• Plasma
• MPD Thrusters
• MHD
• Hall Effect Thrusters
• Erosion
• Scaling

The name "Plasma Thrusters" usually adresses all those devices which generate thrust for space propulsion using a working fluid that remains in the state of plasma throughout the acceleration process.
The present work started with the aim of carrying out a broad investigation of plasma flows inside the acceleration channels of plasma thrusters, paying special attention to the two best known devices belonging to this group: Hall Effect Thrusters (HET) and Magnetoplasmadynamic Thrusters (MPDT). Eventually, the work ended up focusing on two main issues, one related to Hall thrusters and the other one related to MPD thrusters. The thesis has been thus split into two main parts, the first one concerning the problem of defining a proper scaling methodology for Hall Effect thrusters and the second one devoted to numerical investigations of a plasma flow inside an MPD thruster.
About the first topic, a robust scaling methodology for HETs has been developed starting from the physical laws which govern the plasma behaviour inside the acceleration chamber. A reliable scaling method is a valuable tool in the preliminary design of HETs, because it allows the designer to immediately have a taste of what the thruster geometric and operational parameters will be for a chosen power level (or for achieving a desired performance). The method object of this thesis has a great flexibility and can be easily adapted to work satisfactorily both at high and low power levels. The extension of its applicability to low power levels has been possible exploiting Alta's wide experience on a low power HET like the HT-100 and with the aid of a dedicated numerical code describing the plasma flow along the chamber.
The scaling method here proposed has been tested versus a large number of experimental data and has proved to work well in a wide range of conditions, not only for different power levels but also for different thruster configuration(the method has been tested both on conventional Hall thrusters and on thrusters in "anode layer" configuration).
Unfortunately, one of the most important parameters to be considered when designing a new thruster, the operational lifetime, cannot be accurately predicted using the relatively simple equations involved in the scaling method.
The channel erosion process which determines the lifetime of a Hall thruster is a complex phenomenon and has to be treated separately. For this purpose a considerable effort has been devoted to develop a numerical method able to predict the erosion rate during the thruster operation. The method is based on a Monte Carlo Collision (MCC) simulation of the ion impacts with
the walls and it has been coupled with the scaling method (whose output, in terms of thruster geometric and operational parameters, constitutes the input for the numerical simulation of the channel erosion). The combination of the scaling method and the numerical code for HET lifetime prediction turns out to be an effective instrument for designing new Hall effect thrusters.
The second main topic analyzed during this work on plasma thrusters concerns MPD thrusters and consisted in the development of a numerical method to investigate the behaviour of plasma flows inside these devices.
MPD thrusters have always been plagued by plasma instability phenomena, which occur for high intensities of the applied current. These instabilities prevent smooth flow acceleration and severely affect the overall performance.
Understanding the mechanism lying behind their occurrence is crucial to counter their detrimental effects and improve the thruster efficiency.
Here, as a first step, a 1D model based on the equations of magnetohydrodynamics has been developed. The model, as well as the numerical code which comes with it, is very simple but in spite of its simplicity it successfully points
out several interesting aspects. It describes the different plasma acceleration mechanisms in an MPD thruster, giving an estimate of the thruster performance and a rough prediction of the instability threshold (in terms of applied discharge current). However, such a simple model is not able to give any description of flow behaviour after the instability occurrence, nor it can be used for describing a flow in complex duct geometries.
To have a more powerful tool for attempting a description of what happens in real plasma
flows, a 3D code which solves the full magneto-fluid-dynamics (MFD) equations has been developed. MFD equations consist of the Navier-Stokes equations plus the Maxwell equations which describe the evolution of the electromagnetic fields. The 3D code presented in this thesis is based on an existing solver for what concerns the solution of the Navier-Stokes equations (which have been properly modified to take into account the electromagnetic contributions in the momentum and energy conservation equations).
For what concerns the Maxwell equations, an independent code has been developed for solving them in space and time. Then, a strategy for coupling the two sub-codes has been defined and simple preliminary tests have been carried out to validate the full 3D code.