Abstract This thesis examines magnetic reconnection in the solar corona. Magnetic reconnection is the only mechanism which allows the magnetic topology of magnetized plasmas to be changed. Many of the dynamic processes in the Sun's atmosphere are believed to be driven by magnetic reconnection and studying the behaviour of such phenomena is a key step to understanding the reconnection mechanism. In Chapters 1 to 3, we discuss the physical and mathematical framework on which current magnetohydrodynamic reconnection models are based. The aim of the thesis is to investigate theoretical models of magnetic reconnection using variety of analytic and numerical techniques within the theoretical frame work of magnetohydrodynamics (MHD). In Chapter 4 we use a line-tied X-point collapse model for compressible plasmas to investigate the role of viscosity on the energy release mechanism. This model also provides the basis for the investigation of Chapter 5 which explores the impact of Hall currents in the transient X-point energy dissipation. Chapter 6 is concerned with how reconnection is modified in the presence of generalized Ohm's law which includes both Hall current and electron inertia contributions. In contrast to the closed X-point collapse geometry adopted for compressible plasmas previously, we find it more convenient to explore this problem using an open incompressible geometry in which plasma is continually entering and exiting the reconnection region. Specially, we find the scaling of the Hall-MHD system size analytically, rather than numerically as in the X-point problem of Chapter 5. Chapter 7 summarizes the results of investigations in Chapters 4, 5 and 6.

This research thesis seeks to investigate a new method to sense the classical Hall effect in Hall devices under the influence of a magnetic field primarily manufactured in complementary metal oxide semiconductor (CMOS) technologies. The thesis poses a research question enabling the investigation into whether or not the geometrical factor in a classical Hall device can be improved by proposing a new method to sense the Hall effect indirectly in standard CMOS technology. State of the art Hall effect devices rely on low ohmic contacts to sense the Hall voltage effect. These contacts along with the geometry can have an adverse effect on the Hall device sensitivity. Furthermore, the Hall voltage in Silicon can be very limited in comparison to high mobility semiconductor materials. It was found that by replacing the highly doped n-type sensing contacts of the Hall device with highly doped p-type contacts, a vertical bipolar junction transistor could be formed. This transistor, normally considered a parasitic element, ultimately leads to a very useful sensing technique in which the Hall current is sensed and amplified by the transistor forward gain, β + 1. The Hall effect appears as a current through the emitter of the transistor. The major contribution of this research resides in a novel method to measure as well as amplify the Hall effect in a square n-well plate manufactured on a standard CMOS technology. The research also bridges the gap found in literature on the subject of direct versus indirect Hall sensing techniques. The outcome of the research also addresses practical implementations of such alternate methods as well as the effect the methods have on fundamental noise limits and differences in noise between the proposed method and traditional methods. The device although not improving the fundamental geometrical factor of the plate which was found to be dominated by the geometry itself, was proven to be functional as well as behaving according to Hall effect theory. Furthermore, the gain that even low forward gain bipolar transistors contribute to the signal, more than compensates for the loss of Hall effect contributed by the geometrical correction factor. The method also contributes less noise in comparison to typical traditional methods of Hall voltage amplification using operational amplifiers. The proposed method thus allows for a very simple measuring technique that is compatible with standard CMOS technology processes. ## Hierdie navorsings tesis is gemik daarop om 'n nuwe meetmetode te ondersoek om die klassieke Hall effek te meet in Hall toestelle onder die invloed van 'n magneetveld wat primér in komplementêre metaaloksied-halfgeleiertegnologie (CMOS) vervaardig word. Die tesis stel 'n navorsingsvraag wat lei tot die ondersoek van die vraag of die geometriese faktor in 'n klassieke Hall toestel verbeter kan word deur om 'n nuwe metode voor te stel om die Hall effek indirek te meet in standaard CMOS tegnologie. Nuutste navorsing oor meetmetodes in Hall effek toestelle, maak nog steeds staat op lae ohmiese kontakte om die Hall spanning effek te meet. Hierdie kontakte saam met die meetkunde van die toestel, het 'n nadelige uitwerking op die Hall toestel se sensitiwiteit. Verder is die Hall spanning in Silikon baie beperk met vergelyking tot hoë mobiliteit halfgeleier materiale. Daar is gevind dat deur die vervanging van die hoogs gedoteerde n-tipe meetkontakte van die Hall toestel met hoogs gedoteerde p-tipe kontakte, kan vertikale bipolêre transistors gevorm word. Hierdie transistor, gewoonlik beskou as 'n parasitiese element, lei tot 'n baie nuttige meet tegniek waarin die Hall stroom gemeet en versterk word deur die transistor se voorwaartse wins, β + 1. Die Hall effek verskyn as 'n stroom deur die emittor van die transistor. Die grootste bydrae van hierdie navorsing lê in 'n nuwe metode om die Hall effek in 'n vierkantige n-dam plaat wat in standaard CMOS tegnologie vervaardig is te meet sowel as om die sein te versterk. Die navorsing oorbrug ook die gaping gevind in literatuur oor die onderwerp van direkte teenoor indirekte Hall meet tegnieke. Die uitkoms van die navorsing spreek ook die praktiese implementering van die meetmetode aan sowel as die effek wat die meetmetode op fundamentele ruisgrense en verskille in ruis tussen die voorgestelde meetmetode en tradisionele meetmetodes het. Die toestel, hoewel nie gelei het tot ‘n verbetering van die fundamentele geometriese faktor van die plaat wat oorheers is deur die meetkunde van die plaat self, is wel funksioneel bewys, asook dat dit optree volgens Hall effek teorie. Verder is daar gevind dat die wins wat selfs lae voorwaartse wins bipolêre transistors bydra tot die sein, meer as die verlies wat die meetkundige faktor veroorsaak op die Hall effek kan herwin. Dié meetmetode dra ook minder ruis by met vergelyking tot tipiese tradisionele meetmetodes soos operasionele versterkers, wat vir Hall spanning versterking gebruik word. Die voorgestelde meetmetode skep dus ‘n baie eenvoudige meettegniek wat versoenbaar is met standaard CMOS tegnologie prosesse. / Thesis (PhD)--University of Pretoria, 2014. / lk2014 / Electrical, Electronic and Computer Engineering / PhD / unrestricted

Alors que les applications spatiales prennent une place de plus en plus cruciale dans nos vies, les coûts d'opération des satellites doivent être réduits. Ceci peut être obtenu par l'utilisation de systèmes de propulsion électriques, plus efficients que leurs homologues chimiques traditionnellement utilisés. Une des technologies de propulsion électrique la plus performante et la plus utilisée est le propulseur à effet Hall, toutefois ce système reste complexe et peu compris. En effet de nombreuses questions, concernant le transport anormal des électrons ou les interactions plasma/paroi, sont encore ouvertes.Les réponses à ces questions sont basées sur des mécanismes cinétiques et donc ne peuvent être résolues par des modèles fluides. De plus les caractéristiques géométriques et temporelles de ces mécanismes les rendent difficilement observables expérimentalement. Par conséquent nous avons, pour répondre à ces questions, développé un code cinétique bi-dimensionnel.Grâce à un modèle simplifié de propulseur à effet Hall, nous avons observé l'importance de l'instabilité de dérive électronique pour le transport anormal. Ensuite en utilisant un modèle réaliste de propulseur, nous avons pu étudier les effets des interactions plasma/paroi sur la décharge plasma. Nous avons également pu quantifier les effets intriqués des émissions électroniques secondaires et de l'instabilité de dérive sur le transport anormal. Par une étude paramétrique sur les émissions électroniques secondaires, nous avons pu identifier trois régimes de décharge plasma. Finalement l'impact des ergols alternatifs a pu être étudié en utilisant des processus collisionnels réalistes. / As space applications are increasingly crucial in our daily life, satellite operating costs need to be decreased. This can be achieved through the use of cost efficient electric propulsion systems. One of the most successful and competitive electric propulsion system is the Hall effect thruster, but this system is characterized by its complexity and remains poorly understood. Indeed some key questions, concerning electron anomalous transport or plasma/wall interactions, are still to be answered.Answers to both questions are based on kinetic mechanisms, and thus cannot be solved with fluid models. Furthermore the temporal and geometrical scales of these mechanisms make them difficult to be experimentally measured. Consequently we chose, in order to answer those questions, to develop a bi-dimensional fully kinetic simulation tool.Using a simplified simulation of the Hall effect thruster, we observed the importance of the azimuthal electron drift instability for anomalous cross-field electron transport. Then, using a realistic model of a Hall effect thruster, we were able to study the effects of plasma/wall interactions on the plasma discharge characteristics, as well as to quantify the coupled effects of secondary electron emission and electron drift instability on the anomalous transport. Through parametric study of secondary electron emission, three plasma discharge regimes were identified. Finally the impact of alternative propellants was studied.