The azimuthal magnetic field and current density structure of a Plasma Focus device, have been investigated by the observation of the Faraday rotation of a ruby laser probe beam. The magnetic field and current distributions play important roles in plasma compression, heating, confinement, stability, and particle acceleration. However, in over two decades of research, no satisfactory experimental data on the field or the current have been produced. The results reported are of the first measurements of magnetic field and current distribution in the Plasma Focus, using a non perturbing diagnostic technique. A full description of the experimental apparatus and method, the physics of the differential polarimetry (with refraction effects included), and theoretical reviews of Faraday rotation, birefringence, dichroism, and refraction, are given. It was found that during the collapse phase of the discharge, times t = -10 ns to t = 0 ns (peak compression), the current and field are confined to the plasma skin. The penetration depth is 0.56 mm, and the resistivity is classical. During the dense pinch phase, between t = 0 ns and t = +10 ns, the plasma develops a turbulent core, of radius 2 mm, in which the resistivity is highly anomalous (by a factor 6000). This results in a rapid diffusion (lasting approximately 10 ns) of field and current (typically 20 of the total) into the core. Particle acceleration is suppressed at this stage because the ion Hall term is less than unity. Outside this core, the resistivity is classical, and the current is carried in the plasma skin. At times t = +10 ns to t = +15 ns, axial current filamentation was observed. These filaments last less than 2.5 ns, and carry in excess of 12% of the current. Future studies of the filamentation should lead to a better understanding of the intense neutron production observed in Plasma Focus devices.

The frequency spectrum of density fluctuations in a Plasma Focus device has been investigated by Thomson scattering of laser light. A ruby laser scattering diagnostic has been developed to enable the co-operatively scattered ion feature, Si(k,w) to be measured simultaneously along different density fluctuation k vectors. Data derived from this apparatus is interpreted in terms of the time and space variations of local plasma parameters such as electron and ion temperatures, drift velocity, bulk velocity and level of turbulence. The total scattered intensity, Si(k) is shown to depend on the direction in whichthe fluctuations are sampled by the scattering geometry, with scattered intensities along a Je vector parallel to the current flow enhanced considerably above thermal levels. The data is found to be most satisfactorily interpreted in terms of a double radial shell model of the plasma, each shell with its own characteristic particle temperatures, density, drift and bulk velocity. At peak compression of the pinch onto the z-axis of symmetry for example, the core plasma has typically electron and ion temperatures Te = 200 eV, Ti = 250 eV respectively, while the outer sheath region exhibits a shot to shot variation in the temperature structure, with Te=2.3 keV, Ti=850 eV and Te = L.65 keV, Ti = 1.4 keV respectively. An examination of the relative enhancementand broadening of Si(k,w) along the various k-vectors has been interpretedin terms of current driven turbulence. The various mechanisms for inducing turbulence have been considered and lower-hybrid drift, electron-cyclotron drift and ion acoustic instabilities are thought to play a role in the various phases of the plasma discharge. The development of the multiple Je scattering diagnostic has overcome the ambiguity in interpreting scattering results from an irreproduceable inhomogeneous plasma. This problem has restricted the interpretation of the results in previous scattering experiments on the Plasma Focus using single Je vector scattering arrangements.

Wannier functions provide us with a means for the development of rigorous theorems which are analogous to the crude theorems we might derive with a tight binding approximation. However, a good and accurate Wannier function would be extremely difficult to calculate and its structure would be quite complicated. Excluding calculations obtained using the O.A.O. approximation few works exist on the mathematical properties of Wannier functions and only very few have been explicitly determined. The present study attempts to provide a partial solution for this situation and seeks to extend the use and knowledge of these functions. First, a theoretical investigation is made of the mathematical properties of Wannier functions and then some calculations are carried out to obtain some of these functions for various forms of potential fields. The original results obtained concern; I) Free electron Wannier functions for many of the familiar crystal types. II) A method for obtaining Wannier functions from relatively simple functions (unperturbed Wannier functions). The method has been appli ed to several particular cases (potential field with inversional symmetry etc.) and has been modified for other applications. III) Nearly free electron Wannier functions calculated both using analytical methods and the method outlined in section II. IV) The extension of Kohn's one dimensional treatment to three dimensions using a new approach.

A primarily numerical investigation of the nonlinear g mode in the reverse field pinch is presented. A two dimensional study of the nonlinear m=0 g mode is made using two computer codes. One code solves the resistive incompressible MHD equations, for the m=0 mode, using a mixed explicit/alternating direction implicit scheme. Whilst for the second code a truncated Fourier expansion is used to reduce the two dimensional m=0 equations to a larger one dimensional set, which are then solved using a mixed explicit/Crank-Nicholson scheme. A stabilising mechanism has been found in which the g mode acts to flatten the pressure in the vicinity of its singular surface. A quasi-linear scaling argument is given to explain this pressure flattening mechanism. Ohmic heating is found to counteract this stabilising effect by increasing the gross pressure in the pinch. The final nonlinear state of the g mode depends on the competition between the pressure flattening and ohmic heating mechanisms. To study modes of any helicity a spectral code is developed to solve the compressible resistive MHD equations in a periodic cylindrical system. Simulating energy loss processes by removing the ohmic heating terms is shown to lower the final nonlinear growth rate of the m=0 g mode. The m=l mode is examined and the same dominant nonlinear mechanisms are found to apply. Some tentative mixed helicity calculations are also presented, but these studies are far from complete. The two dimensional studies allow the magnitudes of typical magnetic fluctuations due to the g mode to be estimated. Using a field line tracing code these fluctuations are shown to give rise to ergoaic field line behaviour. Estimates of the enhanced electron transport which occurs because of this behaviour are given. The relevance of these results to experimentally observed phenomena is discussed.

A selection of free-standing fine-wire grids with different wire spacings have been wound for use as spectroscopic components at millimetre and submillimetre wavelengths. The performance of the grids has been investigated extensively and found to be in good overall agreement, both qualitatively and quantitatively, with calculations made using a least-squares method developed by Beunen. Where discrepancies occur they are attributed to the effect of uneven spacing of the wires. A microcomputing system based on the Z80 8-bit microprocessor has been built to provide data acquisition and Fourier transformation for a Fourier spectrometer. Measurements have been made of the far infrared optical constants of KC1 and KBr crystals by dispersive Fourier transform spectroscopy at temperatures in the range 7-500K using instruments equipped with both mylar and wire grid beam dividers. The results have been used to calculate the dielectric functions and the an harmonic self energy functions of the q = 0 transverse optic modes in these crystals. The frequencies of the transversive optic (TO) and longitudinal optic (LO) modes determined from the dielectric functions are in good agreement with the accepted values, and in the case of KBr, the frequency-dependence of the an harmonic self-energy functions determined at room temperature is in good agreement with calculations made by Bruce.

High speed optical measurements are important for laser fusion studies. At present, streak cameras provide the most versatile direct optical recording techniques with picosecond time resolution, but they possess limited dynamic range. Their poor performance is believed to be partly due to space charge effects at the electron optical crossover point. This was experimentally investigated in this thesis, but found to be relatively unimportant. Effects inside the photocathode are suggested as an alternative explanation. The dynamic ranges, sweep speeds and linearity of two commercial streak camera systems were measured using a modelocked dye laser and an etalon. The spatial resolution was measured with a test chart. These two streak cameras were then used to study the temporal evolution of the backscattered fundamental and harmonic emission spectra from micro balloon targets when they were irradiated by a neodymium laser. The spectra at the fundamental frequency displayed the characteristic red shift of Brillouin scattering. The spectral features of the 2wq harmonic are explained in terms of ion acoustic turbulence driven by the electron return current. The harmonic spectra were observed to consist of two wings, symmetrically shifted to the blue and red, with a separation depending on the electron temperature. Both the 2w and 3w/2 harmonic emission were found to consist of picosecond pulsations which are attributed to density perturbations driven by the unstable ablation flow across a steepened density profile. Finally, proposals are made for the development of diagnostic techniques in laser produced plasmas.

A quartz crystal resonator has been used to excite shear waves at a frequency of 20.5 MHz in He films above and below the superfluid transition and just above the liquid-gas critical point. The wave has a viscous penetration depth 6-20 nm and the transverse acoustic impedance Z = R - iX of the film was found from changes in the quality factor and resonant frequency of the crystal. The thickness of a He I film was swept at constant temperature by creating a small temperature difference between the He film on the crystal and bulk liquid helium below it. Calculations of the impedance of a homogeneous film as a function of d/6 using transmission line theory show the film's thickness d could be swept from 1.5 to >60 nm . The impedance of six superfluid films of constant thickness in the range 14-23 nm has been measured for 0.4 T T . From the impedance in the ballistic limit, wI >> 1, the average probability of the quantum evaporation of a ⁴He atom by a roton incident upon the liquid-vapourinterface is estimated to be ~0.35 . A resonance, the temperature of which was dependent on film thickness, was observed in the superfluid film and has tentatively been identified with the resonance in the A/4 Kelvin mode of vortices pinned to the crystal surface. The transverse acoustic impedance Z of helium has also been measured 49 mK above the liquid-gas critical point for pressures up to 2000 torr. In the highly compressible critical region, the impedance shows the effects of the large density gradients that develop close to the crystal surface under van der Waals1 forces. At low pressures, the transition to non-hydrodynamic behaviour is observed, and it is estimated that a fraction 0.2 of He atoms incident upon the crystal are diffusely scattered from it.

A study of harmonic generation in Laser produced plasmas is presented. Experiments were performed on Royal Holloway College's carbon-dioxide laser system and on the Rutherford Appleton Laboratory's neodymium-glass laser facility. Various targets were irradiated. The backscattered radiation was spectrally analysed in the vicinity of the incident(w0) and twice incident frequency(2w0). Optical and x-ray diagnostics were also undertaken. Theoretical models for harmonic generation in laser produced plasmas by Cairns, Erokhin, Silin and others are reviewed and compared to the experimental results. It is shown that theories due to Cairns and Silin give reasonable estimates of plasma temperature, from the experimental shift of the second harmonic (2w), though the former requires the plasma density scale-length to be known to a greater accuracy. However, Cairns explains satisfactorily the observed structure of the second harmonic spectra. Other theories account well for the observed dependence of the intensity of the second harmonic to that incident. Finally, an attempt is made to explain features of the 2w spectrum in terms of plasma motion, resonance absorption, density profile modification and ponderomotive forces.

An experimental investigation of the impurity behaviour of the Reversed Field Pinch (RFP) HBTX1A/B is presented. The investigation was initiated by determining the impurity composition of the plasma through spectral surveys utilising both photographic and multi-channel techniques. The principal low Z impurities were found to be carbon and oxygen while the principal high Z impurity was iron with smaller amounts of chromium and nickel. The investigation was extended using quantitative techniques in the Extreme Vacuum Ultraviolet (EVUV), Vacuum Ultraviolet (VUV) and Ultraviolet(UV)/visible regions of the spectrum. A novel technique involving a scintillator imaged on to an Optical Multichannel Analyser (OMA) was used for quantitative work in the VUV region and a unique scanning toroidal mirror system was also developed for this range. It was found that the impurity concentration was a small fraction of the electron density (5% 0, -1% C, -0.2% Fe) and, in conjunction with the bolometric results from other workers, it was found that the impurity radiation was a small fraction (-4%) of the global input power (for I/N >7 x 10-14 A.m) and did not lead to radiative cooling at any position in the discharge. The value of the resistivity calculated from the impurity composition was significantly less than the value obtained from helicity balance calculations, assuming a perfect boundary. The impurity diffusion coefficient for carbon was determined using a unique technique based on spatial measurements of CV emission. The measured value of 100-150 m2.s-1 was anomalously high compared to neoclassical predictions. It was not possible to determine the diffusion mechanisms of either the bulk plasma or the impurities, hence this measurement represents the first step in a more detailed investigation of RFP impurity dynamics.

The effects of quadrupolar interactions on the thermodynamics, statics and dynamics of linear molecules consisting of two Lennard-Jones centres is studied for the liquid phase. This is illustrated by using nitrogen, chlorine and carbon dioxide molecules as representative of the differing bond lengths that can arise in these systems. The changes due to the magnitude of the quadrupole moment are investigated for the chlorine system. Calculations of the structure of two-Lennard-Jones centre fluids is also carried out using the RISM method.