagnetic. We examine the stimulated Brillouin backscattering process (the other decay mode being an ion accoustic wave) from a reference frame in which the plasma is streaming outwards. It is found that, if this velocity is near the sound velocity, the ion acoustic wave has a frequency Doppler-shifted to zero, the electromagnetic waves then having equal frequencies. In such a situation, any reflection of the pump wave at the critical surface will enhance the initial level of the backscattered wave. We find that, allowing for this, there is considerable enhancement of backscatter from the plasma, with consequent energy loss to the pump. Since the effect is noticeably unaffected by 'off- resonance' situations, it is felt that this process could mount a barrier to possible applications. We next consider the stimulated Compton scattering process, where the pump is scattered off the 'bare' or thermal electrons in the plasma. It is found that this rather weak instability occurs predominantly only when electron plasma waves are heavily dampled. Substantial reflection only occurs for high pump powers. Whilst there is little loss to the pump energy, there is substantial perturbation to the background distribution function. However, at the high powers involved filamentation and modulation of the pump can occur with a resulting enhancement of the scattering. Finally, we consider the effect on the decay instability (photon → plasmon + phonon) of the presence of substantial filamentation of the critical surface. It is found that the growth rate is substantially reduced.

The work of this thesis is concerned with the investigation of the propagation of waves in a magnetized plasma containing various parameter gradients, and with the stability of ion acoustic waves in a weakly collisional plasma with a strong temperature gradient. The thesis is divided into three sections. In the first section the intention is to derive in a compact and unambiguous tensor form the dispersion relation describing the propagation of waves in a magnetized plasma containing three-dimensional density and temperature gradients, an E̲⏜ B̲ drift, and differing temperatures parallel and perpendicular to the magnetic field. This is achieved by introducing and extending the polarized co-ordinate system first proposed by Buneman in 1961, and then carrying through the standard procedure of integration along unperturbed trajectories. The "local" approximation of Krall and Rosenbluth is used in order that an analytic result may be derived. The dispersion relation obtained includes certain moment tensors whose elements may be evaluated independently of the gradients involved in the problem. These elements may then be listed and the list referred to in order to obtain the elements required for a specific problem. The second section is concerned with the use of the theory and results of J.P. Dougherty to show that in the high-frequency regime the introduction of a small amount of collisions into a plasma is sufficient to disrupt the gyro-resonances which allow the existence of Bernstein waves at multiples of the gyro-frequencies perpendicular and near- perpendicular to the magnetic field. It is shown that a collision frequency v such that (k ρ) ⁻² ≲ v/Ω < (k ρ) ⁻¹ where k ρ >> 1 is sufficient to do this; k is the wave-number, ρ the Larmor radius, and the gyro-frequency. It is also shown that in this case the ion-acoustic dispersion relation is valid even for propagation perpendicular to the magnetic field. In the final section the result of the second section is used to derive a dispersion relation for high-frequency wave propagation in a weakly-collisional plasma containing an electron temperature gradient. The dispersion relation is solved numerically for various electron-ion temperature ratios and electron temperature gradient drift velocities. Earlier predictions, based on analytic calculations for small temperature ratios and drift velocities, are confirmed and some new results presented. In particular, it is shown that a temperature gradient is a more effective destabilizing agent then a simple drift between ions and electrons. Dispersion plots are given, along with analytic and physical explanations of their form; finally neutral stability curves are presented. The thesis concludes with a summary of the results obtained.

The question of topology in the coronal magnetic field is addressed in this thesis. Magnetic reconnection, which plays a major role in many of the fascinating phenomena seen in the solar atmosphere, is likely to occur at the boundaries between different topological regions of the magnetic field. By modelling the coronal field using discrete sources of flux, to represent the concentrations seen at the photospheric surface, we study the varying topological structures present in the field. We generate a criterion for determining the presence of null points above the photospheric surface and establish that any separatrix surfaces present in the field are due to the presence of either null points, or regions where the field tangentially grazes the surface. We follow the evolution of these separatrix surfaces and, in particular, determine the existence of a well-defined separator field line in the absence of coronal null points. Finally, we look locally at the configuration of the magnetic field in the region surrounding a straight current sheet. We derive an analytical expression to describe the topology of both potential and constant-current force-free fields in the neighbourhood of a sheet, and in so doing generalise the previously known expressions.

Quiescent solar prominences are amongst the most interesting and yet least understood of the phenomena observed on the Sun and provide both the theorist and the observer with equally demanding challenges. The theoretical study of prominences is an important branch of solar physics as it contributes significantly to the overall understanding of the Sun and its atmosphere. One only needs to be presented with the illuminating fact that there is more mass contained in these bodies than in the remainder of the entire corona to be convinced of their importance. Although many of the physical mechanisms associated with prominence theory are important in their own right, they are also of much wider relevance for various other astrophysical phenomena. For example, radiative and magnetic instabilities are explored in detail in the context of solar prominences; yet clearly these are important processes that relate to many other branches of astrophysics. Prominences are intimately associated with solar flares which occur when a prominence loses equilibrium. Also, prominence eruptions are very important as they are closely connected with coronal mass ejections. These account for a large fraction of the total mass lost from the Sun and so are extremely important events, particularly when one considers the consequences as this plasma interacts with the Earth's environment. It is the period of global equilibrium of quiescent prominences, though, that is the focus of this thesis. Various models are proposed to help understand both the topology and supporting mechanisms of the external, coronal magnetic field, and also the internal prominence structure and the way in which the two regimes fit together. In Chapter 3 we extend a model for the equilibrium of a prominence sheet in a twisted magnetic flux-tube, given by Ridgway, Priest and Amari (1991), to incorporate a current sheet of finite height. This removes the discontinuity at the edge of the tube and provides a shear-free outer boundary which enables the tube to be matched onto a background potential field. In addition, internal prominence solutions are found by expanding the sheet to a finite width and matching suitable magnetic profiles across this region. Next we consider a global model for the magnetic field structure surrounding a polar-crown prominence. We examine potential configurations generated from typical distributions of photospheric flux, and select solutions for which there is a location of dipped magnetic field where prominence material may collect and form. Once such a configuration is available, it is necessary to construct the ensuing prominence solution. We achieve this in Chapter 4 by considering a simplified form for the photospheric field. We show that the equilibrium contains a weighted, curved prominence sheet supported in the location of dipped magnetic field. The equilibrium requires an enhanced magnetic pressure below the sheet to support the component of weight in the normal direction. The internal equilibrium of curved or inclined prominence material has not been considered previously and so we formulate, in Chapter 6, a simple one-dimensional isothermal solution for a cut across the prominence. This is developed to allow for variations along the sheet and in this way an internal solution for the curved prominence of Chapter 4 is given, which matches onto the external potential polar-crown field. Finally, in Chapter 7, we rewrite this solution in terms of its constituent internal and external components and show how the composite solution switches between the two in a region of overlap, or transition region. From this, the internal plasma properties are deduced and realistic profiles for the pressure, density and temperature are obtained.