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 o...