3-D Nonstationary Simulation of Hall Thrusters

The thesis summarizes the work carried out by the author during the PhD course in Aerospace Engineering, XXI Cycle, at Universita' di Pisa, Dipartimento di Ingegneria Aerospaziale ”Lucio Lazzarino” (DIA). The goal of this work is to make a macroscopically exhaustive analysis of the physical phenomena involved in the study of Hall Effect Thrusters (HETs). The numerical model utilizes and extrapolates the results of several works on HETs and other electric thrusters. Moreover, we draw knowledge from rudiments and solution techniques by other fields of Computational Physics and include them in our simulation model. Among the different kinds of models for the plasma dynamics description, we have chosen to utilize a multifluid-quasineutral nonstationary model with a 3-D structured discretization of the simulation domain. The 3-D description of the problem is fundamentally focused to consider and accurately explore magnetic field configurations that are inherently non-axysimmetric due to the magnetic circuit construction. Moreover, the model aims to take into account a plasma dynamics inherently 3-D despite an axysimmetric construction. The analysis of the unsteady thruster’s operation aims to verify if the nonstationary phenomena, which were highlighted in several theoretical and experimental works, can be accurately modeled by the fluid framework. The magnetic model was described using the "magnetostatic approximation", thus it can be considered externally applied such an input parameter to the simulation of the plasma dynamics. Moreover, we split up the total magnetic field into two components, the former externally fixed, and the latter depending on the current induced by the motion of the plasma in- side the discharge channel. Taking into account the effects induced by the plasma dynamics on the magnetic circuit properties also permits to analyze configurations of magnetic field in series with the discharge. We started our model description by writing the plasma simulation model in a dimensional form using the fluid equations for a quasineutral three-components plasma. Subsequently, the dimensional fluid equations were expressed in a dimensionless form. The dimensionless form of the model permits to numerically solve it without consider scale effects depending on the value of discharge parameters and extrapolate some typical dimensionless parameters of the problem. Moreover, the dimensionless formulation permits to share the simulation results between different thrusters and effectively present them in scientific publications. Dealing with dimensionless parameters, a scale analysis of physical phenomena can be made. Indeed, using experimental data in the literature expressed in terms of macroscopic quantities for existing HETs, we can write scaling laws able to keep constant some dimensionless parameters for a reference thruster. The dimensionless analysis is considered of worth because it constitutes the basis of the conceptual design of HETs. Finally, a frequency analysis of 1-D discharge properties along the axial direction has been performed. This analysis was mainly focused to highlight the presence of low-frequency longitudinal oscillations, thus to validate the pattern of relevant fields with respect to existing experimental data or to numerical models presented in the literature.