The aim of this thesis is to study coherent plasma effects and collective plasma processes in pulsar environments. Pulsars are one of the most enigmatic objects in the universe. Formed in supernova explosions, pulsars are rapidly rotating neutron stars identified by their periodically pulsed electromagnetic emission. The source of the radiation is believed to be associated with the electron-positron (pair) plasma populating the pulsar magnetosphere. The theory of pulsar radiation is still in its infancy and there is lack of understanding about the energetic processes involved. The initial aim of this thesis is to study a possible emission mechanism in which electrostatic oscillations are coupled to propagating electromagnetic waves by a magnetic field inhomogeneity, thus creating a source of radiation in the pulsar magnetosphere. The full nonlinear equations in cylindrical geometry for a streaming cold pair plasma are solved numerically, together with Maxwell's equations, using a Finite-Difference Time Domain method. Electrostatic oscillations are induced in a streaming plasma in the presence of a non-uniform magnetic field, and the resulting electromagnetic waves are modelled self-consistently. Also presented is the linear perturbation analysis of these model equations perturbed from a dynamical equilibrium in order to probe the fundamental modes present in the system. These simulations successfully exhibit the coupling mechanism and the nonlinear interaction between electromagnetic waves and independent plasma oscillations, confirming the importance of coherent plasma effects and collective plasma processes in the pulsar magnetosphere. The observed electromagnetic signature is characterised by the nature of the emission mechanism and possibly by the menagerie of dust it encounters as it propagates through the surrounding supernova remnant. Supernova remnants are composed of multi-species electron-ion dusty plasmas. Conventional modelling of dust growth in this environment is based upon coagulation and nucleation of gas phase material. The second aim of this thesis is to study a possible spheroidal dust growth mechanism via plasma deposition. Dust grains immersed in a plasma acquire a net negative charge forming a plasma sheath. Ions are accelerated from the bulk plasma into the sheath and are deposited on the surface of the grain altering its shape and size. Grains with an elliptical geometry have a non-radial electric field and further anisotropic growth occurs if the deposited ions are non-inertial. In reality the extent of such growth depends upon the initial kinetic energy of the ions and the magnitude of the electric field in the sheath. Laplace's equation for the electric field for a range grain eccentricities is numerically solved using a bespoke finite difference method, the dynamics of the ions in the sheath are solved, showing how elliptical growth is related to the initial eccentricity and size of the seed relative to the sheath length.

In this thesis I present the results of studies on the influence of solar photospheric back–scatter on Hard X–Ray (HXR) flare diagnostics. Specifically the thesis presented is concerned with the effect of back–scatter photons upon the morphology of the Hard X–Ray photon spectrum and its effect on the inferred parent electron spectrum. I present a theoretical investigation into Compton reflected HXR photons, known as the photospheric Albedo, and explore the effect of photospheric albedo on observations of global flare hard X-ray spectra for isotropic emission. I examine, for the Kramers cross-section, the consequences of ignoring the albedo correction in using observed spectra to infer flare source electron spectra for thin and thick target interpretations and show that the effects are very significant in terms of inferred spectral shape, especially for hard spectra. I extend this investigation to consider the effect of the photospheric albedo on observations of global flare hard X-ray spectra for anisotropic primary photon emission by examining, for the Kramers cross-section, the consequences of ignoring the albedo correction in using observed spectra to infer flare source electron spectra for thin and thick target interpretations. For an energy dependent multiplier α I find that the results for anisotropic emission are similar in shape to isotropic emission when I assume a linear model for the anisotropy. I then explore two complementary techniques for determining the Compton back-scattered component of the observed photon spectrum using a model independent Greens function approach. The first is a matrix based technique developed by Kontar & Brown (2006) which I extend to include anisotropic primary photon emission using an Eddington hemispheric approach along with an empirical fit to published data. The second is a full radiative transfer Greens function approach developed by Poutanen et al. (1996) which I also extend to include anisotropic primary photon emission again using an empirical fit to published data. In both cases I investigate how anisotropic primary photon emission effects the observed photon spectrum by studying the differences in the size and shape of the albedo. In the final chapter I use the results from the anisotropic Eddington hemispheric Greens function approach and the anisotropic full radiative transfer Greens function approach to investigate the findings published in Kontar & Brown (2006) using the Stereoscopic electron spectroscopy technique. I conclude from the results of this comparison that doing a full anisotropic scattering properly does not fundamentally change the findings of Kontar and Brown which are specifically that the electron distribution is nearly isotropic to such a degree of confidence that it casts doubt on models which are based upon beaming such as the collisional thick target (Brown 1971).

In recent years various authors have developed a new numerical approach to cosmological simulations that formulates the equations describing large scale structure (LSS) formation within a quantum mechanical framework. This method couples the Schrodinger and Poisson equations. Previously, work has evolved mainly along two different strands of thought: (1) solving the full system of equations as Widrow & Kaiser attempted, (2) as an approximation to the full set of equations (the Free Particle Approximation developed by Coles, Spencer and Short). It has been suggested that this approach can be considered in two ways: (1) as a purely classical system that includes more physics than just gravity, or (2) as the representation of a dark matter field, perhaps an Axion field, where the de Broglie wavelength of the particles is large. In the quasi-linear regime, the Free Particle Approximation (FPA) is amenable to exact solution via standard techniques from the quantum mechanics literature. However, this method breaks down in the fully non-linear regime when shell crossing occurs (confer the Zel'dovich approximation). The first eighteen months of my PhD involved investigating the performance of illustrative 1-D and 3-D ``toy" models, as well as a test against the 3-D code Hydra. Much of this work is a reproduction of the work of Short, and I was able to verify and confirm his results. As an extension to his work I introduced a way of calculating the velocity via the probability current rather than using a phase unwrapping technique. Using the probability current deals directly with the wavefunction and provides a faster method of calculation in three dimensions. After working on the FPA I went on to develop a cosmological code that did not approximate the Schrodinger-Poisson system. The final code considered the full Schrodinger equation with the inclusion of a self-consistent gravitational potential via the Poisson equation. This method follows on from Widrow & Kaiser but extends their method from 2D to 3D, it includes periodic boundary conditions, and cosmological expansion. Widrow & Kaiser provided expansion via a change of variables in their Schrodinger equation; however, this was specific only to the Einstein-de Sitter model. In this thesis I provide a generalization of that approach which works for any flat universe that obeys the Robertson-Walker metric. In this thesis I aim to provide a comprehensive review of the FPA and of the Widrow-Kaiser method. I hope this work serves as an easy first point of contact to the wave-mechanical approach to LSS and that this work also serves as a solid reference point for all future research in this new field.

A new algorithm for the analysis of gravitational wave data from rapidly rotating neutron stars has been developed. The work is based on the Markov Chain Monte Carlo algorithm and features enhancements specifically targeted to this problem. The algorithm is tested on both synthetic data and hardware injections in the LIGO Hanford interferometer during its third science run ("S3''). By utilising the features of this probabilistic algorithm a search is performed for a rotating neutron star in the remnant of SN1987A within in frequency window of 4 Hz and a spindown window of 2E-10 Hz/s. A method for setting upper limits is described and used on this data in the absence of a detection setting an upper limit on strain of 7.3E-23. A further application of MCMC methods is made in the area of data analysis for the proposed LISA mission. An algorithm is developed to simultaneously estimate the number of sources and their parameters in a noisy data stream using reversible jump MCMC. An extension is made to estimate the position in the sky of a source and this is further improved by the implementation of a fast approximate calculation of the covariance matrix to enhance acceptance rates. This new algorithm is also tested upon synthetic data and the results are presented here. Conclusions are drawn from the results of this work, and comments are made on the development of MCMC algorithms within the field of gravitational wave data analysis, with a view to their increasing usage.

Chapter One introduces the theory of galactic microlensing and develops the necessary formulae needed to discuss extended source events in the subsequent Chapters. Some of the complications encountered by groups observing such events are discussed, as are a few of the more notable events themselves. In Chapter Two an extended source model for microlensing is presented and applied to different atmosphere models, with different surface brightness profiles including simple one and two parameter limb darkening models and the more sophisticated and recently developed "Next Generation" stellar atmosphere models. It is shown that microlensing can distinguish between these different surfaces brightness profiles and thus, the underlying stellar atmosphere models, for realistic observational strategies. In Chapter Three a second stellar atmosphere models is introduced. This model includes the effects of a non-radial surface brightness profile, i.e. starspots. Such effects are interesting for several reasons. Firstly, the existence or otherwise of starspots is an important indicator of stellar surface activity and would provide valuable information for the testing and development of more sophisticated stellar atmosphere models. Additionally, there has been concern that starspots could mimic planetary microlensing lightcurves making it important to consider how their observational signatures could be distinguished from those of planets. The microlensing signatures of starspots are considered for point mass lens in Chapter Three and for fold caustic crossings in Chapter Four. In Chapter Five the extended source model used previously is applied to a source model with a small level of radial and temperature variability, to allow examination of how such events, if observed, would compare to standard microlensing events. In Chapter Six an investigation is made of the spectroscopic signatures of microlensing from circumstellar envelopes and the opportunities of using microlensing to diagnose bulk motion in these envelopes during caustic crossing events is examined.

The aim of this thesis is the investigation of stars which show very low levels of polarimetric variability. A sample of such stars has been observed and assessed statistically to determine small differences, and temporal changes in polarisation. A statistical test has been improved upon, and used in a more rigorous, but more conservative fashion, emphasising the need for great care and thorough statistical assessment of such sources, to detect true temporal change. A new idea for an astronomical polarimeter has been introduced and discussed. The device, incorporating liquid crystals as phase modulators, has been theoretically modelled, designed and developed. Finally the instrument has been tested to ascertain its sensitivity and to investigate the repeatability of any results accrued from its use. Chapter 2 is concerned with measurements taken over seven nights in May 1996 on the 0.75m telescope at Sutherland, South Africa, using the Cape Town Polarimeter. The concern of Chapter 3 is to investigate the use of the Kolmogorov statistical technique (Conover (1980)) as a means of detecting low levels of polarimetric variability. The development of a Twin Liquid Crystal Polarimeter is the theme of Chapter 4. The need for a polarimeter with no mechanically moving components is explained, and to this end, the possible use of liquid crystals is discussed. Initially a device incorporating just one liquid crystal is described, but inevitably this system still requires some mechanical rotation. The subsequent theory behind developing a system with two liquid crystals, to eliminate the need for any rotation, is then developed. It is made apparent that for successful operation for such a device, the cells need be aligned very precisely to each other. Procedures for doing this are considered and assessed.

This thesis concerns continuous gravitational wave signals from non-axisymmetric neutron stars and ground-based interferometric detectors. These detectors are currently being upgraded and this thesis explores relevant issues and methods to prepare for the advanced detector era. A study into sensitivity dependence on the addition of a southern hemisphere detector for a targeted continuous wave search is first presented. Next, we study the effect of close and/or high velocity neutron stars on the ability of a blind, all-sky search to make a detection. Initial results from a narrowband search for signals from the Crab Pulsar and a blind hardware injected signal are then presented. Finally, we describe the development and initial implementation of a large-scale mock data challenge designed to test current continuous wave algorithms to explore various issues before we enter the advanced detector era.

This thesis investigates heating and thermal and non-thermal X-ray emission from magnetic loops in active regions of the solar atmosphere using numerical simulations. The simulations also allow investigation of Type III radio emission. In our model we vary a number of physical parameters such as magnetic field configuration and density models, investigating the effect they have on emission and loop heating as a result of the propagation of a beam of fast electrons moving through the ambient coronal plasma. Chapter 1 presents an overview of the Sun and the magnetic processes at work in the solar atmosphere. It also contains a summary of observations and current work corresponding to the phenomena discussed in later chapters, as well as current theories of particle acceleration and transport in an active region loop. Chapter 2 describes the theory behind, and implementation of, the numerical simulations used, and initial tests of the accuracy of the simulations by comparing results with analytical results for simplified models. The simulations are built on a core which models the evolution of the electron distribution function through stochastic processes. We derive the Fokker-Plank equation from which we obtain the expressions describing the progress along a magnetic field of an electron undergoing Coulomb collisions with particles of a background plasma. We describe the field and density models used, and consider the effects of gradient and curvature drifts on particles. In Chapter 3 we present results showing the non-thermal X-ray emission from magnetic loops with various density models and field configurations. We show results from a straightforward field model with no curvature as described in MacKinnon & Brown (1990), and then results from a more complex (and more realistic) X-point field model as described in Priest & Forbes (2000). These results illustrate the significant effects the field model and density of the background coronal plasma have on the loop emission, both in intensity and position (i.e. at which part of the loop the emission originates from). We also investigate the correlation between loop footpoint size and X-ray intensity, theoretically verifying work done by Schmahl et al. (2006) in which they present observations showing that X-ray intensity increases with footpoint size. In Chapter 4 we present results showing the evolution of the loop temperature profile over time. As the fast electrons collide with the particles of the ambient background plasma they lose energy, which is transferred to the plasma, increasing it's temperature. We include in these calculations the effects of radiative and conductive cooling of the loop, but we do not consider chromospheric evaporation (whereby heated plasma from the photosphere rises into the loop at the footpoints as a result of bombardment by the beam of fast electrons) or other bulk plasma effects. This would require a combination of stochastic and hydrodynamic simulations, which we do not cover in this work. Again, we show the effects of changing density and field models on the temperature profile. In Chapter 5 we investigate the thermal X-ray emission from the particles of the background plasma in the heated loop. We then combine the thermal and non-thermal emission to produce X-ray spectra from photon energies 6 - 100 keV, similar to those observed by satellites such as the Reuven-Ramaty High Energy Solar Spectroscopic Imager (RHESSI), thus verifying that our simulations successfully model some of the processes present in active regions. We also consider the limitations of our simulations and models and discuss what parameters and changes would produce results close to observational data. Chapter 6 is separate from the preceding chapters and is a brief study of the production of Reverse-Drift Type III radio bursts in a loop, specifically the position in the loop at which the condition for their development originates, given various plasma densities and particle injection profiles. In a beam of injected electrons, the faster (higher energy) electrons propagate along the loop more quickly than the slower particles, causing an instability to develop in the beam distribution. This instability leads to the growth of Langmuir waves, which in turn result in emission at radio wavelengths. We show the development of the condition leading to this emission from a loop as a function of time and position, with various field and density models and particle injection profiles. Chapter 7 summarises the main body of work in this thesis and discusses possible further development of these methods in investigating the physical processes and parameters at work in active region magnetic loops.

Light passing near a massive object (star) will take longer to arrive at the Earth than it would if the object was not present. This additional time is called the Shapiro delay. In globular clusters, where there are millions of stars, the cumulative effect of the Shapiro delay from these stars will affect pulsar timings by introducing an additional noise term. This effect has been previously assumed to be small, yet no definite investigation has been done to determine its magnitude. In this thesis a model of the globular cluster 47 Tucanae was created in order to determine the effect of the change in Shapiro delay (called the Shapiro noise) for an observed duration of 3600 days -- the current longest observation period for pulsar timing. This noise was then added to the pulsar time of arrival (TOA) as the only noise source in pulsar timing. A polynomial fit was then used to subtract the first two orders from the pulse arrival time (the f and \dot{f} terms) to determine the timing residuals. This model was then realised 100 times to obtain the average root mean square (RMS) timing residual for every pulsar. The model showed that the Shapiro noise has a significant, and observable effect on pulsar timing, especially for pulsars situated close to the core of the globular cluster. From the model the average RMS timing residuals were of the order of 10^{-5} to 10^{-7} seconds and the variance of the RMS timing residuals were significantly larger in magnitude, ranging from 10^{-4} to 10^{-7} seconds for every pulsar. The importance of this result motivated further investigation of the stellar distribution of the globular cluster. In addition an investigation on how the effect of gravitational acceleration (produced by stars situated close to the pulsar) affects pulsar timing residual was also done. While the acceleration has an effect, the effect is smaller than that of the Shapiro noise. From the timing residuals produced by the Shapiro noise, it was then discussed whether any star close to the LOS would have an affect on the pulsar timing residuals. From additional simulations it was determined that stars anywhere along the LOS will have an affect on pulsar timing, however the stellar density of such a region would have to be greater than \rho_{min} > 10^{5} M_{\sun} pc^{-3}. The implications of this result for other pulsars in (other) globular clusters is discussed.

In 1905, Einstein postulated that the speed of light is not only finite, but that its speed in vacuum is a universal limit that no process can exceed. The Theory of General Relativity later extended this concept to include gravitational interactions, and Eddington's timely measurements of stellar positions during a solar eclipse in 1919 confirmed that gravity's effect on spacetime is both real and entirely physical -- not merely a mathematical curiosity. With the death of Newton's notions of universal time and instantaneous gravity came the idea of gravitational waves as distortions in space-time that propagate the gravitational interaction at the speed of light. These gravitational waves are emitted from any object undergoing a non-axi-symmetric acceleration of mass, but -- due to the exceptionally weak coupling between gravitational waves and matter -- are expected to induce displacements of the order of 10^-18 m in kilometre-scale detectors: the extraordinary diminutiveness of this effect has thus far precluded any direct detection of the phenomenon. Numerous gravitational wave detectors have been built since the 1960s, in the form of both interferometric detectors and resonant mass devices. Interferometric detectors currently represent the most promising form of detector, due to their relatively wide-band response to gravitational wave signals and promising levels of sensitivity. In recent years a worldwide network of these interferometric detectors (LIGO, GEO600, Virgo and TAMA300) have begun to approach (or indeed reach) their design sensitivities. Although these detectors have started to provide upper limit results for gravitational wave emission that are of astrophysical significance, there have as yet been no direct detections. As such, work is underway to upgrade and improve these detectors. However, increasing the signal sensitivity necessarily leads to an increase in their sensitivity to their limiting noise sources. Two critical noise limits that must be characterised, understood, and hopefully reduced for the benefit of future detectors, are thermal noise (from mirror substrates, reflective coatings and suspension systems) and photon noise -- associated with the intrinsic shot noise of light and the noise due to light's radiation pressure. Two interferometric experiments designed to help inform on these phenomena were constructed at the University of Glasgow's Institute for Gravitational Research. The first experiment compared the relative displacement noise spectra of two specially constructed optical cavities, to extract the thermal noise spectrum of a single test mirror. In future experiments, this optic could be changed and the thermal noise spectrum for any suitable combination of mirror substrate and reflective coating evaluated. The second experiment involved the investigation of suitable control schemes for a three-mirror coupled optical cavity. As the resonant light power in interferometers increases in future devices (in order to decrease the photon shot noise) the need to de-couple the control schemes that govern the respective cavities so that they can be controlled independently, becomes more important. As a three-mirror cavity effectively represents a simple coupled system, it provides a suitable test-bed for characterising suitable control schemes for more advanced interferometers. Together, these experiments may provide information useful to the design of future gravitational wave interferometers.