Electron transport and azimuthal oscillations in hall thrusters

The Hall Effect Thruster (HET) is a type of satellite electric propulsion device initially developed in the 1960’s independently by USA and the former USSR. The development continued in the shadow during the 1970’s in the Soviet Union to reach a mature status from the technological point of view in the 1980’s. In the 1990’s the advanced state of this Russian technology became known in western countries, which rapidly restarted the analysis and development of modern Hall thrusters. Currently, there are several companies in USA, Russia and Europe manufacturing Hall thrusters for operational use. The main applications of these thrusters are low-thrust propulsion of interplanetary probes, orbital raising of satellites and stationkeeping of geostationary satellites. However, despite the well proven in-flight experience, the physics of the Hall Thruster are not completely understood yet. Over the last two decades large efforts have been dedicated to the understanding of the physics of Hall Effect thrusters. However, the so-called anomalous diffusion, short name for an excessive electron conductivity along the thruster, is not yet fully understood as it cannot be explained with classical collisional theories. One commonly accepted explanation is the existence of azimuthal oscillations with correlated plasma density and electric field fluctuations. In fact, there is experimental evidence of the presence of an azimuthal oscillation in the low frequency range (a few kHz). This oscillation, usually called spoke, was first detected empirically by Janes and Lowder in the 1960s. More recently several experiments have shown the existence of this type of oscillation in various modern Hall thrusters. Given the frequency range, it is likely that the ionization is the cause of the spoke oscillation, like for the breathing mode oscillation. In the high frequency range (a few MHz), electron-drift azimuthal oscillations have been detected in recent experiments, in line with the oscillations measured by Esipchuk and Tilinin in the 1970’s. Even though these low and high frequency azimuthal oscillations have been known for quite some time already, the physics behind them are not yet clear and their possible relation with the anomalous diffusion process remains an unknown. This work aims at analysing from a theoretical point of view and via computer simulations the possible relation between the azimuthal oscillations and the anomalous electron transport in HET. In order to achieve this main objective, two approaches are considered: local linear stability analyses and global linear stability analyses. The use of local linear stability analyses shall allow identifying the dominant terms in the promotion of the oscillations. However, these analyses do not take into account properly the axial variation of the plasma properties along the thruster. On the other hand, global linear stability analyses do account for these axial variations and shall allow determining how the azimuthal oscillations are promoted and their possible relation with the electron transport.

Analytical models for the power subsystem and the attitude control subsystem of a microsatellite

El trabajo realizado en la presente tesis doctoral se debe considerar parte del proyecto UPMSat-2, que se enmarca dentro del ámbito de la tecnología aeroespacial. El UPMSat-2 es un microsatélite (de bajo coste y pequeño tamaño) diseñado, construido, probado e integrado por la Universidad Politécnica de Madrid (España), para fines de demostración tecnológica y educación. El objetivo de la presente tesis doctoral es presentar nuevos modelos analíticos para estudiar la interdependencia energética entre los subsistemas de potencia y de control de actitud de un satélite. En primer lugar, se estudia la simulación del subsistema de potencia de un microsatélite, prestando especial atención a la simulación de la fuente de potencia, esto es, los paneles solares. En la tesis se presentan métodos sencillos pero precisos para simular la producción de energía de los paneles en condiciones ambientales variables a través de su circuito equivalente. Los métodos propuestos para el cálculo de los parámetros del circuito equivalente son explícitos (o al menos, con las variables desacopladas), no iterativos y directos; no se necesitan iteraciones o valores iniciales para calcular los parámetros. La precisión de este método se prueba y se compara con métodos similares de la literatura disponible, demostrando una precisión similar para mayor simplicidad. En segundo lugar, se presenta la simulación del subsistema de control de actitud de un microsatélite, prestando especial atención a la nueva ley de control propuesta. La tesis presenta un nuevo tipo de control magnético es aplicable a la órbita baja terrestre (LEO). La ley de control propuesta es capaz de ajustar la velocidad de rotación del satélite alrededor de su eje principal de inercia máximo o mínimo. Además, en el caso de órbitas de alta inclinación, la ley de control favorece la alineación del eje de rotación con la dirección normal al plano orbital. El algoritmo de control propuesto es simple, sólo se requieren magnetopares como actuadores; sólo se requieren magnetómetros como sensores; no hace falta estimar la velocidad angular; no incluye un modelo de campo magnético de la Tierra; no tiene por qué ser externamente activado con información sobre las características orbitales y permite el rearme automático después de un apagado total del subsistema de control de actitud. La viabilidad teórica de la citada ley de control se demuestra a través de análisis de Monte Carlo. Por último, en términos de producción de energía, se demuestra que la actitud propuesto (en eje principal perpendicular al plano de la órbita, y el satélite que gira alrededor de ella con una velocidad controlada) es muy adecuado para la misión UPMSat-2, ya que permite una área superior de los paneles apuntando hacia el sol cuando se compara con otras actitudes estudiadas. En comparación con el control de actitud anterior propuesto para el UPMSat-2 resulta en un incremento de 25% en la potencia disponible. Además, la actitud propuesto mostró mejoras significativas, en comparación con otros, en términos de control térmico, como la tasa de rotación angular por satélite puede seleccionarse para conseguir una homogeneización de la temperatura más alta que apunta satélite y la antena. ABSTRACT The work carried out in the present doctoral dissertation should be considered part of the UPMSat-2 project, falling within the scope of the aerospace technology. The UPMSat-2 is a microsatellite (low cost and small size) designed, constructed integrated and tested for educational and technology demonstration purposes at the Universidad Politécnica de Madrid (Spain). The aim of the present doctoral dissertation is to present new analytical models to study the energy interdependence between the power and the attitude control subsystems of a satellite. First, the simulation of the power subsystem of a microsatellite is studied, paying particular attention to the simulation of the power supply, i.e. the solar panels. Simple but accurate methods for simulate the power production under variable ambient conditions using its equivalent circuit are presented. The proposed methods for calculate the equivalent circuit parameters are explicit (or at least, with decoupled variables), non-iterative and straight forward; no iterations or initial values for the parameters are needed. The accuracy of this method is tested and compared with similar methods from the available literature demonstrating similar precision but higher simplicity. Second, the simulation of the control subsystem of a microsatellite is presented, paying particular attention to the new control law proposed. A new type of magnetic control applied to Low Earth Orbit (LEO) satellites has been presented. The proposed control law is able to set the satellite rotation speed around its maximum or minimum inertia principal axis. Besides, the proposed control law favors the alignment of this axis with the normal direction to the orbital plane for high inclination orbits. The proposed control algorithm is simples, only magnetorquers are required as actuators; only magnetometers are required as sensors; no estimation of the angular velocity is needed; it does not include an in-orbit Earth magnetic field model; it does not need to be externally activated with information about the orbital characteristics and it allows automatic reset after a total shutdown of attitude control subsystem. The theoretical viability of the control law is demonstrated through Monte Carlo analysis. Finally, in terms of power production, it is demonstrated that the proposed attitude (on principal axis perpendicular to the orbit plane, and the satellite rotating around it with a controlled rate) is quite suitable for the UPMSat-2 mission, as it allows a higher area of the panels pointing towards the sun when compared to other studied attitudes. Compared with the previous attitude control proposed for the UPMSat-2 it results in a 25% increment in available power. Besides, the proposed attitude showed significant improvements, when compared to others, in terms of thermal control, as the satellite angular rotation rate can be selected to achieve a higher temperature homogenization of the satellite and antenna pointing.

Optimum sizing of bare-tape tethers for de-orbiting satellites at end of mission

De-orbiting satellites at end of mission would prevent generation of new space debris. A proposed de-orbit technology involves a bare conductive tape-tether, which uses neither propellant nor power supply while generating power for on-board use during de-orbiting. The present work shows how to select tape dimensions for a generic mission so as to satisfy requirements of very small tether-to-satellite mass ratio mt/MS and probability Nf of tether cut by small debris, while keeping de-orbit time tf short and product tf ×× tether length low to reduce maneuvers in avoiding collisions with large debris. Design is here discussed for particular missions (initial orbit of 720 km altitude and 63° and 92° inclinations, and 3 disparate MS values, 37.5, 375, and 3750 kg), proving it scalable. At mid-inclination and a mass-ratio of a few percent, de-orbit time takes about 2 weeks and Nf is a small fraction of 1%, with tape dimensions ranging from 1 to 6 cm, 10 to 54 μμm, and 2.8 to 8.6 km. Performance drop from middle to high inclination proved moderate: if allowing for twice as large mt/MS, increases are reduced to a factor of 4 in tf and a slight one in Nf, except for multi-ton satellites, somewhat more requiring because efficient orbital-motion-limited electron collection restricts tape-width values, resulting in tape length (slightly) increasing too.

Contribution to the improvement of communication services in nanosatellite constellations using delay and disruption tolerant networking based architectures

Esta tesis se desarrolla dentro del marco de las comunicaciones satelitales en el innovador campo de los pequeños satélites también llamados nanosatélites o cubesats, llamados así por su forma cubica. Estos nanosatélites se caracterizan por su bajo costo debido a que usan componentes comerciales llamados COTS (commercial off-the-shelf) y su pequeño tamaño como los Cubesats 1U (10cm*10 cm*10 cm) con masa aproximada a 1 kg. Este trabajo de tesis tiene como base una iniciativa propuesta por el autor de la tesis para poner en órbita el primer satélite peruano en mi país llamado chasqui I, actualmente puesto en órbita desde la Estación Espacial Internacional. La experiencia de este trabajo de investigación me llevo a proponer una constelación de pequeños satélites llamada Waposat para dar servicio de monitoreo de sensores de calidad de agua a nivel global, escenario que es usado en esta tesis. Es ente entorno y dadas las características limitadas de los pequeños satélites, tanto en potencia como en velocidad de datos, es que propongo investigar una nueva arquitectura de comunicaciones que permita resolver en forma óptima la problemática planteada por los nanosatélites en órbita LEO debido a su carácter disruptivo en sus comunicaciones poniendo énfasis en las capas de enlace y aplicación. Esta tesis presenta y evalúa una nueva arquitectura de comunicaciones para proveer servicio a una red de sensores terrestres usando una solución basada en DTN (Delay/Disruption Tolerant Networking) para comunicaciones espaciales. Adicionalmente, propongo un nuevo protocolo de acceso múltiple que usa una extensión del protocolo ALOHA no ranurado, el cual toma en cuenta la prioridad del trafico del Gateway (ALOHAGP) con un mecanismo de contienda adaptativo. Utiliza la realimentación del satélite para implementar el control de la congestión y adapta dinámicamente el rendimiento efectivo del canal de una manera óptima. Asumimos un modelo de población de sensores finito y una condición de tráfico saturado en el que cada sensor tiene siempre tramas que transmitir. El desempeño de la red se evaluó en términos de rendimiento efectivo, retardo y la equidad del sistema. Además, se ha definido una capa de convergencia DTN (ALOHAGP-CL) como un subconjunto del estándar TCP-CL (Transmission Control Protocol-Convergency Layer). Esta tesis muestra que ALOHAGP/CL soporta adecuadamente el escenario DTN propuesto, sobre todo cuando se utiliza la fragmentación reactiva. Finalmente, esta tesis investiga una transferencia óptima de mensajes DTN (Bundles) utilizando estrategias de fragmentación proactivas para dar servicio a una red de sensores terrestres utilizando un enlace de comunicaciones satelitales que utiliza el mecanismo de acceso múltiple con prioridad en el tráfico de enlace descendente (ALOHAGP). El rendimiento efectivo ha sido optimizado mediante la adaptación de los parámetros del protocolo como una función del número actual de los sensores activos recibidos desde el satélite. También, actualmente no existe un método para advertir o negociar el tamaño máximo de un “bundle” que puede ser aceptado por un agente DTN “bundle” en las comunicaciones por satélite tanto para el almacenamiento y la entrega, por lo que los “bundles” que son demasiado grandes son eliminados o demasiado pequeños son ineficientes. He caracterizado este tipo de escenario obteniendo una distribución de probabilidad de la llegada de tramas al nanosatélite así como una distribución de probabilidad del tiempo de visibilidad del nanosatélite, los cuales proveen una fragmentación proactiva óptima de los DTN “bundles”. He encontrado que el rendimiento efectivo (goodput) de la fragmentación proactiva alcanza un valor ligeramente inferior al de la fragmentación reactiva. Esta contribución permite utilizar la fragmentación activa de forma óptima con todas sus ventajas tales como permitir implantar el modelo de seguridad de DTN y la simplicidad al implementarlo en equipos con muchas limitaciones de CPU y memoria. La implementación de estas contribuciones se han contemplado inicialmente como parte de la carga útil del nanosatélite QBito, que forma parte de la constelación de 50 nanosatélites que se está llevando a cabo dentro del proyecto QB50. ABSTRACT This thesis is developed within the framework of satellite communications in the innovative field of small satellites also known as nanosatellites (<10 kg) or CubeSats, so called from their cubic form. These nanosatellites are characterized by their low cost because they use commercial components called COTS (commercial off-the-shelf), and their small size and mass, such as 1U Cubesats (10cm * 10cm * 10cm) with approximately 1 kg mass. This thesis is based on a proposal made by the author of the thesis to put into orbit the first Peruvian satellite in his country called Chasqui I, which was successfully launched into orbit from the International Space Station in 2014. The experience of this research work led me to propose a constellation of small satellites named Waposat to provide water quality monitoring sensors worldwide, scenario that is used in this thesis. In this scenario and given the limited features of nanosatellites, both power and data rate, I propose to investigate a new communications architecture that allows solving in an optimal manner the problems of nanosatellites in orbit LEO due to the disruptive nature of their communications by putting emphasis on the link and application layers. This thesis presents and evaluates a new communications architecture to provide services to terrestrial sensor networks using a space Delay/Disruption Tolerant Networking (DTN) based solution. In addition, I propose a new multiple access mechanism protocol based on extended unslotted ALOHA that takes into account the priority of gateway traffic, which we call ALOHA multiple access with gateway priority (ALOHAGP) with an adaptive contention mechanism. It uses satellite feedback to implement the congestion control, and to dynamically adapt the channel effective throughput in an optimal way. We assume a finite sensor population model and a saturated traffic condition where every sensor always has frames to transmit. The performance was evaluated in terms of effective throughput, delay and system fairness. In addition, a DTN convergence layer (ALOHAGP-CL) has been defined as a subset of the standard TCP-CL (Transmission Control Protocol-Convergence Layer). This thesis reveals that ALOHAGP/CL adequately supports the proposed DTN scenario, mainly when reactive fragmentation is used. Finally, this thesis investigates an optimal DTN message (bundles) transfer using proactive fragmentation strategies to give service to a ground sensor network using a nanosatellite communications link which uses a multi-access mechanism with priority in downlink traffic (ALOHAGP). The effective throughput has been optimized by adapting the protocol parameters as a function of the current number of active sensors received from satellite. Also, there is currently no method for advertising or negotiating the maximum size of a bundle which can be accepted by a bundle agent in satellite communications for storage and delivery, so that bundles which are too large can be dropped or which are too small are inefficient. We have characterized this kind of scenario obtaining a probability distribution for frame arrivals to nanosatellite and visibility time distribution that provide an optimal proactive fragmentation of DTN bundles. We have found that the proactive effective throughput (goodput) reaches a value slightly lower than reactive fragmentation approach. This contribution allows to use the proactive fragmentation optimally with all its advantages such as the incorporation of the security model of DTN and simplicity in protocol implementation for computers with many CPU and memory limitations. The implementation of these contributions was initially contemplated as part of the payload of the nanosatellite QBito, which is part of the constellation of 50 nanosatellites envisaged under the QB50 project.