• Magnetohydrodinamic
• modeling
• rotational
• instability
• hollow
• cathodes
• kink
• MHD
• resistive
• electric propulsion
• Hall
• thruster
• magnetoidrodinamica
• modellazione
• rotazionale
• instabilità
• catodo
• cavo
• resistivo
• propulsione elettrica
• propulsore

The thesis is focused on the study of the rotational instability encountered in the plume of high-current hollow cathodes when an axial magnetic field is applied. The goal of this work is to develop an analytical description of the plasma column behaviour through a magnetohydrodynamic (MHD) approach. The instability is identified and treated as an external kink.
The perturbed equation of motion of the plasma column has been derived. Under necessary simplifying hypotheses, an equation describing the relation between frequencies and wavelengths of plasma instabilities has been obtained. The mathematical complexity of the equation hindered the direct imposition of boundary conditions. Experimental observations have been used to try to overcome the problem and obtain useful data from the relation. A parametric study has been performed to investigate the effect of plasma parameters variation on the growth rate, rotational frequency and wavelength of the instability. The general trends that have been obtained are in line with existing literature. Tuning of the parameters allowed the recreation of the experimentally observed behaviour of the plasma column. The obtained results confirm that the interpretation of the instability as an external kink is adequate.