Scaling of thrust in self-field magnetoplasmadynamic thrusters

The magnetoplasmadynamic thruster (MPDT) has recently passed milestones in performance and lifetime that have prompted renewed interest in its unique advantages for energetic space missions. Mission and system studies, as well as ongoing performance characterization, require the use of simple relations for the scaling of performance parameters. The Maecker formula has long played such a role for the thrust of the self-field MPDT. The formula is shown to be too simplistic to account for the trends in measured thrust data that exhibit departures from the model, particularly at low current. We show that at high currents, the departures can be explained by the evolution of the current densities over the electrode surfaces that influence the spatial distribution of the volumetric Lorentz force densities. At low current levels the departures are attributed to the scaling of gasdynamic pressure distributions induced by the pinching components of the volumetric electromagnetic forces. The insight was used to formulate a more accurate empirically based model for the scaling of the thrust of an MPDT.