Impulsive solar electron beams have an attractive diagnostic potential for poorly understood particle acceleration processes in solar flares. Solar flare accelerated electron beams propagating away from the Sun can interact with the turbulent interplanetary media, producing Langmuir waves and type III radio emission. In this thesis, we simulate electron beam propagation from the Sun to the Earth in the weak turbulent regime taking into account the self-consistent generation of Langmuir waves. We show that an injected single power-law spectrum will be detected at 1 AU as a broken power-law due to wave-particle interaction in the inhomogeneous plasma. We further extend these results by investigating the Langmuir wave interaction with background electron density fluctuations from low frequency MHD turbulence. We find a direct correlation between the spectra of the double power-law below the break energy and the turbulent intensity of the background plasma. Solar flares are believed to accelerate both upward and downward propagating electron beams which can radiate emission at radio and X-ray wavelengths correspondingly. The correlation between X-ray and radio emissions in a well observed solar flare allowed us detailed study of the electron acceleration region properties. We used the Nancay Radioheliograph, Phoenix-2 and RHESSI to infer the type III position, type III starting frequency and spectral index of the HXR emission respectively. Using these datasets and numerical simulations of the electron beam transport in the corona plasma, we were able to infer not only the location (the height in the corona), but to estimate the spatial length of the electron acceleration site.

A test particle approach is used to study two distinct plasma physics situations. In the first case, the collisionless response of protons to cold plasma fast Alfven waves propagating in a non-uniform magnetic field configuration (specifically, a two-dimensional X-point field) is studied. The field perturbations associated with the waves, which are assumed to be azimuthally-symmetric and invariant in the direction orthogonal to the X-point plane, are exact solutions of the linearized ideal magnetohydrodynamic (MHD) equations. The protons are initially Maxwellian, at temperatures that are consistent with the cold plasma approximation. Two kinds of wave solution are invoked: global perturbations, with inward- and outward-propagating components; and purely inward-propagating waves, localised in distance from the X-point null, the wave electric field E having a preferred direction. In both cases the protons are effectively heated in the direction parallel to the magnetic field, although the parallel velocity distribution is generally non-Maxwellian and some protons are accelerated to highly suprathermal energies. This heating and acceleration can be attributed to the fact that protons undergoing E x B drifts due to the presence of the wave are subject to an effective force in the direction parallel to B. The localised wave solution produces more effective proton heating than the global solution, and successive wave pulses have a synergistic effect. This process, which could play a role in both solar coronal heating and late-phase heating in solar flares, is effective for all ion species, but has a negligible direct effect on electrons. However, both electrons and heavy ions would be expected to acquire a temperature similar to that of the protons on collisional timescales. In the second case the same approach is used to study the collisional transport of impurity ions (carbon, mainly, although tungsten ions are also simulated) in spherical tokamak (ST) plasmas with transonic and subsonic toroidal flows. The efficacy of this approach is demonstrated by reproduscing the results of classical transport theory in the large aspect ratio limit. The equilibrium parameters used in the ST modelling are similar to those of plasmas in the MAST experiment. The effects on impurity ion confinement of both counter-current and co-current rotation are determined. Various majority ion density and temperature profiles, approximating measured profiles in rotating and non-rotating MAST plasmas, are used in the modelling. It is shown that transonic rotation (both counter-current and co-current) has the effect of reducing substantially the confinement time of the impurity ions. This effect arises primarily because the impurity ions, displaced by the centrifugal force to the low-field region of the tokamak, are subject to a collisional diffusivity that is greater than the flux surface-averaged value of this quantity. for a given set of plasma profiles, the carbon ions are found to be significantly less well-confined in co-rotating plasmas than in counter-rotating plasmas, although the difference in confinement time between co- and counter-rotation lessens as the mass of the impurity increases. In the case of carbon ions the poloidal distribution of losses exhibits a pronounced up/down asymmetry that is consistent with the direction of the net vertical drift of the impurity ions. Increasing the mass of the impurity ion is also found to significantly decrease the confinement time in the rotating cases, though the confinement time for the case of a stationary plasma is increased. Such studies of impurity transport within tokamaks are important because it is desirable to expel impurity ions from the plasma to avoid both dilution of the fuel ions and unacceptable radiation losses from the plasma.

This thesis describes a detailed research for the decay B°s (r) J/ψh, within data taken from p collisions at √s=1.8TeV. Proton anti-proton collisions contain many different physics processes. From these processes many are of lesser interest. The trigger logic specific to selecting a sample of data rich in processes relevant to this particular study is described in detail. The analysis method proceeds as follows. The simulation program used to model acceptances of B+ (r) J/ψK+ and B°s (r) J/ψh samples is described. Within this description theoretical inputs and assumptions made are given in detail. Constraints made on each generated sample are then outlined. From the simulation, the discussion turns to the reconstruction of B+ (r) J/ψK+ and the search for B°s (r) J/ψh within the CDF data. All stages of data selection are discussed. The analysis then turns to acceptance and efficiency factors considered. Specific effort is made to fully describe the photon reconstruction efficiency. Photon reconstruction efficiency is studied in the CDF environment by introducing a data based Monte Carlo program. This detailed simulation is discussed and final photon reconstruction efficiencies are given. Systematic uncertainties are analysed in detail. The generator level simulation is used to provide error propagation for acceptance and efficiency parameterisations introduced. Systematic uncertainties from the analysis of data are also given. The results of the B (r) J/ψK+ reconstruction and the search for B°s (r) J/ψh are given. From an integrated luminosity of 110pb-1, 1178171 J/ψ (r) m+ m- events were collected. 490 ± 23 B+ (r) J/ψK+ events were isolated. From the sample of J/ψ(r) m+m- events a branching ratio limit of B(B°s (r) J/ψh) < 6.3 x 10-3 is set at a 90% confidence limit.

Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by e.g. Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In a model consisting of such events it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the energy density would remain unaffected. The particular evolution of the scale factor of the universe in this model that results in a singular behaviour of the pressure also admits acceleration in the current era. In this thesis we will present the results of our confrontation of one example class of SFS models with the available cosmological data from high redshift supernovae, baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB). We then discuss the viability of the model under consideration in light of the data.\\ More importantly however in this pursuit, we will make the case that the cosmological constraints employed in this analysis were not blindly applied to the non-standard model in question, which is not unfortunately the practice that is always followed in the cosmology community. This applicability issue is a very important one which if neglected could potentially result in biased and unreliable outcomes. Hence, although we have worked on one example non-standard cosmological model in this thesis, this work could be viewed as a demonstration of a thought through process of testing one's model against observations which can be applied to every other preferred model.

This thesis considers the propagation of accelerated electron beams in plasma. We consider the wave particle interactions these undergo which cause their evolution, the effects of plasma density inhomogeneities on these interactions, and the effects this may have on the production of hard X-ray and radio emission by the beam. Chapter 1 introduces the important background material on the Sun and solar flares, and some basic plasma physics. We discuss the acceleration and propagation of electrons beams and their production of hard X-ray emission, and the various observed types of radio emission from the Sun. We end by discussing details of the mechanism by which radio emission can be produced by beam generated Langmuir waves at GHz frequencies. Chapter 2 contains the mathematical derivation of the effects of plasma density fluctuations on Langmuir waves. This is found to be described by a diffusion of the waves in wavenumber space. We consider the situation in both one and three dimensions, for elastic and inelastic scattering of the Langmuir waves, discussing how our model expands on that previously considered in the literature, and develop a model for the fluctuations applicable to the electron beams we consider in this thesis. We derive the relevant diffusion coefficients for a few commonly observed density fluctuation spectra, then end with a brief discussion of the expected effects of the Langmuir wavenumber diffusion on the waves and electrons for a few representative cases. Chapter 3 uses the model derived in Chapter 2 in quasi-linear simulations of electron beam evolution. We consider two initial electron beam distributions, either a Maxwellian or a power law, and simulate the Langmuir wave generation and evolution, and the back-reaction of this on the electron beam. We find an electron acceleration effect to occur, and explore the parameters for which this is strongest. In addition we consider the production of hard X-ray emission from an initially power law beam, and the effects of the electron acceleration on this. Chapter 4 considers the radio emission from an electron beam via the generation of Langmuir waves. We first derive an angle-averaged model for emission at the second harmonic of the plasma frequency, and combine this with the simulations from the previous chapters. We include the effects of density fluctuations on the Langmuir waves, and discuss how this affects the radio emission produced. Chapter 5 concludes the thesis with a summary of the effects of density inhomogeneity on Langmuir waves, and consequently on fast electron beams and their hard X-ray and radio emissions in the solar corona. Appendix 1 contains the derivation of a mathematical model for radio emission from an electron beam at the fundamental of the local plasma frequency, which is unimportant in the parameter ranges considered in Chapter 4, but essential for radio bursts in the higher corona and solar wind.

This thesis presents an analytical and computational approach to modelling partially ionised, spatially-inhomogeneous and recombining plasmas. The specific context for this study is astrophysical plasmas, the early Universe in particular. Two models are investigated in detail: a magnetohydrodynamic (MHD) plasma model to simulate partially ionised plasmas; and a fully electromagnetic/kinetic model, used to study recombining plasmas. The first section further develops an existing computational model of a partially ionised plasma as a mixture of two cospatial fluids: an MHD plasma and a neutral gas. In order to model the interaction between the plasma and neutral gas populations ab initio, a collisional momentum exchange term was added to the momentum equation of each fluid. The model was used to investigate the combined response to different wave modes driven in the plasma or the neutral gas. The momentum coupling between the plasma and the neutral gas leads to complex interactions between the two populations. In particular, the propagation of plasma waves induces waves in the neutral gas by virtue of the collisional momentum exchange between the velocity fields of each fluid. This means that the normal wave modes of each independent fluid are modified to produce a combined, hybrid response, with the intriguing possibility that neutral gas can not only respond indirectly to magnetic fluctuations but also generate them via sound waves. This model is used to examine an existing observational method known as the ‘Chandrasekhar-Fermi method’ (CF53) for the diagnosis of magnetic fields in astrophysical plasmas. CF53 is commonly applied to objects such as nebulae and molecular clouds which are partially-ionised plasmas. It assumes that the gas motion can be used to infer the magnetic field strength, given coupling between Alfv´en waves in the plasma and the thermal motion of the neutral gas. Computational results show that this method may need to be refined, and that certain assumptions made should be re-evaluated. This is consistent with reports in the literature of CF53 under- or over-estimating the magnetic fields in objects such as molecular clouds. The second part of this thesis concentrates on the non-equilibrium evolution of magnetic field structures at the onset of the large-scale recombination of an inhomogeneouslyionised plasma, such as the Universe was during the epoch of recombination. The conduction currents sustaining the magnetic structure will be removed as the charges comprising them combine into neutrals. The effect that a decaying magnetic flux has on the acceleration of remaining charged particles via the transient induced electric field is considered. Since the residual charged-particle number density is small as a result of decoupling, the magnetic and electric fields can be considered essentially to be imposed, neglecting for now the feedback from any minority accelerated population. The electromagnetic treatment of this phase transition can produce energetic electrons scattered throughout the Universe. Such particles could have a significant effect on cosmic evolution in several ways: (i) their presence could influence the overall physics of the recombination era; and (ii) a population of energetic particles might lend a Coulomb contribution to localized gravitational collapse. This is confirmed by a numerical simulation in which a magnetic domain is modelled as a uniform field region produced by a thin surrounding current sheet. The imposed decay of the current sheet simulates the formation of neutrals characteristic of the decoupling era, and the induced electric field accompanying the magnetic collapse is able to accelerate ambient stationary electrons (that is, electrons not participating in the current sheet) to energies of up to order 10keV. This is consistent with theoretical predictions.

This thesis summarises my work in relation to data analysis for gravitational wave detection. Most of the personal contribution relates to the assessment of the detectability of potential burst-type gravitational wave signals from the galactic population of neutron stars and to the parameter estimation of the models used to represent these signals. A small part of the work, confined to the last chapter, describes the experimental work carried at the beginning of the research period and aimed to measure the shot-noise level of the modulated laser-light in the gravitational wave detectors. Chapter 1 is introductory and presents generic information about gravitational wave radiation, a postulate of the theory of general relativity. The polarisation of the radiation and the approximate values of amplitudes and frequencies of the signals expected from astrophysical events are presented, together with most important gravitational radiation sources for ground-based detectors. Chapter 2 presents the study on the detectability of burst-type gravitational wave signals incoming from neutron stars located in our galaxy. Three differently shaped galactic neutron star populations are introduced and the detectability of ground-based detectors to signals of different polarisation degree coming from these source populations is investigated. Based on the time- and polarisation-averaged antenna pattern and antenna power values, approximated by Monte Carlo methods, detectability is measured in terms of a) the geographical location and orientation of hypothetical detectors, and b) the current detectors, either working individually or as a part of a network. Also, the sidereal times at which each detector is more sensitive to the sources of the neutron star populations defined are inferred. Chapter 3 introduces a mathematical model of the burst-type gravitational wave ringdown signal investigated in this work, which represents a short-lived gravitational polarised radiation generated by an oscillating neutron star: an exponentially damped sinusoid comprised of a sine and a cosine component, of the same frequency but different amplitude, as the two polarisation components of the signal. The model of the signal is given, in the time- and in the frequency-domain. Chapter 4 is devoted to present the Bayesian probability tools necessary to carry out ‘model comparison’ and ‘parameter estimation’ for the detectability study of our particular burst-type signal. Comparison of models allows choosing the one that better represents the data and subsequently focusing on in order to compute the most likely parameter values of that model. Also, in this section, the way in which the detector data can be simulated in the frequency domain, combining the signal and a noise realisation corresponding to the power spectrum of the noise that characterizes the detector, is explained. The likelihood function for a signal corresponding to one oscillation mode and seen by one detector is derived both in the time- and in the frequency-domain. The nested sampling technique is summarised, a useful tool to compute effectively the marginal likelihood of the hypotheses considered. Chapter 5 presents the results of the model selection and the parameter estimation exercise. The expression of the likelihood is generalised so that it can adopt more than one oscillation mode and been seen by various detectors of a network. Depending whether one, f-mode, or two oscillation modes, f and p, are suspect, two different scenarios of various hypotheses are considered. For each hypothesis the minimum strength of the signal to claim detection is studied and a parameter estimation exercise is carried out to characterise the signal and define the location of the source in the sky. Signals of known parameters and differing strengths were injected into the synthetic noise of three advanced detectors comprising a network. The values of the parameters were estimated using Bayesian inference for two different scenarios: when only the f-mode is suspect (scenario 1), or when both f- and p-modes are suspect (scenario 2). Posterior probabilities of the parameters in Scenario 1 are better defined and constrained than those for Scenario 2, due to the added uncertainty of including another oscillation mode. As expected, the uncertainty of the probability distributions of the parameter values decreases and the mode shifts toward the exact injected value as the signal strength increases. For both scenarios the frequency value can be accurately estimated, but not so well the damping time, especially for the p-mode oscillation, which is suspected to have longer time durations than f-modes, typically several seconds. The ability to estimate the polarisation degree of the signal is also quite limited and strong signals are required for the mode of the distribution to approximate the exact value. Similarly, determining the most probable location for the source is possible in both scenarios. The two-fold degeneracy of the sky position and related to the travel time of the signal to the detectors has been broken; relatively strong (high SNR) signals, especially for scenario 2, are needed for the source location to be constrained with accuracy. Chapter 6 presents the experimental work carried out, by which the measuring of the shot-noise level of differently modulated and demodulated laser light was intended. Due to the poor outcome of this experiment and the lack of useful results the emphasis has been placed on a detailed description of the modulation apparatus, opto-electronic set up and the control system put together. Chapter 7 looks to the future and briefly presents how to take this data analysis work forward.

For several decades, quasi-periodic pulsations (QPP) in flares have been a signature feature of solar dynamics. In the last fifteen years, the advent of new observational instruments has led to a much-improved scope for studying and understanding such phenomena. These events are particularly relevant to the field of coronal seismology, where impulsive events are used as diagnostic tools to estimate the physical parameters of the solar atmosphere remotely. In this thesis we investigate quasi-periodic pulsations in flares from both a numerical and observational perpective, mostly in terms of magnetohydrodynamic (MHD) waves. It has long been suggested that MHD modes may be the cause of QPP in flares as they are capable of modulating a wide range of observable quantities. We study one such mode in detail: the sausage mode. For a model including significant gas pressure, the characteristic period, the ratio of the mode harmonics and the behaviour of the wavenumber cutoff are all considered. Although the period and wavenumber are only marginally affected by this gas pressure, the density contrast ratio and length are important factors. An observational study of a flaring QPP event was undertaken, where new techniques were developed in an attempt to successfully diagnose the QPP mechanism. Cross-correlation mapping was applied to spatially resolved radio data, showing how the strength and phase relationship of a flaring oscillation can be mapped in space. Using this information, we were able to exclude many mechanisms as possible drivers for this event, and suggest that an MHD sausage mode is the likely candidate. A second flaring QPP event was considered, based on the possibility of multiple harmonic oscillations. A sequential spectral peak filtering method was used to demonstrate the presence of multiple significant periods in the flare. Analysis of the harmonic ratios indicated that an MHD wave such as a kink mode was the probable cause. Finally we explore the potential of a new technique in the context of the solar corona, the combination of empirical mode decomposition (EMD) and the Hilbert spectrum. It was established that, under certain circumstances, this method compared favourably with existing analysis techniques such as the Morlet wavelet, and may lead to significant future observational results.

We study the effects of the supersonic collision of molecular clouds using smoothed particle hydrodynamics (SPH) simulations. We review the observational evidence for cloud-cloud collision and previous computational work. We describe the SPH method, the algorithms used in the SPH code SEREN, and how we have extended the parallelization of SEREN. We review the non-linear thin shell instability (NTSI) and gravitational instability in a shock-compressed layer. We present the results of two sets of SPH simulations. In the first set of simulations we collide supersonic flows of gas without self-gravity. We impose a range of velocity perturbations, including monochromatic perturbations, white noise perturbations and both subsonic and supersonic turbulence. The colliding flows create a dense shock-compressed layer which is unstable to the NTSI. We examine the effect of the differing initial perturbations on the NTSI, and calculate rates of growth of both bending modes and breathing modes as a function of time and wavenumber. We compare our results to the time-independent result predicted by Vishniac (1994) for a one-dimensional monochromatic perturbation, and examine how this result can be extended to two-dimensional perturbations and non-monochromatic perturbations. In our second set of simulations we model the head-on supersonic collision of two identical uniform-density spheres. We include self-gravity, allowing the dense layer to become gravitationally unstable and produce stars. We explore the effect of increasing collision velocity, and show that the NTSI is present only at higher collision velocities. At the highest collision velocities the NTSI severely disrupts the layer, and the collision does not produce stars. Although the global properties of the collision, such as the thickness of the layer, the size of the star-forming region and the time of first star formation, depend on the collision velocity, most individual properties of the stars do not.

In this thesis we investigate the development and use of numerical methods to study astrophysical problems, particularly the formation and evolution of objects via gravitational instability in circumstellar discs. We begin with a comprehensive overview of the development, validation and optimisation of numerical tools. These formed the basis of SEREN, a Smoothed Particle Hydrodynamics (SPH) code for modelling self-gravitating fluid dynamics. SEREN has been rigorously tested and optimised, and is now being used for high-performance research in various areas of star formation. We then consider in some depth the problems associated with shocks, instabilities and shear flows in numerical simulations, detailing why such problems arise and what can be done to alleviate them. Finally we model circumstellar discs, investigating the influence of both physical and computational parameters upon the formation of objects via gravitational instability. We then model the interaction of discs with stars and other disc systems, investigating the influence of the orbital parameters upon the evolution of a marginally stable disc. Ultimately we find that gravitational instability in massive extended circumstellar discs is a viable mechanism for the formation of brown dwarfs and massive planets, and provides an explanation for the "brown dwarf desert" and free-floating planets. We also find that while disc-star and disc-disc interactions might produce accretion bursts and exert an influence over the disc evolution, they are not a likely mechanism for triggering fragmentation in marginally stable discs.