This paper presents results obtained from numerical simulations of the spoke oscillation with a linearised time-dependent 2D code of the Hall discharge. These results are used to analyze the mechanism of the spoke from a physical point of view. There exist several hints pointing to a connection with an azimuthal variation of the ionization process and this is investigated in detail here. Moreover, the influence on the spoke properties of different operating parameters such as discharge voltage, mass flow, magnetic field, and thruster size is analysed by means of various parametric variations. The work presented here builds on previous studies by the authors 1, 2 where the azimuthal stability of the Hall discharge was analysed from a global point of view, as opposed to the more common local stability analyses. The simulations in Ref.[2] show both axial and azimuthal oscillations in the low frequency regime, typically known as breathing mode and spoke respectively. One of the drawbacks of the formulation used in Ref.[2] is the lack of heat conduction terms in the model causing large temperature gradients and a narrow ionization region. These issues are resolved in the current study by modifying the formulation and solution method in order to include heat conduction terms. Additionally, a comparison of the results obtained from local and global stability analyses is also presented here.

I dedicate this dissertation work to my family, especially to my parents, who have always supported me in this major endeavour.I take also this opportunity to sincerely thank professor Eduardo Ahedo, who has led me wisely through the path of research since the beginning and for more than a decade now.