Analytical model of a Hall thruster

Hall thrusters are one of the most successful and prevalent electric propulsion systems for spacecraft in use today. However, they are also complex devices and their unique E×B configuration makes modeling of the underlying plasma discharge challenging. In this work, a steady-state model of a Hall thruster is developed and a complete analytical solution presented that is shown to be in reasonable agreement with experimental measurements. A characterization of the discharge shows that the peak plasma density and ionization rate nearly coincide and both occur upstream of the peak electric field. The peak locations also shift as the thruster operating conditions are varied. Three key similarity parameters emerge that govern the plasma discharge and which are connected via a thruster current–voltage relation: a normalized discharge current, a normalized discharge voltage, and an amalgamated parameter, α¯, that contains all system geometric and magnetic field information. For a given normalized discharge voltage, the similarity parameter α¯ must lie within a certain range to enable high thruster performance. When applied to a krypton thruster, the model shows that both the propellant mass flow rate and the magnetic field strength must be simultaneously adjusted to achieve similar efficiency to a xenon thruster (for the same thruster geometry, discharge voltage, and power level).