Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (p. 208-217).

Thesis (Ph. D.)--University of Chicago, Department of Physics, December 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 222-223).

Thesis (Ph.D.) - University of St Andrews, May 2010.

This thesis investigates the topology of the magnetic field in the solar corona. It is important have an understanding of how the highly complex coronal magnetic field behaves in order to study many fundamental coronal phenomena, such as coronal heating events, solar flares and polar plumes. The magnetic fields due to three or four discrete sources are investigated and the corresponding topological states are found. The locations of these states in parameter space is calculated and the bifurcations between states are analysed. A complete analysis has been undertaken for the three-source case and a selective one for the four-source case in order to identify new non-generic behaviour. The thesis goes on to study the topological behaviour of a coronal bright point. Different phases during the lifetime of the bright point are identified and the responsible topological behaviour due to the movement of the magnetic fragments in the photosphere is discussed.

Low-mass star-forming regions have a lifetime which is greater than their dynamical time and must therefore be, in an average sense, in mechanical equilibrium. The work presented here proposes that an equilibrium exists between the self-gravity, gas pressure, and the magnetic field and the waves it supports. Specifically the equilibrium in the direction perpendicular to the ordered magnetic field is given by the Lorentz force, while that parallel to the field is given by an Alfvén wave pressure force. The work detailed in this thesis models a low-mass star-forming region as a one-dimensional gas slab with a magnetic field lying perpendicular to the layer. Analytical, self-consistent models are formulated to study the equilibrium parallel to the background magnetic field. It is found that both short-wavelength (modelled using the WKB approximation) and large-amplitude, long-wavelength Alfvén waves can provide the necessary support parallel to the magnetic field, generating model cloud thicknesses that are consistent with the observations. The effect of damping by the linear process of ion-neutral friction is considered. It is found that the damping of the waves is not a necessary condition for the support of the cloud although it is an advantage. The possible sources of these waves are discussed. The Alfvén waves are also found to make an important contribution to the heating of a low-mass star-forming region. By modelling the dominant heating and cooling mechanisms in a molecular cloud, it is discovered that a cloud supported against its self-gravity by short-wavelength Alfvén waves will be hotter at its outer edge than in the central regions. These models successfully describe a low-mass star-forming region in equilibrium between its self-gravity, the gas pressure and an Alfvén wave pressure force. The question of the stability of such an equilibrium is considered, specifically that of an isothermal gas slab supported by short-wavelength Alfvén waves. The initial results suggest that the presence of a magnetic field and its associated Alfvén waves have a stabilising effect on the layer, and encourage further consideration of the role of Alfvén waves in low-mass star-forming regions.

The possibility of beat wave current drive in tokamaks is considered in this thesis in steady state 2D geometry. The problem is considered by including in the analysis the 2D toroidal inhomogeneity effect and the effect of finite spatial width of the pump microwave pulses on the beat wave excitation. Both a Langmuir beat wave as well as an obliquely propagating upper-hybrid cyclotron beat wave are considered in this study. The three wave coupled system of equations in a magnetized plasma has been derived and solved numerically for this purpose. It has been found that Langmuir type beat wave excited by two almost antiparallel pump microwaves is more efficient for action transfer than a cyclotron beat wave. It has also been found that for the same input parameters, right hand polarized pumps are more efficient than left hand polarized pump microwaves for depositing power in the beat wave. The second part of the thesis considers the relativistic excitation mechanism of a large amplitude plasma wake field by a single ultra-short laser pulse. This type of large amplitude wake field has been proposed for particle acceleration to very high energies for future generation of accelerators. The problem has been modeled self consistently in ID geometry and the relevant coupled system of equations have been solved numerically. It has been found that the shape of the laser pulse profile and the ratio of the ambient plasma frequency to the incident laser frequency play an important role for the excitation of the wake-field and the stability of the laser pulse profile.

In this thesis, the behaviour of Kelvin-Helmholtz unstable modes on the magnetospheric flanks and in the magnetotail are investigated. A model of a straight bounded magnetosphere connected to a semi-infinite field-free magnetosheath which is flowing with a uniform speed is used. First the magnetosphere is taken to be uniform with the magnetic field perpendicular to the flow in the magnetosheath and it is shown that the increase in Pc5 wave power observed for high solar wind flow speeds correlates well with the onset of instability of the fast body modes. A condition for the exact onset of instability of these modes is derived and the behaviour of fast surface and slow body and surface modes is also investigated. Using a non-uniform magnetosphere, it is shown that these unstable body modes may couple to field line resonances. The fastest growing modes are found to have a common azimuthal phase speed which depends only on the local conditions at the magnetopause and may be predicted using the theory of over-reflection. A finite width boundary layer is then added to the uniform magnetosphere model to investigate the space-time evolution of wave-packets on the magnetopause. Fast surface mode wave-packets are found to grow rapidly as they convect around the flanks so that non-linear effects will be important. Fast cavity mode wave-packets will remain relatively small on the flanks, explaining the robustness of the body of the magnetosphere here. Slow modes are found to grow very little in this region. Finally, a uniform magnetosphere with the magnetic field parallel to the flow in the magnetosheath is considered. Here, the fast modes are unlikely to be Kelvin-Helmholtz unstable for realistic flow speeds, and the magnetopause boundary may be reasonably assumed to be perfectly reflecting. The low value of the plasma pressure is this region suggests that slow modes will be unimportant.

A study has been made of wave propagation in two regions of the solar atmosphere in which magnetic forces are significant. Sunspot observations indicate a rich variety of characteristic modes of oscillation roughly divided into three categories: three minute umbral oscillations, five minute umbral oscillations and penumbral waves. Outside of intense magnetic flux concentrations the oscillation spectrum is dominated by the five minute period. These waves are trapped in a cavity whose upper boundary may be affected by the magnetism of the chromosphere. A sunspot has been modelled by a uniform cylindrical flux tube. The allowable modes of oscillation are found to vary as the atmospheric parameters change with depth. Umbral three minute oscillations are interpreted as slow body modes. The umbral five minute oscillations arise through a complicated interaction with acoustic waves outside the sunspot. This drives fast body modes as well as waves simply passing through the flux tube. The former may propagate upwards and become fast surface waves. Fast and slow surface waves may explain some of the oscillations of the penumbra. The magnetic structure of the chromosphere has been modelled as an isothermal atmosphere permeated by a uniform and horizontal magnetic field. A dispersion relation for the trapped waves below such an atmosphere has been derived and both asymptotic and numerical solutions found. The effect of a uniform magnetic field is to increase the frequency of the trapped modes. A physical explanation for these changes in frequency has been put forward. Observational evidence may indicate that such effects are indeed seen. This model has been further generalised to take some account of the variation in canopy height which has been observed.

The model of Heyvaerts and Priest (1992) for steady-state heating of the turbulent medium within a sheared solar coronal arcade structure is here developed. The energy input into the corona is calculated at the large scales of the model. At the smaller scales the effects of coronal turbulence are modelled in the form of an enhanced turbulent viscosity and magnetic diffusivity, which are related to the injected power density in the steady state. Matching the expressions for the injected and dissipated power enables the calculation of a heating power consistent with both boundary motions and turbulent effects with a minimum of arbitrary parameters - the price to be paid is that the inertial range spectrum must be prescribed and imposed at all scales. While it is capable of reproducing the observed levels of coronal heating (300 Wm−2 3x105 erg cm−2 s−i for the quiet Sun, 800 Wm−2 (8 x 105 erg cm−2 s−i) for a coronal hole and 104 Wm −2 (107 erg cm−2 s−i) for an active region (Withbroe and Noyes, 1977)), there are some mathematical and physical difficulties present. These are eliminated as far as is possible and it is found that the final results for heating levels differ little from the original model although there is a much greater consistency between the imposed and predicted energy power spectra. The modified approach is applied to the problems of photospheric motions twisting a coronal flux tube and of rapid motions injecting Alfven waves into an arcade. In the former case comparable levels of heating are obtained. For a driven and damped standing wave, however, desired levels of heating are only obtained when a global resonance occurs. Attempts are also made to find similar steady-state equilibria possessing flow for fusion experiments in order to apply the above procedure to investigate turbulence in laboratory plasmas. This has been hampered by the difficulty in finding simple appropriate equilibria with many scales present.