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School of Chemistry and Physics

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Browsing School of Chemistry and Physics by Author "Abdul, Reginald Francis."

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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.
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    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.