No description available.

No description available.

In recent years, there has been an increasing interest in probing the properties of two-dimensional materials, starting with graphene. This one-atom-thick sheet has important features. Thus, we employ an accurate quantum many-body formalism, the coupled-cluster method, to study the electronic correlation effects on the quantum state of two-dimensional materials described by Hubbard model. In particular, we examine the ground and excited states of the model. To get a quantitative description of the quantum properties of the Hubbard model, we calculate the ground and excited state energies in addition to the staggered magnetisation which is the ordered parameter considered in this work. We report results for the 1D chain, honeycomb lattice, and in a few occasions, also for square lattice. We first of all investigate number of approximations within the normal version of the coupled-cluster method. With hoping terms only, one-body correlations are significant and it is capable of producing the exact results of the 1D chain. For the square and honeycomb lattices, the results are identical to the solution of mean-field theory in that limit. At strong coupling, only nearest-neighbour spin fluctuations survive, and the results converge as expected to those of the Heisenberg model. However, the approximation fails to predict the existence of a symmetric state in the 1D chain at non-zero coupling and does not show a phase transition between a semi-metal and antiferromagnetic phases in the honeycomb lattice. The single charge excitation converges, at zero-coupling, to the dispersion relation of the tight-binding model and there is no effect of the two-body correlations in that limit. One approximation, which is based on a model state that embodies long-range spin fluctuations, succeeds to produce a symmetric state for the 1D chain. However, it fails to show a phase transition in the honeycomb lattice. Next, we apply the extended version of the coupled-cluster method. One approximation in particular shows results close to mean-field solution at intermediate coupling and converges to the Heisenberg solution at strong coupling.

Doppler backscattering (DBS) in 1D is an established and powerful fusion plasma diagnostic technique. In this thesis we explore the capability of the novel Synthetic Aperture Microwave Imaging diagnostic (SAMI) in performing proof-of-principle 2D DBS experiments on the Mega Ampere Spherical Tokamak (MAST) and the National Spherical Torus eXperiment Upgrade (NSTX-U). Phenomena observed previously using 1D DBS systems such as intrinsic plasma spin up, momentum injection from neutral beams and sharp changes in power and turbulence velocity coinciding with the L-H transition are re-observed. In addition, SAMI’s unique 2D DBS capability has enabled the first ever 2D maps of Doppler backscattered radiation to be constructed. These 2D maps reveal that, due to turbulence elongated along field lines, Doppler backscattered power is concentrated in directions perpendicular to the magnetic field. This distribution of backscattered power allows magnetic pitch angle to be measured. Results from the utilisation of this technique are presented using MAST and NSTX-U data. This procedure constitutes a new independent channel for diagnosing magnetic pitch angle and is the first case of pitch angle being measured using a microwave diagnostic. A method utilising microwave diagnostics is of particular interest as this presents the possibility of high temporal and spatial magnetic pitch measurements enabling, through application of Amp`ere’s law, measurement of edge current density: an important parameter in governing pedestal stability. The new capabilities and limitations resulting from implementation of a 2D DBS phased array system are discussed. How such a 2D device might be further optimised is examined and areas of further study are proposed.

Operating with an edge transport barrier (ETB) is central to ITER's goal of attaining a fusion energy gain of ten. The evolution and stability of this ETB is governed through the interplay of MHD modes and microinstabilities. The ballooning formalism is a mathematical framework that can be utilised to understand the characteristics of these modes in the linear regime. When applied to toroidal drift microinstabilities (e.g. ITG), the ballooning formalism predicts two distinct classes of global eigenmodes: the strongly growing Isolated Mode (IM) that exists under special conditions, and the relatively benign General Mode (GM) that is more generally accessible. Here we present findings from a new initial-value code, developed to study the dynamics of these linear branches in the presence of a time-evolving equilibrium toroidal flow-shear. The code has been further extended to incorporate the (quasi-linear) effect of intrinsic flow generated by these global structures on the modes themselves. The IM/GM dynamics could provide physical insights into understanding small-ELM regimes and intrinsic rotation - two unresolved physics issues that are of great significance to ITER. Firstly, the IM is seen to form more rapidly than the GM. For our chosen fluid-ITG model, even though both structures are likely to form deep into the nonlinear regime, there is indication that close to marginal stability, these global modes might form much sooner to subsequently influence the nonlinear evolution. Secondly, in the presence of a critical flow-shear, a GM-IM-GM transition can take place to trigger a burst in the growth rate as the IM is accessed. These dynamics can occur on the right time-scale and form the basis of a new model for small-ELMs outlined in this work. Transient bursts are seen in the linear growth rate at high flow-shears, which may provide an alternative trigger for small-ELMs. Certain other seemingly robust features are reported, which could guide experimental efforts to test this theory. Finally, allowing for the feedback of the intrinsic flow on the mode structure, the IM seems to be a stable equilibrium when the external flow-shear is weak, whereas when strong equilibrium flow-shears dominate over the intrinsic flow, the GM solution is more likely. An approach to model the intrinsic flow profile from these global structures is suggested.

The effects of spherical particles ('dust grains') in plasmas are investigated. The importance of dust grains in plasmas is highlighted, especially with regards to fusion energy production in magnetically confined plasmas. The investigation focuses on dust grains that are at the extremes of scale compared to the Debye length. Large dust grains, i.e. dust grains much larger than the Debye length, are investigated by the use of a simple fluid model, which is similar to compressible gas dynamics. Professor John Allen was the first to draw attention to the similarity of the model to compressible fluid dynamics in his 2007 paper [Allen, 2007]. The equations derived, which resemble those of compressible fluid dynamics are solved numerically with the help of a code written specifically for this purpose. The results are similar to PIC code results, with some differences in the shape of the downstream disturbance; more specifically, the downstream disturbance generated by our code is more elliptical than conical, and similar to the disturbance caused by a sphere in neutral fluids at moderate Reynolds numbers. This is to be contrasted with the results in the literature which are conical in shape, especially for low values of tau (Ti/Te). This may be an indication that the difference in shape is due to the ion pressure or the electron inertia, both of which we are neglecting in our assumptions. Small dust grains are investigated using a kinetic model. The model is a continuation and evolution of the model used by Filippov [Filippov et al, 2007], to include plasma flow. The equations of the model are solved analytically and the results reveal the presence of upstream structures, even in the case of supersonic flow, a result not commented on before in the relevant literature. The work also reviews relevant analytic theories, such as ABR and OML. ABR is extended by the author to include finding the geometrical width of the sheath. This extension, if confirmed, could be used for predicting the position of the sheath edge in relation to the dust grain. In addition, the work on deriving the Bohm criterion for a spherical dust grain is investigated, using a similar approach to the one taken in the literature for a planar wall. The result indicates that there is no such limitation in the spherical case.

No description available.

SNO+ is a liquid scintillator experiment designed to study a wide range of neutrino-related physics goals, such as solar neutrinos, reactor and geo-neutrinos, and neutrinoless double beta decay. The success of the experiment depends in part on the ability to accurately characterise the detector's optical properties, and also develop effective methods to suppress contributions from unwanted backgrounds. This thesis presents one of the central calibration systems which will be used to make measurements of the detector's optical scattering properties. The hardware and its integration into the wider detector will be discussed. A simplifed analysis of simulated water data is also presented, in order to show that the scattering properties can be accurately measured. The reconstruction of photons' scattering position, length and angles can be achieved to a high degree of accuracy, with a small reconstruction bias and resolution in comparison to the scale of the detector itself. This thesis also presents a study into the rejection of two important radioactive backgrounds that will be encountered during the scintillator phases of SNO+: the (212Bi + 212Po) and (214Bi + 214Po) beta-alpha chains, where both components of each chain occur within a single detector trigger window, creating what is known as a BiPo pileup event. Two methods have been considered: one using a comparison between the cumulative time residual distributions of BiPo pileup and double-beta signal events, and the other using a log-likelihood difference method. Both methods perform extremely well, with the first being capable of rejecting > 95% of BiPo pileup events for a 1% loss of signal, and the second rejecting > 97% of backgrounds for the same signal loss.

No description available.

Warm dense matter is an area of the phase diagram between solids and classical plasmas, but poorly described by theoretical descriptions of both. Collective oscillations and quantum effects all play significant roles in its structural behaviour and equations of state. Aside from its complexity, work on this state is significant as a stepping stone towards achieving energetically viable nuclear fusion, as well as representing a laboratory analogue for planetary cores and other astrophysical phenomena. X-ray scattering, using beams from X-ray free electron lasers, is used to probe the structure of samples in this state, and is shown to compare well to theoretical descriptions. Angle-resolved scattering showed sharper than expected peaks, suggesting stronger interparticle correlation than expected. Using the beam in self-seeded mode, scattering from ion acoustic waves in warm dense matter was observed for the first time, confirming theoretical descriptions of the phenomena but raising further questions due to an elastic peak in the spectra. Similar experiments in the future will allow models of ionic behaviour to be tested directly, and potentially determine the source of this feature. X-ray diffraction was used to study the evolution of samples heated by proton, electron or photon irradiation, with the aim of resolving the temperature evolution of the species within the sample. The results suggest that, although the behaviour in metallic samples is well described by lowtemperature approximations, that of graphite is more complex and does not agree with the models available.