• hollow cathodes
• plasma
• plume
• electric propulsion
• CFD modeling

The use of electric propulsion in spacecraft applications is rising globally. The modeling of hollow cathodes used in flight thrusters, such as Hall and Ion ones or in other types of plasma sources, have advanced significantly in recent years. Hollow cathodes are devices necessary to generate plasma discharges. They are rich in plasma physics and research issues to be investigated and resolved. One of the most interesting region of the hollow cathode is the plume for the different phenomena that occur inside it, including waves and instabilities.
To give some insight into plasma plume dynamics a full 2D code is necessary.
Nevertheless the complexity of this kind of models limit their applicability. There is the need of developing simpler codes that describe the plasma plume in terms of properties of physical interest and have lower computational weight.
\\The present project aims to build a 1D model of governing equations that take into account time and space variation of the variables and also collisions. The choice of a 1D model is related even to the necessity of coupling the work with another existing code that has already been developed by University of Pisa as part of ASPIRE, a European project.
Firstly the present research is focused on the selection of the proper approach to describe the plasma plume and the formulation of the the governing equations. The characteristics of the flow in the hollow cathode varies between the interior, where the mean free path is small enough to allow for the application of fluid models, and the exterior, where the mean free path can become sufficiently large to challenge the continuum approximation. Despite this, a many fluid theory is chosen to obtain the governing equations describing the plume dynamics, due to the easiness in managing this approach and for the above mentioned willingness of having a 1D code to be coupled with another mono dimensional one. In the second phase the attention is set on finding a solving strategy and writing an algorithm to numerically solve the conservation laws. A Computational Fluid Dynamics (CFD) technique is selected to solve the system of partial differential equations (PDE’s), strongly coupled and non linear.
Eventually the results obtained are compared with experimental data. Unfortunately there are not many empirical informations in the literature and it is necessary to improve the 1D code enriching it with many other phenomena that have been neglected in this model.
This work paves the way to future numerical mono dimensional investigations used to simulate the plasma plume behaviour.