This thesis describes the application of in-situ surface X-ray diffraction (SXRD) experiments to the study of electrochemical interfaces. Measurements performed at synchrotron radiation facilities are used to provide in-sight into the surface structure of electrodes and the electrochemical double layer. The impact of structural changes on electrochemical reactivity, and likewise the impact of electrochemical processes on electrode structure are discussed. Measurements of the Au (111) reconstruction in alkaline solution indicate that the presence of CO causes the partial lifting of the reconstruction; it is suggested that this leads to an increase in defects and this is the underlying reason for CO promoted gold catalysis. In-situ SXRD measurements with a non-aqueous electrolyte are presented, representing a technological advance in the study of electrochemical interfaces. Crystal truncation rods (CTRs) measured at the Pt (111) / non-aqueous acetonitrile interface are used to determine the structure of both the electrode surface and the electrolyte close to the interface. The results indicate that acetonitrile undergoes a potential dependant reorientation but, in the presence of molecular oxygen, the acetonitrile molecules close to the electrode are dissociated and therefore cannot reorient. Measurements of CTRs at the Pt (111) / electrolyte interface for several aqueous electrolytes are combined with CTRs measured in non-aqueous acetonitrile to explore the dependence of surface relaxation on adsorption. Fits to CTRs are also used to determine the double layer structure at aqueous Pt (111) / acetonitrile interfaces and how it varies with acetonitrile concentration. The results indicate that the acetonitrile adsorption increases with concentration and that the double layer region compresses.

The primary focus of this thesis is understanding the production of magnetic fields during laser-plasma experiments. Each chapter investigates a different mechanism of producing magnetic fields. The first is from the by-product of launching asymmetric shocks which drive Biermann battery generated magnetic fields. The second looks at the reconnection of magnetic fields between two laser focal spots and the third is from fields produced around a current carrying loop target. Blast waves are investigated in the laboratory using a fast framing camera to capture multiple images on a single shot. In analysing the images, the blast wave's trajectory is compared to a Sedov-Taylor solution and the coupling of the laser energy into the shock wave is calculated to be 0.5-2%. The evolution of the blast wave's shape is characterised by fitting an ellipse to the outer edge and is observed to progress into a more symmetrical shape. Calculations show that two shocks produced in the interaction cause the change in ellipticity. We experimentally demonstrate that when two laser spots are placed in close proximity reconnection occurs. Diagnostics, including proton radiography, X-ray detectors and an optical probe, record and diagnose the existence of a semi-collisional reconnection event. The experimental data and simulations show that both Nernst and anisotropic pressure effects need to be taken into account for understanding and predicting the correct plasma dynamics observed. Magnetic fields are produced by driving a current through a loop attached to two plates and new measurements recording the voltages induced are presented in this thesis. It is found that the predicted values for the resistance, capacitance and inductance do not match those extracted from the experimental data and reasons for these are presented. Ideas for furthering this research to enhance our understanding in this area are given.

In the high confinement mode (H-mode) of tokamak operation, sharp gradients and the resulting high bootstrap current near the edge of a tokamak plasma (the pedestal) typically trigger eruptions called edge localised modes (ELMs). On the ITER scale, these have the potential to cause unacceptable erosion of materials. However, there exist scenarios, such as the quiescent H-mode (QH), where there are no ELMs. The ELITE code was originally developed to efficiently calculate the edge ideal MHD stability properties of tokamaks, optimised for the intermediate-high toroidal mode number, n, modes associated with ELMs. In QH-mode the limiting MHD is typically low n. Chapter 3 presents the extension of the ELITE code to arbitrary n. Chapter 4 presents successful benchmarks against the original ELITE code as well as GATO and MARG2D at low n. A first application of the new ELITE code was to study the stability of the QH-mode pedestal in DIII-D. Results from this study are presented in Chapter 5, which show the presence of low n phenomena. Additionally, understanding the pedestal performance losses in JET ITER-like wall (ILW) plasmas is vital to the success of future JET and ITER experiments. Chapter 6 presents an inter-ELM pedestal stability study, which compares the pedestal evolution to the criteria of the pedestal structure model, EPED. These results suggest that maximising the region of plasma that has second stability access will lead to the highest pedestal heights and, therefore, best confinement - a key result for optimising the fusion performance of JET and future tokamaks, such as ITER.

The flow of a Newtonian fluid is known to become unstable when the viscosity does not dominate its dynamics. This behaviour has traditionally been characterised by the non-dimensional Reynolds number, which measures the ratio between inertial and viscous forces. However, in some complex fluids, instabilities may be driven by an elastic mechanism that is determined by the evolution of the fluid microstructure. Molecular dynamics simulations offer a methodology for studying the dynamics of molecular fluids at the microscale. Macroscopic-type flow instabilities are examined with novel molecular dynamics simulations of shear flow between two concentric rotating cylinders. The basic flow of a Newtonian fluid bifurcates at a critical Reynolds number within 3% of the theoretical prediction, where beyond this value counter-rotating vortices form in the Taylor-Couette flow configuration. A spontaneous development of waviness in the vortices is observed at higher Reynolds numbers, and further simulations with polymers in solution as the sheared fluid are performed. Molecular dynamics simulations, however, become prohibitively expensive for large macroscopic flows. The present work addresses this problem for the context of planar shear flow of a Newtonian solvent over polymers grafted to a solid substrate, using a new software library developed for performing massively-parallel continuum-molecular hybrid simulations.

This thesis presents theoretical research on microscopic measuring devices and thermal machines constructed from single trapped atoms. We study several variants on this theme, with a particular emphasis on their application to ultracold atom physics. The first part of the thesis is about quantum refrigerators powered by thermal absorption rather than by external work. We propose and detail how such a machine may be practically constructed with a trapped atom placed inside an optical cavity, and employed to cool the atom close to absolute zero temperature using only collimated sunlight as an energy source. We then show that quantum absorption refrigerators in the strong-coupling regime exhibit coherent oscillations, thus enabling one to outperform a typical classical refrigerator by reaching lower temperatures than the steady state in a finite time using quantum coherence. The second part of the thesis studies the use of impurity atoms as probes of ultracold atomic gases. We discuss two different thermometry methods using impurities which are sensitive to temperature differences on the order of nanokelvin or less. We characterise the precision of the proposed thermometers by explicit calculations in the context of both weakly and strongly interacting atomic Bose gases. Finally, we study impurities immersed in a cold atomic Fermi gas realising a superfluid. We show that the impurities' energy dissipation rate probes the spectrum of density fluctuations in the gas, providing nondestructive access to various properties of the superfluid order parameter along the crossover from a Bardeen-Cooper-Schrieffer (BCS) state to a Bose-Einstein condensate (BEC).

The microscopic picture for fractional quantum Hall effect (FQHE) is difficult to work with analytically for a large number of electrons. Therefore to make predictions and attempt to describe experimental measurements on quantum Hall systems, effective theories are usually employed such as the chiral Luttinger liquid system. In this thesis the Monte Carlo method is used for Laughlin-type quantum Hall systems to compute microscopic observables. In particular such computations are carried out for the large system size expansion of the free energy. This work was motivated by some disagreement in the literature about the form of the free energy expansion and is still an ongoing project. Tunnelling in the FQHE is an interesting problem since the tunnelling operators are derived from an effective theory which has not yet been checked microscopically. To perform a test for the effective tunnelling Hamiltonian, microscopic calculations were performed numerically for charges tunnelling across the bulk states of a FQH device. To compute these matrix elements, two methods were found to overcome a phase problem encountered in the Monte Carlo simulations. The Monte Carlo results were compared to the matrix elements predicted by the effective tunnelling Hamiltonian and there was a good match between the data. Performing this comparison enabled the operator ordering in the effective tunnelling Hamiltonian to be deduced and the data also showed that the quasiparticle tunnelling processes were more relevant than the electron tunnelling processes for all system sizes, supporting the idea that when tunnelling is considered at a weak barrier, the electron tunnelling process can be neglected.

In this work we study new ways to observe and characterize specific fractional quantum Hall (FQH) states. In the first chapter we investigate the possibility to realize specific FQH states in bilayer graphene (BLG). BLG is a novel material in which the electron-electron interaction can be tuned with the help of external parameters. This allows one to make one or another FQH state favourable. We develop a framework for theoretical investigation of the stability of FQH states in BLG. We apply our framework to investigate the stability of the Pfaffian state. We find that the region in which our framework allows for making reliable predictions is quite restricted because of Landau level mixing effects. However, within that region we find the conditions under which the Pfaffian is more stable than in the conventional "non-relativistic" systems. These conditions can, in principle, be realized experimentally. In the second chapter we focus on characterizing the FQH states with the help of measurements of the noise of the electric current tunnelling between two FQH edges. We develop a theoretical framework allowing for analysing such data, and test it by successfully applying it to describe the results of the experiment [Bid et al., Nature 466, 585 (2010)]. We further develop our framework and show that it is possible to determine the tunnelling quasiparticle scaling dimension from such measurements. We also investigate experimental conditions necessary for this.

In this thesis we consider the implications of radiation reaction for the behaviour of electric and electromagnetic waves propagating through a plasma. A plasma contains a very large number of particles, and obtaining a description of the dynamical behaviour of each individual particle is impractical. In Section 2 we detail how one can model such a plasma by treating the plasma as a fluid, and rather than examining the individual particles we instead look at the bulk properties of the fluid. Such a model is based upon the equation that describes the motion of a single particle, hence we introduce this first in Section 1. As such, Section 1 should be viewed as an introduction to the necessary background one needs in order to understand the subsequent sections. We begin by reviewing the Lorentz force equation, from which one can determine the motion of a charged point particle in the absence of radiation reaction. Finding solutions to this equation, and plotting the particle's subsequent trajectory not only allows us to introduce notation that will be used throughout this thesis, but is also a point of comparison that can be referred back to in the subsequent sections. The concept of radiation reaction is first introduced in Section 1.1.2, where we learn that the Lorentz Force Law does not describe the motion of a charged particle completely. It is here that we describe the origin of radiation reaction, as well as introducing the Abraham-Lorentz-Dirac (ALD) equation, the first covariant equation derived that determines the motion of a particle when the effects of radiation reaction are included. Not only is this equation of great historical significance, but it is used in the derivation of the equations of motion of Section 2.2, and hence is pivotal to the work carried out within. It is well known that not all solutions to the ALD equation are physically reasonable. Considering the importance of the ALD equation in this thesis, it is prudent to review this property, and we do so in Section 1.1.2. Many alternative models to the ALD equation have been proposed in an attempt to eliminate these unwanted solutions. We must also attempt to eliminate such unwanted behaviours from our solutions, and so Section 1.1.3 reviews the approach used to generate the Landau-Lifshitz (LL) equation. We carry out a similar procedure with our equations, and so a review of the LL equation is called for. This completes the necessary background in radiation reaction, however we still need to introduce some fundamentals of a plasma. All of the work within this thesis is carried out within the warm fluid approximation, which we detail in Section 2.2. This allows us to use a perturbative approach when seeking solutions; we assume that the solution we seek is that of the cold fluid, plus a small correction term. As such, it is necessary to first review the properties of a cold plasma. We end the introductory section with an example of where experiments are currently taking place that involve electromagnetic waves travelling through plasma. Section 2 reviews the creation of the model we use in our description of a plasma. In Section 2.2 we build upon a recently developed kinetic model of a collection of charged point particles that incorporates radiation reaction. From this model, we proceed to generate an infinite hierarchy of moment equations that describes our system. We subsequently introduce a new closure mechanism to this model, inspired by closure mechanisms associated with the warm fluid approximation, thus obtaining a finite system of equations. Although this kinetic model has been used previously to generate a system of moment equations, the method used to close them was ad hoc, and the solutions predicted by the fluid model did not match up with that predicted by the kinetic model itself. The closure mechanism we use is a simple extension of that of the warm fluid, and needs no additional assumptions regarding the nature of the system. Additionally we show that the results it predicts are identical to those derived directly from the kinetic theory upon which it is based. Hence, the finite system of moment equations we derive is new work. The remainder of Section 2 is focussed on using this model to determine the bulk properties of such a fluid in equilibrium (solutions which we perturb around in subsequent sections) and also represents entirely new work. In Sections 3 and 4 we use what we have learned in the previous sections to model small amplitude electric and electromagnetic waves propagating through the plasma. We examine the dispersion relations of such waves, as well as (when possible) how such waves modify the bulk properties of the plasma. Finally, in Section 5, we turn our attention to electric waves of arbitrarily strong amplitude. Sections 3 - 5 represent entirely new work.

This thesis is concerned with plasmas and high field physics. We investigate the oscillations of relativistic plasmas using a kinetic description (Chapter II), a macroscopic fluid moment description (Chapter III), a quantum description (Chapter IV as a brief exploration) and Born-Infeld electrodynamics (Chapter V). Using a kinetic description, we examine the non-linear electrostatic oscillations of waterbag-distributed plasmas and obtain the maximum electric field Emax (Chapter II). Using a macroscopic fluid moment description with the closure of the Equations Of State (EOSs), we obtain the maximum electric field Emax of electrostatic oscillations for various waterbag-distributed electron fluids, which may imply the advantages of some fluids with particular EOSs in the aspect of particle acceleration. Furthermore, we find that fluids with a more general class of EOSs may have the same advantages (Chapter III). A brief numerical calculation of an ODE system originating from the Maxwell equations and a Madelung decomposition of the Klein-Gorden equation with a U(1) field shows that electrostatic oscillations decay in a Klein-Gorden plasma due to quantum effects (Chapter IV). With calculations using the Born-Infeld equations and the Lorentz equation, we investigate the electrostatic and electromagnetic oscillations in cold plasmas in Born-Infeld electrodynamics (Chapter V). For the electrostatic oscillations we find that the electric field of Born-Infeld electrodynamics behaves differently from that of Maxwell electrodynamics. However, Born-Infeld electrodynamics gives the same prediction as Maxwell electrodynamics for the maximum energy that a test electron may obtain in an electrostatic wave (Section VA). For electromagnetic waves, the dispersion relation and the cutoff frequencies of the “R”, “L” and “X” modes of electromagnetic waves in Born-Infeld cold plasma are deduced to be different from those in Maxwell cold plasma. The cutoff frequencies (when the index of refraction n → 0) are also obtained, showing the advantage of “O” mode waves for the acceleration of particles (Section VB).

A discussion on the momentum evolution of an impurity interacting via a finite delta potential repulsion with a non-interacting fermionic background gas is presented. It has recently been shown that the momentum evolution of this system displays two interesting features, namely a non-zero thermalised value and a longlived quantum mechanical oscillation around this plateau named “quantum flutter” [Mathy, Zvonarev, Demler, Nat. Phys. 2012]. We discuss revivals in the momentum of the impurity, which have been seen before but not yet thoroughly investigated. Subsequently it is shown the quantum flutter and revivals are caused by disjoint sets of eigenstate transitions, and this fact is used to interpret some of their aspects. This attribution of momentum features to different eigenstate subsets allows quantitative reproduction of these features with much less computational expense than has so far been possible. Finally some results on the distribution of the momentum of eigenstates and their relation to the momentum of the impurity once the system has been thermalised are presented along with a discussion on the time averaged infinite time value of the momentum and its comparison to different eigenstate subsets.