One-dimensional stationary model of a hall thruster

Although Hall thrusters are one of the most successful and prevalent electric propulsion technologies used by satellites today, they are also complex devices and their unique crossed-field configuration makes modelling of the underlying plasma discharge challenging, particularly when trying to identify important scaling and similarity laws. In this work, we propose a time-independent one-dimensional model of a Hall thruster with the aim of understanding the overall discharge behaviour when input parameters (such as propellant type, mass flow rate, discharge voltage/current, and magnetic field topology) are varied. We obtain a complete analytical solution of the model, and we uncover several key similarity parameters, together with relations connecting them, that control system operation and performance.