Browsing by Author "Mace, Richard Lester."

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1-D particle-in-cell simulations of plasmas with kappa velocity distributions.
(2013) Abdul, Reginald Francis.; Mace, Richard Lester.
The main aim of this project was the development of a particle-in-cell (PIC) plasma simulation code. While particle-in-cell simulations are not new, they have largely focused on using an initial Maxwellian particle loading. The new feature the code implemented for this project is the use of kappa distributions as an initial loading. This specialises the code for the investigation of waves and instabilities in space plasmas having kappa-type velocity distributions. The kappa distribution has been found to provide a better fit to space plasma particle velocity distributions than the Maxwellian in a wide variety of situations. In particular, it possesses a power law tail which is a frequent feature of charged particle velocity distributions in space plasmas. Traditionally, the treatment of such out-of-equilibrium velocity distributions has been via a summation over several Maxwellians with different temperatures and average number densities. Instead, the approach used in this work is guided by recent advances in non-extensive statistical mechanics, which provide a rigorous underpinning for the existence of kappa distributions. As case studies, the simulation code was used to investigate the ion-acoustic instability as well as electrostatic Bernstein waves in both Maxwellian and kappa plasmas. Results were compared to kinetic theory and the differences in the Maxwellian and kappa plasma behaviours are discussed. To analyse the instabilities various diagnostics were used, including Fourier analysis of the wave fields to determine the dispersion relation, and particle binning to determine the particle velocity distributions. Both the Maxwellian and kappa particle loading algorithms were found to agree well with the theoretical velocity distributions and the dispersion relations were found to agree with kinetic theory for both kappa and Maxwellian plasmas. The code was developed in the C programming language using an incremental approach that enabled careful testing after each new level of sophistication was added. A version of the code was parallelised using Message Passing Interface (MPI) to take advantage of the distributed supercomputing environment provided by the CHPC.
2D3V electromagnetic particle-in-cell simulations of plasmas having kappa velocity distributions.
(2018) Abdul, Reginald Francis.; Mace, Richard Lester.
It is now well established that the kappa distribution is a more appropriate kinetic model for space plasmas than the Maxwellian distribution. In particular it possesses a power-law tail, frequently observed in space plasmas. The research presented in this thesis outlines the development of a two-dimensional electromagnetic particle-in-cell (PIC) simulation code, designed to run on general purpose graphics processing units (GPGPUs), and presents results from simulations of waves and instabilities obtained using it. While PIC simulations are not new, the majority have focussed on the old paradigm of initial particle loadings with a Maxwellian velocity distribution, or one of its variants. Distinguishing this research from previous PIC simulations is the use of the kappa distribution for the initial particle loading. To achieve this, a fast and e cient algorithm for generating multi-dimensional kappa distributed deviates was developed. The code is rst applied to the study of waves in an electron-ion plasma, in a stable equilibrium con guration with a constant background magnetic eld. Both species are modelled by isotropic (a) kappa and (b) Maxwellian velocity distributions. In each case, spectral analysis of the eld uctuations is performed, allowing mode identi cation. For parallel propagation, the maximum uctuation intensities follow the dispersion relations for the L and R modes, respectively, while those at perpendicular propagation follow the dispersion relations for the X, O and electromagnetic electron and ion Bernstein waves. The variation of wave intensity for the oblique angles is also investigated. For the kappa case, this yields new and important information presently unavailable by analysis alone. The e ects of the kappa distribution on wave intensity, as well as its e ect on the dispersion relations of the modes is discussed in detail. The second application is to the simulation of the electron temperature anisotropy driven whistler instability in an electron-ion plasma, where the electron species is modelled by the (a) bi-kappa and (b) bi-Maxwellian velocity distribution. For parallel propagation, the maximum eld uctuation intensities agree well with the dispersion relation for the whistler instability in a kappa plasma. While most of the wave intensity is in the parallel whistler mode, the oblique modes also contribute signi cantly to the overall uctuation spectrum, but their intensities vary with angle of propagation relative to the magnetic eld. The dependence of the growth rate on the index e of the electron kappa distribution is discussed in detail and compared with the well known Maxwellian results. Saturation of the instability via pitch angle scattering, reducing the electron temperature anisotropy, is observed.
L and R mode electromagnetic instabilities in space plasmas having kappa velocity distributions.
(2014) Henning, Farran Dominique.; Mace, Richard Lester.
Abstract available in PDF file.
Linear and nonlinear electron-acoustic waves in plasmas with two electron components.
(1991) Mace, Richard Lester.; Hellberg, Manfred Armin.; Bharuthram, Ramesh.
Measurements of broadband electrostatic wave emIssons in conjunction with particle distributions in the earth's magnetosphere, have provided motivation for a number of studies of waves in plasmas with two electron components. One such wave-the electron-acoustic wave-arises when the two electron components have widely disparate temperatures (Watanabe & Taniuti 1977), and has a characteristic frequency that lies between the ion and electron plasma frequencies. Because of this broadband nature and because it is predominantly electrostatic, it provides a likely candidate for the explanation of the electrostatic component of "cusp auroral hiss" observed in the dayside polar cusp at between 2 and 4 earth radii as well as the broadband electrostatic noise (BEN) observed in the dayside polar regions and in the geomagnetic tail. The electron-acoustic wave and its properties provide the subjects for much of the investigation undertaken in this thesis. The thesis is divided into two parts. Part I is concerned with certain aspects of the linear theory of the electron-acoustic wave and is based on a kinetic description of the plasma. The dispersion relation for plane electrostatic waves obtained via linearisation of the Vlasov-Poisson system is studied in detail using analytical and numerical/geometrical techniques, and conditions under which the electron-acoustic wave arises are expounded. This work represents an extension of earlier works on Langmuir waves (Dell, Gledhill & Hellberg 1987) and the electron-acoustic wave (Gary & Tokar 1985). The effects of electron drifts and magnetization are investigated. These result, respectively, in a destabilization of the electron-acoustic wave and a modification of the dispersive properties. In this plasma configuration the model more closely replicates the conditions to be found in the terrestrial polar regions. We extend the parameter regimes considered in earlier works (Tokar &Gary 1984) and in addition, identify another electron sound branch related to the electron-cyclotron wave/instability. Effects of ion-beam destabilization of the electron-acoustic wave are also investigated briefly with a view to explaining BEN in the geomagnetic tail and also to provide a comparison with the electron-driven instability. In part II the nonlinear electron-acoustic wave is studied by employing a warm hydrodynamic model of the plasma components. We first consider weak nonlinearity and employ the asymptotic reductive perturbation technique of Washimi &Taniuti (1966) to render the hydrodynamical equations in the form of simpler evolutionary equations describing weakly-nonlinear electron-acoustic waves. These equations admit solitary-wave or soliton solutions which are studied in detail. Wherever possible we have justified our small amplitude results with full numerical integration of the original hydrodynamical equations. In so doing we extended the range of validity of our results to arbitrary wave amplitudes and also find some interesting features not directly predicted by the small amplitude wave equations. In this respect we were able to determine the important role played by the cool- to-hot electron temperature ratio for soliton existence. This important effect is in accordance with linear theory where the electron temperature ratio is found to be critical for electron-acoustic wave existence. The effects of magnetization on electron-acoustic soliton propagation is examined. We found that the magnetized electron-acoustic solitons are governed by a Korteweg-de Vries-Zakharov-Kusnetsov equation. In addition, it is shown that in very strong magnetic fields ion magnetization can become important yielding significant changes in the soliton characteristics. Multi-dimensional electron-acoustic solitons, which have greater stability than their plane counterparts, are also briefly discussed. Employing a weakly-relativistic hydrodynamic model of the plasma, the effect of a cool, relativistic electron beam on such soliton parameters as width, amplitude and speed is studied in detail. Both small- and large amplitude solitons are considered. The arbitrary-amplitude theory of Baboolal et al. (1988) is generalised to include relativistic streaming as well as relativistic thermal effects. The importance of the cool electron (beam)to- hot electron temperature in conjunction with the beam speed is pointed out. Finally, we derive a modified Korteweg-de Vries (mKdV) equation in an attempt to establish whether electron-acoustic double layers are admitted by our fluid model. Although double layers formally appear as stationary solutions to the mKdV equation, the parameter values required are prohibitive. This is borne out by the full fluid theory where no double layer solutions are found.
Linear and nonlinear waves in space plasmas.
(2014) Nsengiyumva, Francois.; Hellberg, Manfred Armin.; Mace, Richard Lester.
The work presented in this thesis is about a study of some linear and nonlinear plasma waves. Firstly, a kinetic-theoretical approach is used to study ion Bernstein waves in an electron-proton plasma with a kappa velocity distribution. The effects of the parameter kappa on the dispersion relation of ion Bernstein waves are discussed in detail, considering various values of the ratio of the ion plasma frequency to the ion cyclotron frequency, ωpi/ωci, allowing application of the results to various space environments. For a fixed value of ωpi/ωci, we have found that the dispersion relation depends significantly on the parameter kappa of the ions, κi, but is independent of the electron kappa. Over all cyclotron harmonics, the dispersion curves are shifted to higher wavenumbers (k) if κi is reduced. When the value of ωpi/ωci is increased, the fall-off of the wave frequency, ω, at large k is smaller for lower κi, and curves are shifted towards larger wavenumbers. For large values of ωpi/ωci, the ion Bernstein wave dispersion curves within and above the lower hybrid frequency band exhibit coupling for the Maxwellian case, unlike the kappa case. We have suggested that this result may be a useful diagnostic for determining whether the ion velocity distribution possesses a power law tail. Considering parameter values that have been observed in the Earth’s plasma sheet boundary layer, and neighbouring environments, it has been found that the dispersion curves of ion Bernstein waves are typical of those obtained for the case of a high-density plasma immersed in a weak magnetic field. Secondly, a fluid model is used to study linear and nonlinear ion acoustic waves supported by a two-adiabatic-ion plasma in which both ion species are positively and singly charged. This plasma model supports the propagation of two modes with different phase speeds. By normalising variables with respect to the characteristics of the hotter ion species, the thermal effects of the cooler ion species and the electrons on the two modes are discussed in detail. The main thrust has been to study arbitrary amplitude ion acoustic solitons and double layers, using the fully nonlinear Sagdeev potential theory, but we have also considered linear theory and the KdV theory as a useful background. The thermal effects of the cooler ion species and the electrons on the soliton existence domain and on the soliton/double layer speed, amplitude, and maximum profile steepness are discussed in detail. While some of the results are consistent with the results that are in the literature, there are many new results which have not been reported previously. These include the existence of a novel stopband in the existence domain of fast solitons. By a stopband, we mean a range of Mach numbers between two passbands of an existence domain over which solitary wave propagation does not occur. The presence of a stopband is dependent on the ion-ion mass ratio and the hotter ion to electron temperature ratio, and it exists only when the thermal effects of the cooler ion species are small.
Studies of linear and nonlinear acoustic waves in space plasmas.
(2011) Baluku, Thomas Kisandi.; Hellberg, Manfred Armin.; Mace, Richard Lester.
Superthermal particle effects on solitons in a symmetric four-species electron-positron plasma.
Gogo, Tamirat Gebeyehu.; Hellberg, Manfred Armin.; Mace, Richard Lester.
Abstract available in PDF file.