• anode sheath
• coupling
• coupling voltage
• Hall effect thruster
• hollow cathode
• near anode region
• plasma sheath

In the present work a study of the plasma behaviour at the extremity of the accelerating channel of an Hall effect thruster, namely the near anode region and the region in which the plasma exiting the discharge chamber couples with that generated in the cathode, was carried out. The aim of this study was to provide physically representative boundary conditions for a preexisting first order model of the thruster channel with 2D magnetic coordinates, and to investigate their influence on the plasma flow in these devices.
In order to provide a suitable boundary condition for the near anode region a complete research on the problem of plasma sheath formation was performed, and an original sheath model which takes into account the effect of the electrons transmitted to the wall was developed. The potential of the plasma in front of the anode is given by the sum of the discharge voltage plus the sheath potential fall, which is calculated as a function of the plasma parameters at the extremity of the integration domain. A modified Bohm condition for the ion velocities at the anode, which depends on the total sheath potential fall, was also determined. Simulations of the plasma flow for a real thruster configuration (SITAEL HT-5k) were performed using the new anode boundary condition and the thruster channel model; the results have been presented as a function of the thruster operating conditions. For the simulated operative points, the classic sheath theory provides sufficiently accurate results in terms of total potential fall. However, the new sheath model is able to better describe situations in which the anode sheath tends to vanish, whose existence has been experimentally verified.
The second part of this thesis represents a first tentative to provide an estimation of the coupling voltage, which is defined as the voltage difference between the cathode common and the thruster beam plasma potential, as a function of the thruster operating condition. Due to its extreme complexity, the problem has been simplified approximating the coupling voltage with the potential difference between the cathode insert and the cathode far plume, during stand-alone operations. A reduced order model for the cathode interior has been used to obtain an approximated value of the plasma parameters at the orifice exit, then the solution has been used as boundary condition for a simplified 1-D fluid model of the cathode plume. The results obtained agree only in part with the experimental data available in literature. This is probably due to the fact that the model used is not able to describe the fundamental kinetic effects and instabilities in the cathode plume, besides the 2-D nature of the problem.
Finally, the two boundary conditions derived for the near anode and cathode regions have been coupled with the thruster channel model in order to simulate several operating conditions of the HT-5k Hall Thruster. The influence of the modifications made on the plasma profiles inside the channel have been analyzed, and the performance calculated before and after the implementation of the new conditions have been compared, together with the experimental data. The results, reported in terms of integral performances, showed a general improvement of a few percent in the model predictions. In particular the predicted performance are, on average, closer to the experimental data and the absolute error is always lower than 10% with respect to the measured parameter, while the predictions of the original code could differ also of 20%.
In conclusion, the objectives that were stated at the beginning of the work were fulfilled, and the baseline model was improved with physically representative descriptions of the anode and cathode regions. This upgraded model has proved effective in recreating the experimental performance and can be used to gather additional insight in the physics and operation of Hall thrusters.