The most common type of electric propulsion in space exploration is the Hall Effect Thruster (HET), mainly due to its high specific impulse and high thrust to power ratio. However, uncertainties about the thruster's lifetime prediction have prevented widespread integration of HETs. Among these limitations, wall erosion of acceleration channel is of greatest concern. The experimental methods of erosion are time consuming and costly, and they are often limited to one single configuration. Hence, developing a computational model not only decreases the costs but also shortens the design time of a HET. This thesis investigates the feasibility of a uid erosion modelling with a multi-physics software (COMSOL) to further decrease the time and the development cost. First of all, this thesis provides an overview of available plasma modelling techniques and the physics behind the erosion phenomenon. Moreover, the effective parameters and available modules in the multiphysics software as well as their theoretical background were studied and discussed in detail. The Electron Anomalous phenomenon and pressure instability are determined as the main limiting factors for such a model. A non-magnetized model is included to find an optimal value for pressure and to reduce the probability of pressure instability occurrence in magnetized model. To fulfill this task, several simulations for various pressure values (0.005 Torr, 0.05 Torr, and 0.5 Torr) were conducted. Next, the simulation of magnetized/full model has been carried out with addition of magnetic coils in non-magnetized model. To avoid the Electron Anomalous phenomenon, the Bohm diffusion approach was implemented. In addition, a full Particle-In-Cell (PIC) simulation of a typical HET (SPT-100) with the similar input parameters as in fluid model was conducted, and the results were compared and validated using experimental data. The PIC model was intended to be utilized to investigate the accuracy of erosion model in multiphysics software. The results of this thesis indicate that current application of erosion model in COMSOL is not possible whilst high accuracy of the erosion model based on PIC approach can be achieved. Finally, the application of semi-empirical method through direct input of magnetic field data can allow short time simulation of a HET in COMSOL to gain insight about the preliminary behaviour of plasma, however, the simulation of an erosion model requires either a built-in PIC algorithm in COMSOL or a PIC based code.

Current state-of-the-art plasma thrusters are limited in power density and thrust density by power losses to plasma-facing walls and electrodes. In the case of Hall effect thrusters, power deposition to the discharge channel walls and anode negatively impact the efficiency of the thruster and limit the attainable power density and thrust density. The current work aims to recreate thruster-relevant wall-interaction physics in a quiescent plasma and investigate them using electrostatic probes, in order to inform the development of the next generation of high-power-density / high-thrust-density propulsion devices. Thruster plasma-wall interactions are complicated by the occurrence of the plasma sheath, a thin boundary layer that forms between a plasma and its bounding wall where electrostatic forces dominate. Sheaths have been recognized since the seminal work of Langmuir in the early 1900’s, and the theory of sheaths has been greatly developed to the present day. The theories are scalable across a wide range of plasma parameters, but due to the difficulty of obtaining experimental measurements of plasma properties in the sheath region, there is little experimental data available to directly support the theoretical development. Sheaths are difficult to measure in situ in thrusters due to the small physical length scale of the sheath (order of micrometers in thruster plasmas) and the harsh plasma environment of the thruster. Any sufficiently small probe will melt, and available optical plasma diagnostics do not have the sensitivity and/or spatial resolution to resolve the sheath region. The goal of the current work is to experimentally characterize plasma sheaths xxvi in a low-density plasma that yields centimeter-thick sheath layers. By generating thick sheaths, spatially-resolved data can obtained using electrostatic probes. The investigation focuses on the effects of electron emission from the wall and several factors that influence it, including wall material, wall temperature, wall surface roughness and topology, as well as the scaling of sheaths from the low-density plasma environment towards thruster conditions. The effects of electron emission and wall material are found to agree with classical fluid and kinetic theory extended from literature. In conditions of very strong emission from the wall, evidence is found for a full transition in sheath polarities rather than a non-monotonic structure. Wall temperature is observed to have no effect on the sheath over boron nitride walls independent of outgassing on initial heat-up, for sub-thermionic temperatures. Wall roughness is observed to postpone the effects of electron emission to higher plasma temperatures, indicating that the rough wall impairs the wall’s overall capacity to emit electrons. Reductions in electron yield are not inconsistent with a diffuse-emission geometric trapping model. Collectively, the experimental data provide an improved grounding for thruster modeling and design.Current state-of-the-art plasma thrusters are limited in power density and thrust density by power losses to plasma-facing walls and electrodes. In the case of Hall effect thrusters, power deposition to the discharge channel walls and anode negatively impact the efficiency of the thruster and limit the attainable power density and thrust density. The current work aims to recreate thruster-relevant wall-interaction physics in a quiescent plasma and investigate them using electrostatic probes, in order to inform the development of the next generation of high-power-density / high-thrust-density propulsion devices. Thruster plasma-wall interactions are complicated by the occurrence of the plasma sheath, a thin boundary layer that forms between a plasma and its bounding wall where electrostatic forces dominate. Sheaths have been recognized since the seminal work of Langmuir in the early 1900’s, and the theory of sheaths has been greatly developed to the present day. The theories are scalable across a wide range of plasma parameters, but due to the difficulty of obtaining experimental measurements of plasma properties in the sheath region, there is little experimental data available to directly support the theoretical development. Sheaths are difficult to measure in situ in thrusters due to the small physical length scale of the sheath (order of micrometers in thruster plasmas) and the harsh plasma environment of the thruster. Any sufficiently small probe will melt, and available optical plasma diagnostics do not have the sensitivity and/or spatial resolution to resolve the sheath region. The goal of the current work is to experimentally characterize plasma sheaths xxvi in a low-density plasma that yields centimeter-thick sheath layers. By generating thick sheaths, spatially-resolved data can obtained using electrostatic probes. The investigation focuses on the effects of electron emission from the wall and several factors that influence it, including wall material, wall temperature, wall surface roughness and topology, as well as the scaling of sheaths from the low-density plasma environment towards thruster conditions. The effects of electron emission and wall material are found to agree with classical fluid and kinetic theory extended from literature. In conditions of very strong emission from the wall, evidence is found for a full transition in sheath polarities rather than a non-monotonic structure. Wall temperature is observed to have no effect on the sheath over boron nitride walls independent of outgassing on initial heat-up, for sub-thermionic temperatures. Wall roughness is observed to postpone the effects of electron emission to higher plasma temperatures, indicating that the rough wall impairs the wall’s overall capacity to emit electrons. Reductions in electron yield are not inconsistent with a diffuse-emission geometric trapping model. Collectively, the experimental data provide an improved grounding for thruster modeling and design.

The current technological age is embodied by a constant push for increased performance and efficiency of electronic devices. This push is particularly observable for technologies that comprise free electron sources, which are used in various technologies including electronic displays, x-ray sources, telecommunication equipment, and spacecraft propulsion. Performance of these systems can be increased by reducing weight and power consumption, but is often limited by a bulky electron source with a high energy demand. Carbon nanotubes (CNTs) show favorable properties for field electron emission (FE) and performance as electron sources. This dissertation details the developments of a uniquely designed Spindt type CNT field emission array (CFEA), from initial concept to working prototype, to specifically prevent electrical shorting of the gate. The CFEA is patent pending in the United States. Process development enabled fabrication of a CFEA with a yield of up to 82%. Furthermore, a novel oxygen plasma etch process was developed to reverse shorting after CNT synthesis. CFEA testing demonstrates FE with a current density of up to 293 μA/cm² at the anode and 1.68 mA/cm² at the gate, with lifetimes in excess of 100 hours. A detailed analysis of eighty tested CFEAs revealed three distinct types of damage. Surprisingly, about half of the damaged chips are not electrically shorted, indicating that the CFEAs are very robust. Potential applications of this technology as cathodes for spacecraft electric propulsion were explored. Exposure to an operating electric propulsion thruster showed no significant effect or damage to the CFEAs, marking the first experimental study of CNT field emitters in an electric propulsion environment. A second effort in spacecraft propulsion is a collaboration with the Air Force Institute of Technology (AFIT). CFEAs are the payload on an AFIT developed Cube Satellite, called ALICE, to test electron emission in the space environment. ALICE has passed flight tests and is awaiting launch scheduled for 5 December 2013.

Hall Effect Thrusters (HETs) are a form of electric propulsion device which uses external electrical energy to produce thrust. When compared to various other electric propulsion devices, HETs are excellent candidates for future orbit transfer and interplanetary missions due to their relatively simple configuration, moderate thrust capability, higher thrust to power ratio, and lower thruster mass to power ratio. Due to the short history of HETs, the current design process of a new HET is a largely empirical and experimental science, and this has resulted in previous designs being developed in a narrow design space based on experimental data without systematic investigations of parameter correlations. In addition, current preliminary low-thrust trajectory optimizations, due to inherent difficulties in solution procedure, often assume constant or linear performances with available power in their applications of electric thrusters. The main obstacles come from the complex physics involved in HET technology and relatively small amounts of experimental data. Although physical theories and numerical simulations can provide a valuable tool for design space exploration at the inception of a new HET design and preliminary low-thrust trajectory optimization, the complex physics makes theoretical and numerical solutions difficult to obtain. Numerical implementations have been quite extensively conducted in the last two decades. An investigation of current methodologies reveals that to date, none provide a proper methodology for a new HET design at the conceptual design stage and the coupled low-thrust trajectory optimization. Thus, in the first half of this work, an efficient, robust, and self-consistent numerical method for the analysis of HETs is developed with a new approach. The key idea is to divide the analysis region into two regions in terms of electron dynamics based on physical intuition. Intensive validations are conducted for existing HETs from 1 kW to 50 kW classes. The second half of this work aims to construct a simultaneous design optimization environment though collaboration with experts in low-thrust trajectory optimization where a new HET and associated optimal low-thrust trajectory can be designed simultaneously. A demonstration for an orbit raising mission shows that the constructed simultaneous design optimization environment can be used effectively and synergistically for space missions involving HETs. It is expected that the present work will aid and ease the current expensive experimental HET design process and reduce preliminary space mission design cycles involving HETs.

All satellites need a propulsion system for orbit correction maneuvers. Electric Hall effect thrusters are an interesting technology for space applications. The big advantage compared to chemical propulsion devices is the higher specific impulse Isp, a higher ejection speed and thus a substantial gain in terms of propellant consumption. In a Hall effect thruster the ions are created and accelerated in a low pressure discharge plasma in a magnetic field. The first part of the work concerns scaling laws for Hall effect thrusters. A semi-empirical scaling model based on analytical laws and relying on simplifying assumptions is developed. This scaling model can be used to extrapolate existing thruster technologies in order to meet new mission requirements. In a second part, the influence of the channel width on the thruster performance level is investigated. It has been demonstrated that enlarging the channel width of a low power Hall effect thruster leads to an increase in thruster efficiency. Finally, electron properties are measured by means of electrostatic probes in the plume of different Hall effect thrusters. Experimental data on electron properties is of great interest for the validation of numerical plume models that are essential for the integration of the thruster on the satellite. Time-averaged and timeresolved measurements of the electron properties have been carried out for different operating conditions of the thruster. A fast-moving probe system has been developed in order to perform measurements of the electron properties close to the thruster exit plane.

Chaque satellite nécessite un système de propulsion pour des corrections d’orbite. Les propulseurs électriques à effet de Hall sont une technologie intéressante pour des applications spatiales. Le grand avantage par rapport à la propulsion chimique est une impulsion spécifique Isp plus élevée, une vitesse d’éjection plus élevée et donc un gain substantiel en termes de consommation de carburant. Dans un propulseur à effet Hall les ions sont créés et accélérés dans une décharge plasma à basse pression dans un champ magnétique. La première partie de ce travail concerne les lois d’échelle pour les propulseurs à effet Hall. Un modèle de dimensionnement semi-empirique basé sur des lois analytiques et reposant sur des hypothèses simplificatrices a été développé. Ce modèle de dimensionnement peut être utilisé pour une extrapolation des propulseurs existants afin de répondre aux exigences pour de nouvelles missions. Dans une deuxième étape, l’influence de la largeur du canal sur les performances d’un propulseur est étudiée. Il a été démontré qu’augmenter la largeur du canal conduit à une amélioration de l’efficacité du propulseur. Finalement, les propriétés électroniques ont été mesurées à l’aide de sondes électrostatiques dans la plume de différents propulseurs à effet Hall. Des données expérimentales concernant les propriétés électroniques sont très intéressantes pour la validation des modèles numériques de la plume indispensables pour l’intégration du propulseur sur le satellite. Des mesures moyennées et résolues en temps des propriétés électroniques ont été réalisées pour différents points de fonctionnement du propulseur. Un système de déplacement rapide pour les sondes a été développé afin de pouvoir faire des mesures des propriétés électroniques dans la zone proche du plan de sortie du propulseur. / All satellites need a propulsion system for orbit correction maneuvers. Electric Hall effect thrusters are an interesting technology for space applications. The big advantage compared to chemical propulsion devices is the higher specific impulse Isp, a higher ejection speed and thus a substantial gain in terms of propellant consumption. In a Hall effect thruster the ions are created and accelerated in a low pressure discharge plasma in a magnetic field. The first part of the work concerns scaling laws for Hall effect thrusters. A semi-empirical scaling model based on analytical laws and relying on simplifying assumptions is developed. This scaling model can be used to extrapolate existing thruster technologies in order to meet new mission requirements. In a second part, the influence of the channel width on the thruster performance level is investigated. It has been demonstrated that enlarging the channel width of a low power Hall effect thruster leads to an increase in thruster efficiency. Finally, electron properties are measured by means of electrostatic probes in the plume of different Hall effect thrusters. Experimental data on electron properties is of great interest for the validation of numerical plume models that are essential for the integration of the thruster on the satellite. Time-averaged and timeresolved measurements of the electron properties have been carried out for different operating conditions of the thruster. A fast-moving probe system has been developed in order to perform measurements of the electron properties close to the thruster exit plane.

Hall-effect thrusters (HETs) are among the most commonly used propulsion systems for attitude and orbit control of satellites. As an arrangement in a cluster or individually, equipped with a mechanical suspension, thrust in all three spatial directions can be generated, but requires additional mechanisms and components. Therefore, the Technische Universität Dresden (TU Dresden) is currently working on a concept for developing a Hall-effect thruster with integrated thrust vector control, which would allow steering in all three spatial directions with just a single thruster. This new concept is intended to work solely by influencing the ion beam and should not have any additional mechanical components. The HET will come with a segmented anode to set different electrical potentials at the anode and cause an inhomogeneous distribution of the electric field within the discharge channel, which results in an inhomogeneous force vector distribution at the exit plane. It is assumed that this will generate turning moments around the center of gravity. Deliberately causing those turning moments can therefore be used for steering with just one thruster. This work presents the concept of the propulsion system, gives an outlook on the advantages of its technology and shows capabilities for space applications.

Les propulseurs électriques sont de plus en plus utilisés pour des missions de correction de trajectoire des satellites et pourront dans un avenir proche être utilisés pour le transfert d’orbite. Ces propulseurs constituent une excellente alternative aux propulseurs chimiques grâce à leur rendement élevé et une substantielle économie de carburant réalisée par rapport aux propulseurs chimiques. Les propulseurs à effet Hall créent la poussée par l’accélération d’ions positifs de xénon ou de krypton dans un plasma confiné par un champ magnétique. L’objet de ce manuscrit concerne principalement les caractéristiques de l’accélération des ions et des atomes dans un propulseur à effet Hall. Les influences de la largeur du canal de décharge, de la topologie magnétique et de la cathode sur l’efficacité d’accélération des ions sont étudiées. Des pistes d’optimisation de l’architecture du propulseur sont alors proposées qui pourraient être particulièrement avantageuses sur les propulseurs de petite taille, comme l’élargissement du canal et l’augmentation du champ magnétique près des parois du canal. L’influence de la position et du potentiel de la cathode sur la déviation du faisceau ionique est révélée. L’évolution temporelle basse fréquence du champ électrique est mesurée par comptage synchrone de photons et suggère que la température atomique joue un rôle important dans les oscillations basse fréquence de la décharge. Par ailleurs, l’influence du champ magnétique sur les performances d’un propulseur proche des modèles de vol a été mesurée grâce à l’utilisation d’un moteur doté d’une topologie magnétique flexible. Ceci a montré la difficulté de définir un paramètre numérique capable de synthétiser l’information complexe de la répartition spatiale du champ magnétique dans le canal de décharge. Les très faibles modifications des performances par le champ magnétique soulignent l’importance de la précision dans la mesure. / Electric propulsion systems are more and more often used for trajectory correction of satellites and may soon be used for orbit transfer. These devices represent a great alternative to classic chemical propulsion devices thanks to their high efficiency and propellant mass savings. Hall effect thruster provide thrust by the acceleration of xenon or krypton ions in a magnetized confined plasma. The study presented in this manuscript mainly addresses characteristics of ion and atom acceleration in a Hall effect thruster. Influence of channel width, magnetic topology and cathode parameters on ion acceleration efficiency is investigated. Ways to optimize thruster architecture are suggested that may be particularly relevant for low power thrusters, such as widening thruster channel and increasing magnetic field amplitude near channel walls. Influence of cathode position with respect to the thruster channel exit plane and its potential with respect to ground on ion beam deviation has been revealed with two thrusters. Low frequency time evolution of the accelerating electric field was measured using lock-in photon counting system. Results strongly suggest that the atom temperature plays a crucial role in low frequency time evolution of the whole plasma discharge. Measurement of performances as a function of the magnetic field demonstrated that numeric parameters are compulsory to carry on a relevant parametric study. These parameters would summarize the 2D information of magnetic topology. Weak influence of magnetic topology revealed that thrust measurement precision needs to be increased by at least one order of magnitude if one wants to reach a better understanding of plasma confinement in a Hall effect thruster.

Dans ces travaux, nous présentons des méthodes d'optimisation théoriques et numériques pour la conception optimale de circuits magnétiques pour propulseurs à effet Hall. Ces problèmes de conception sont des problèmes inverses très difficiles à résoudre que nous formulons sous forme de problèmes d'optimisation topologique. Les problèmes resultant sont non convexes avec des contraintes aux équations différentielles de Maxwell. Au cours de ces travaux, des approches originales ont été proposées afin de résoudre efficacement ces problèmes d'optimisation topologique. L'approche de densité de matériaux SIMP (Solid Isotropic Material with Penalization) qui est une variante de la méthode d'homogénéisation a été privilégiées. De plus, les travaux de ma thèse ont permis la mise en place de codes d'optimisation dénommé ATOP (Algorithm To Optimize Propulsion) utilisant en parallèle les logiciels de calculs scientifiques Matlab et d'élément finis FEMM (Finite Element Method Magnetics). Dans ATOP, nous utilisant à la fois des algorithmes d'optimisation locale de type descente basés sur une analyse de la sensibilité du problème et des algorithmes d'optimisation globale principalement de type Branch and Bound basés sur l'Arithmétique des Intervals. ATOP permettra d'optimiser à la fois la forme topologique des circuits magnétiques mais aussi le temps et le coût de production de nouvelles génération de propulseurs électriques. / In this work, we present theoretical and numerical optimization method for designing magnetic circuits for Hall effect thrusters. These design problems are very difficult inverse ones that we formulate under the form of topology optimization problems. Then, the obtained problems are non convex subject to Maxwell equations like constraints. Some original approaches have been proposed to solve efficiently these topology optimization problems. These approaches are based on the material density model called SIMP approach (Solid Isotropic Material with Penalization) which is a variante of the homogenization method. The results in my thesis allowed to provide optimization source code named ATOP (Algorithm To Optimize Propulsion) unsung in parallel two scientific computing softwares namely Matlab and FEMM (Finite Element Method Magnetics). In ATOP, we use both local optimization algorithms based on sensitivity analysis of the design problem; and global optimization algorithms mainly of type Branch and Bound based on Interval Arithmetic analysis. ATOP will help to optimize both the topological shape of the magnetic circuits and the time and cost of production (design process) of new generations of electrical thrusters.

Des années 50 à nos jours, la propulsion électrique n'a cessé d'évoluer afin de s'imposer dans le domaine de la propulsion spatiale. Les Propulseurs à effet Hall (PEH) sont principalement utilisés pour des missions de correction de trajectoire ou de maintien en orbite des satellites. Ils délivrent des faisceaux d'ions à forte densité de courant et à faible énergie, ce qui en font de bons candidats potentiels pour d'autres applications comme la microélectronique ou encore les traitements de surfaces. Le xénon est l'ergol le plus utilisé en raison de sa masse élevée et de son faible énergie d'ionisation. Cependant son coût élevé et la difficulté d’approvisionnement motivent la recherche d'alternatives pour le fonctionnement des MEH. C'est dans ce cadre que cette thèse s'est inscrite avec l'idée d'un développement d'une source de faible puissance fonctionnelle en argon. L'amorçage d'une telle décharge n'étant pas immédiat, une démarche progressive qui passe par des décharges de mélange de gaz a été adoptée. Les décharges Xe-Ar se sont révélées très intéressantes pour la compréhension des mécanismes physiques qui régissent les PEH. La caractérisation en vitesse des ions Xe II (par Fluorescence Induite par Laser) associée à l'analyse en énergie par RPA a permis de remonter à des informations utiles sur les zones d'ionisation et d'accélération. Une technique originale de résolution temporelle du RPA basée sur une interruption rapide de la décharge ou sur les oscillations naturelles du courant de décharge, a été développée et a permis l'identification et la quantification des différentes espèces présentes dans le jet d'ions. Grâce aux résultats de l'étude paramétrique des décharges de mélange Xe-Ar, une décharge d'argon pur a pu être amorcée et caractérisée pour la première fois dans un PEH de faible puissance. / Since the 50s, electric propulsion has improved in order to establish itself on space propulsion field. The Hall Effect Thruster (HET) are mainly used for trajectory correction or satellites orbit maintaining. The HET provide high current densities and low energy ion beam that making it a good candidate for other applications such as microelectronics or surface treatments. Xenon propellant is most commonly used due to its high atomic mass and its low ionization energy. However, the high cost and difficult supply of xenon, leads to looking for alternative propellant for HET operation. In this context, this PhD thesis had as goal the development of a functional Argon low power source. Argon discharge ignition is not immediate, that why a progressive approach which involves gas mixture discharges was adopted. The Xe-Ar discharge gives very interesting results for the understanding of physical mechanisms governing HET. The characterization of Xe II ions velocity (Laser Induced Fluorescence) associated to the energy analysis by RPA have provided access to useful information on ionization and acceleration areas. An original time resolved RPA technique, based on an ultra-fast discharge interruption or on the discharge current oscillations, has been developed. This technique allows the identification and the quantification of different species present in the ion beam. Thanks to the discharge Xe-Ar study, a pure argon discharge could be initiated and characterized for the first time in a low power HET.