# Masters Degrees (Physics)

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Item Theoretical studies of the crossfield current-driven ion acoustic instability.(1979) Bharuthram, Ramashwar.; Hellberg, Manfred Armin.Abstract available in PDF file.Item X-ray crystallographic study of a trinuclear ruthenium organo-metallic complex.(1984) Subramony, Loganathan.; Engel, D. W.; Moodley, K. G.The crystal structure of Ru₃ (C0)₁₀(C₆H₅)₂PN(C₂H₅) P(C₆H₅)₂ (RUC)PNP) has been determined by single crystal X-ray analysis. The crystals are tri-- clinic with space group PĪ. The unit cell of dimensions a = 14,732; b = 12,386; c = 10,982 Å; α = 104,52; β = 100,64; γ = 94,89° contains two formula units. The unit cell and space group were determined by photographic deJong-Bouman and precession techniques using CuKα radiation. A procedure was developed for more accurate alignment of the crystal for rotating crystal techniques. Intensity data were collected on a Philips PW1100 four-circle diffractometer with MoKα radiation. The positions of the Ru atoms were determined from Patterson syntheses and the remaining atoms located using successive Fourier synthesis. The structure was refined by blocked full-matrix least-squares methods to a residual of R = 0,0537 for 3538 independent reflections with I > 5σ(I) with 300 parameters in the final refinement. The phenyl rings and the CH₂ and CH₃ moities were refined as rigid groups with H-atoms included at fixed positions. A difference Fourier synthesis was done and showed no significant peaks. RUCOPNP is derived from Ru₃(CO)₁₂ by substitution of two equatorial carbonyl ligands by the P atoms of a single edge-bridging (C₆H₅)₂PN(C₂H₅)P( C₆H₅)₂ ligand (PNP). In both complexes the Ru atoms are arranged in a triangle and have distorted octahedral geometry. The introduction of the PNP ligand to the symmetrical parent Ru₃(CO)₁₂ has the following effects: (a) It causes a contraction of the ligand-bridged Ru-Ru bond distance to 2,798 Å whereas the other Ru-Ru distances are 2,860 and 2,848 Å which are close to the distances in the parent compound; (b) It causes the adjacent equatorial carbonyl ligands to rotate towards the PNP ligand by 11,4°. (c) It causes considerable deviations of some of the axial carbonyl ligands from the normal to the plane containing the Ru atoms.Item A study of the 90Zr(n,d)89Y reaction.(1986) Bawa, Ahmed Cassim.; Bharuth-Ram, Krishanlal.; McMurray, W. R.A study has been made of the 90 Zr(n,d) 89 Y reactlion at an incident neutron energy of 22 MeV. The experimental aspect of the study was performed at the Van der Graaf facility at the National Accelerator Centre, using a particle spectrometer developed by K Bharuth-Ram and W R McMurray for the study of neutron-induced charged-particle emissions. The spectrometer, which consists of a telescope of three multiwire proportional counters and a curved plastic scintillator, permits the simultaneous accumulation of data over an angular range of 80°. Solid-angle- calculations have been performed to correct for the effect of the geometry of the system on the angular distribution of the cross-sections. A review has been made of the shell model of the nucleus, the optical potential model and the distorted waves method (or DWBA) for the analysis of direct nuclear reactions. A distorted-waves method analysis of the reaction is performed with the code DWUCK 4 and the resulting angular distribution of the various cross-sections are compared with the experimentally obtained data. ThIs comparison produces spectroscopic factors which are used to perform some analysis of the nuclear structure of the 90 Zr nucleus.Item The crossfield current-driven ion acoustic instability in a two-ion plasma.(1987) Govender, Jagathesan.; Bharuthram, Ramesh.The behaviour of the crossfield current-driven ion acoustic instability in a plasma containing two ion species is theoretically examined. In our model the electrons are assumed to be hot and the ions cold, i.e. Tₑ »Tᵢ (~ 0), where both ion species are given the same temperature. The length and time scales are such that the electrons are magnetized and the ions unmagnetized. The linearised Vlasov equation is used to set up a dispersion relation for electrostatic waves for Maxwellian equilibrium velocity distributions of the electrons and ions. For the ion acoustic wave, a study is made of the dependence of the critical electron drift velocity (Vͨₒ) required to excite an instability on several parameters. The parameters include light ion fraction, heavy to light ion mass ratio, magnetic field strength and the propagation angle. In general the maximum value of Vͨₒ is found to be smaller than that for an unmagnetized plasma. Approximate analytic solutions of the dispersion relation are used to make comparisons with solutions from the full dispersion relation. The effect of drifts due to inhomogeneities in external magnetic field, perpendicular electron temperature and electron density on the growth rate of the ion acoustic instability are investigated in the ion rest frame. Finally, in a reference frame in which the electrons are stationary, both ion species are given external drifts. The effects of the ion drift velocities (both equal and unequal), electron to ion temperature ratio, light ion fraction, and heavy to light ion mass ratio on the growth rate of the ion acoustic instability are then studied.Item Nuclear structure studies with (n,d) reactions.(1988) Naidoo, Ravenderan Yagambaram.; Bharuth-Ram, Krishanlal.; McMurray, W. R.The ²⁷AI(n,d)²⁶Mg and ⁵⁶Fe(n,d)⁵⁵Mn reactions have been studied at 22 MeV incident energy. The 6MV Van de Graaff facility at the National Accelerator Centre, Faure was used for the experimental aspects. An (n, charged particle) spectrometer was used to detect the energy and angle of the outgoing deuterons. The spectrometer allows for accumulation of particle discriminated data over an angular range of 80⁰. The intrinsic geometry of the spectrometer limits its' angular resolution to ~ 5⁰ (FWHM). The spectrometer has an energy resolution of ~ 0.7MeV(FWHM). A detailed study of the experimental system has been conducted and the proportional counters in particular were extensively investigated. A review of the relevant nuclear models for the target and residual nuclei is presented, together with a theoretical outline of the reaction mechanism for the (n,d) reaction. The distorted waves method approach is used in the analysis of the reaction cross sections. Optical potentials are used to simulate the incoming and outgoing distorted waves and thus generate the theoretical cross sections for the (n,d) reactions. The shapes of the angular distributions of the reaction cross sections for different orbital angular momentum transfers are compared to obtain a fit. Comparison of experimental and theoretical cross sections produce the spectroscopic factors which reveal the occupancy or vacany of level states and hence the single particle nature of these states. It was concluded from the study that the shell model of the nuclei under investigation gives a very good description of the results obtained for the (n,d) reactions.Item Profile analysis of X-ray powder diffraction data.(1988) Naicker, Vishnu Visvanathan.; Engel, D. W.Various strategies have been tested for obtaining integrated intensities from x-ray powder diffractometer data. An asymmetric pseudo-Voigt profile function was used to fit the pattern in the region above 2θ = 35̊ (Cu-Kα radiation). At lower angles where the asymmetry was strongest and the profile function not suitable the peaks were integrated numerically. A smooth background function was estimated from the regions of minimum intensity of the pattern. The profile parameters were initially refined in small ranges of about 10̊ 2θ in order to determine their 2θ-dependence. Thereafter final refinements of peak intensities were undertaken using the profile parameters thus determined. Analysis of data from the mineral Fe-akermanite, Ca₂Mg₀. ₄Fe₀. δSi₂O₇, generated 173 integrated intensities with 1 > 2δ(1) out of 187 positions separated in 2θ by more than 0,02̊. Of the total of 213 reflections in the range, those overlapping exactly or separated by < 0,02̊ were treated as single peaks. The structure was refined using an overall isotropic temperature parameter and a parameter to compensate for preferred orientation, giving an unweighted residual of 10,4% for 14 parameters.Item A study of the interaction of strong electromagnetic waves and anisotropic ion beams with a background plasma.(1989) Singh, Pravin.; Bharuthram, Ramesh.The interaction of an anisotropic (in velocity space) ion beam with an isotropic background hydrogen plasma is theoretically investigated. The length and time scales are such that both the ions and electrons are magnetized. Using linear theory, the electrostatic dispersion relation is derived, and solved fully, using no approximations. It is shown that the anisotropy can significantly enhance the instability growth rates as compared to the isotropic case. The importance of ion magnetization is illustrated. Comparisons are made with unmagnetized plasma results. The modulational instability of an arbitrarily-large-amplitude electron cyclotron wave along the external magnetic field is investigated, taking into account the relativistic electron quiver velocity and the relativistic ponderomotive force. Three types of plasma slow responses, the forced-Raman, quasistatic and forced-quasistatic, are considered and a parameter study of the instability growth rates is carried out.Item High repetition rate continuously tunable CO2 laser system investigation.(1990) Botha, Lourens Rasmus.; Michaelis, Max M.The purpose of this thesis was to investigate certain factors important for the operation of a high repetition rate continuously tunable CO2 laser. The tuning range of specific importance for this research program was the R30 region within the ten micron band, since this frequency is of great importance for the laser isotope separation of uranium. This research program focused on: (i) Lowering the pressure at which viable continuous tunability could be achieved. {ii)Resonator design and analysis. {iii)Investigating the feasibility of using water capacitors in a high repetition rate laser system. A theoretical as well as an experimental investigation was done into the use of CO2 isotopes to lower the pressure at which continuous tunability in the R30, ten micron band could be achieved. A theoretical analysis was done into the use of a three mirror resonator with an etalon and a grating to ensure single longitudinal mode tuning in the R30 region. Such a resonator was designed and experimental results obtained were compared with those predicted by the theoretical analysis. A study was done into the use of water as a dielectric medium in a high repetition rate pulse power supply. A mathematical model, describing the electric breakdown of water,was developed. This was compared with published experimental results. Certain parameters important for the design of a water capacitor were experimentally measured. These include the intrinsic time constant,dielectric constant and resistivity of the water. A design proposal as well as a comparison between a water capacitor and other capacitor technologies are presented.Item Linear properties of the cross-field ion acoustic instability in a double plasma device.(1990) Dempers, Clemens Arnold.; Barrett, P. J.This thesis deals with the dependence of the linear spatial growth rate of the cross-field ion acoustic instability on various plasma parameters. A kinetic theory model, with elastic and inelastic ion-neutral collisions included, is presented and used to conduct a numerical survey of the instability. The growth rate is computed as a function of distance into the plasma, taking into account the attenuation of the ion beam by charge exchange collisions. Further calculations show the variation in growth rate as a function of the following quantities: electron and ion beam temperature, electron density, beam velocity, background ion temperature, magnetic field, the angle between magnetic field direction and wave vector and the finite width of the plasma. The instability was observed in a double plasma device where an ion beam was passed through a background of stationary magnetized electrons. The magnetic field was sufficiently weak to allow approximately rectilinear ion motion. The growth rate of the wave was studied using interferometer techniques. It was identified by the dispersion relation as the cross-field ion acoustic wave propagating as the slow mode of the beam. It was found that the background ions play an important role in determining the phase velocity. Experimental data of the growth rate dependence on wave number, beam velocity and magnetic field strength were found to be well described by the theoretical model. The growth rate dependence of magnetic field direction on plasma width was furthermore found to be in qualitative agreement with the model.Item Plastic shear in a model amorphous solid.(1992) Moji, Nthobane Cable.; Jackson, Paul J.Abstract available in PDF.Item Shape invariance in supersymmetric quantum mechanics.(1992) Welter, Allard.; De Lange, Owen Leon.Abstract available in PDF.Item Mössbauer study of the hyperfine magnetic field and electric field gradient at Fe sites in synthetic diamond.(1992) Govender, Nadaraj.; Bharuth-Ram, Krishanlal.Mossbauer Spectroscopy has been used to investigate the site of Fe inclusions in a suite of synthetic diamonds (de Beers MDAS). Information on the hyperfine magnetic fields and electric field gradients at Fe sites in the diamond grains were obtained from Mossbauer Spectroscopy of diamond grains ranging in size from 25 to 250 um. The Fe inclusions in these samples resulted from the synthesis of the diamond grains in which Fe was used as a catalytic solvent. The Mossbauer measurements were carried at room temperature with a constant acceleration spectrometer operating in transmission geometry. The samples with the largest grain size of 180-250 um gave a well defined six component magnetically split spectrum, similar to the Zeeman split sextet obtained for natural iron. As the grain sizes decreased the intensity of the magnetically split components became greatly reduced and a strong paramagnetic component appeared. At grain sizes 105-45 um the spectra are dominated by a central single line with some evidence of an asymmetric doublet. For the finest grain size 38-25 um, the reappearance of the six magnetic hyperfine splitting components together with the strong central single paramagnetic component was observed. The change in the Mossbauer patterns observed with decreasing grain size suggest that a rapid phase transition of the Fe inclusions from ferromagnetic to superparamagnetic takes place. The analysis of Mossbauer spectra yielded a value of the hyperfine magnetic field of Bhf = -32.4(4) T and an electric field gradient in the range of Vzz = 1.4(4) 1.8( 7) X 10'8 V.cm- 2 at the site of the probe s7Fe nucleus. These values compare favourably with other measurements.Item A satellite and ground based study of fine structure in VLF whistlers.(1992) Caldeira, Paulo S.; Hughes, Arthur R. W.The matched filtering technique for improving the spectral resolution of VLF whistlers, originally developed by Bhegin and Siredey (1964), has proven to be useful for extracting information about the magnetospheric plasma ducts along which a whistler has travelled. Ground based whistlers recorded at Sanae and Halley Bay, Antarctica, on day 149, 1985, show similarities in fine structure, namely a trace splitting at frequencies below 3.720 kHz. The travel time differences between the two traces below this frequency increase with decreasing frequency. It is shown that the path length of whistler energy is frequency dependant, and since electron gyrofrequency increases with decreasing altitude, the plasma density enhancement requirements for the wave to remain trapped in the duct increases with decreasing altitude. If this increasing enhancement is not present the wave will escape from the duct, the lower frequencies escaping first. It is proposed that the trace splitting observed in the fine structure analysis of these whistlers are the lower frequencies escaping from the topside and bottomside of the duct, and so travelling along two paths to the receiver having different path lengths and hence different travel times, The higher frequencies remain trapped in the duct, and therefore display only one trace. A satellite receiving system to receive the VLF data received by the Signal Analyser and Sampler (SAS) equipment aboard the ACTIVE satellite has been constructed at Durban. The design and construction is described in chapter 3. Due to the high noise environment no data has been collected to date in Durban. It is hoped that the receiving system can be moved further inland to a noise-free site for testing. This thesis is read with the "Whistler Analysis Software using Matched Filtering and Curve Fitting techniques - Users Reference Manual" written by the author to facilitate use of the matched filtering software.Item Instrumentation and operation of a new fatigue tester.(1993) Bird, Jeanette.; Jackson, Paul J.Abstract available in PDF.Item A study of plasma source ion implantation.(1993) Thomas, Kim.; Alport, Michael J.The work described in this thesis is an analysis of the Plasma Source Ion Implantation (PSII) process. A metal target is placed within a plasma, and pulsed to a high negative potential (10 - 50 kV). The electrons in the plasma close to the target are then repelled very rapidly, leaving an area of uniform positive charge. This causes an electric field to be set up between the plasma and the metal target. The ions close to the target are then accelerated towards the target by the electric field. The ions reach the target at high velocities, and implant deeply into the metal (-5 x 10-8 m), and form nitrides, which pin dislocations within the metal's atomic structure. The strength of the metal is therefore increased, and other properties such as the corrosion resistance of the metal are also improved. Metals that have undergone the PSII process have widely diverse applications. For example, in the motor industry, ion implanted metal punches last much longer than nitrided punches, while in the medical industry ion implanted metals are used for artificial limbs. A combination of a number of different analytic, numerical and simulation models are used to describe the PSII process, including the plasma behaviour and final nitrogen implantation profile in the metal target after the application of the voltage pulse. In all cases, a specific attempt has been made to realistically describe as closely as possible, the actual experimental arrangement at the University of Natal. For example: a waveform with a fast rise time, short plateau and exponential decay was used; the nitrogen plasma was more realistically described by a two species fluid to account for the measured N+, N; mix; and finally, the actual atomic composition for 304 stainless steel was used in the TAMIX particle simulation. This work thus models the whole PSII process, and could form the basis of future studies for the optimisation of the process.Item Radiating solutions with heat flow in general relativity.(1994) Govender, Megandren.; Hughes, Arthur R. W.; Maharaj, Sunil Dutt.In this thesis we model spherically symmetric radiating stars dissipating energy in the form of a radial heat flux. We assume that the spacetime for the interior matter distribution is shear-free. The junction conditions necessary for the matching of the exterior Vaidya solution to an interior radiating line element are obtained. In particular we show that the pressure at the boundary of the star is nonvanishing when the star is radiating (Santos 1985). The junction conditions, with a nonvanishing cosmological constant, were obtained. This generalises the results of Santos (1985) and we believe that this is an original result. The Kramer (1992) model is reviewed in detail and extended. The evolution of this model depends on a function of time which has to satisfy a nonlinear second order differential equation. We solve this differential equation in general and thereby completely describe the temporal behaviour of the Kramer model. Graphical representations of the thermodynamical and gravitational variables are generated with the aid of the software package MATHEMATICA Version 2.0 (Wolfram 1991). We also analyse two other techniques to generate exact solutions to the Einstein field equations for modelling radiating stars. In the first case the particle trajectories are assumed to be geodesics. We indicate how the model of Kolassis et al (1988) may be extended by providing an ansatz to solve a second order differential equation. In the second case we review the models of de Oliveira et al (1985, 1986, 1988) where the gravitational potentials are separable functions of the spatial and temporal coordinates.Item Modelling of the ballooning instability in the near-earth magnetotail.(1995) Dormer, Lee Anne.; Walker, Anthony David Mortimer.In recent years, many alternative models of the substorm process have been proposed to explain different aspects of this magnetospheric phenomenon. Some features in these competing models are compatible while others, such as the nature and location of substorm onset, remain controversial. The objective of this thesis is to assess the viability of the ballooning instability as a mechanism for initiating substorms. A review of the history and development of magnetospheric substorm research as well as a review of substorm models is presented. In these models, the crosstail current disruption responsible for the onset of the expansion phase is usually ascribed to the onset of some microinstability. An alternative triggering mechanism is a macroscopic magnetohydrodynamic instability such as the ballooning instability. To derive a threshold condition for the ballooning instability, a simplified magnetotail geometry with cylindrical symmetry near the equatorial plane is assumed. In such circumstances, the torsion of the magnetic field lines is zero and they can be characterised by their curvature. The hydromagnetic equations with isotropic pressure are linearised to find the dispersion relation. This leads to a threshold condition which depends on the pressure and magnetic field intensity gradients. In order to obtain realistic numerical results for the threshold condition, a quasistatic, self-consistent, two-dimensional numerical model of the magnetotail during conditions typical of substorm growth phase is used. The model involves solving the Grad-Shafranov equation with appropriate boundary conditions. It provides time-dependent magnetospheric magnetic field configurations that are characterised by the development of a minimum in Bz in the equatorial plane. Calculations of the detailed configuration of the magnetotail during onset allow an estimate of the instability criterion. In a model which does not allow an increase of pressure with radius, it is found that the magnetotail is not unstable to ballooning. Part of this work has been presented at a conference, viz.: Dormer, L.A. and A.D.M. Walker, Investigation of local MHD instabilities in the magnetotail using a two-dimensional magnetospheric convection model. Poster presented at the 39th annual South African Institute of Physics conference, University of Bophuthatswana, 1994.Item Phase transitions in induced lattice gauge models.(1995) Moodley, Mervlyn.; IIchev, Assen.The present research is based on the study of the phase structure of lattice models incorporating selfinteracting scalars and gauge background fields otherwise known as induced gauge models. Emphasis is placed on the effect the choice of the integration measure over the radial modes of the scalar fields have on the phase structure of these models. Both numerical simulations and analytical results based on the mean field approximations are presented. In Chapter 1 an introduction to quantum field theory is given leading to the formulation of Euclidean quantum field theory. In Chapter 2 global and local gauge invariance together with the mechanism of spontaneous symmetry breaking are discussed. In Chapter 3 the formulation of quantum field theory on the lattice is introduced. The lattice regularization entails discretizing space and time and presents an elegant approach to studying certain phenomena of the continuum theory which are beyond the reach of standard perturbative analysis. In Chapter 4 the Monte Carlo methods for evaluating the Euclidean Feynman path integral as applied to lattice gauge theory are discussed. In Chapter 5 numerical studies of some lattice gauge models are presented. Both pure lattice gauge models and gauge-Higgs models are examined. In Chapter 6 the Kazakov-Migdal model which presents an interesting approach to inducing QCD is discussed. In Chapter 7 the mixed fundamental-adjoint induced model is introduced. This model succeeds in breaking the local ZN symmetry of the Kazakov-Migdal model by adding to it scalar fields in the fundamental representation of the gauge group. The effect of the choice of the radial integration measure on the phase structure of a class of Abelian induced models is studied.Item An interferometric investigation of the quadratic electro-optic effect in KDP.(1995) Gunning, Mark Julian.; Raab, Roger Edouard.Abstract available in PDF.Item Two-dimensional plasma sheath observations in plasma source ion implantation.(1996) Meyer, Kevin Alan.; Alport, Michael J.Plasma Source Ion Implantation (PSII) is the process of implanting high energy ions [10-50 keV] into metallic targets, by pulsing them negatively whilst immersed in a background plasma. PSII achieves surface hardening, and increased wear and corrosion resistance. Numerous papers have been published describing numerical simulations and models of the PSII process, most of which have been limited to one dimension. This thesis presents the results of work carried out III the Plasma Processing Laboratory at the University of Natal, Durban, during 1994-1995. In particular, measurements of two-dimensional plasma sheath effects due to spherical and complex shaped targets are compared with a particle-in-cell simulation code. The simulation results are used to define a relationship between the plasma potential of the sheath edge and the saturation currents. Thus allowing for the saturation currents to be used to trace sheath evolution. These results are compared with the experimental measurements from the spherical target. Results from the rectangular and complex saw-tooth targets show a lack of sheath conformality. The ion saturation currents were susceptible to electron swamping, which occured in localised regions associated with target structure. It is thought that secondary electrons ejected from the target are focused and accelerated by the high target potential into these regions, where they swamp the ion current.