AIAA Propulsion and Energy 2017, July 10–12, Atlanta, GA A Critical Review of Thrust Models for Applied-Field Magnetoplasmadynamic Thrusters William J. Coogan ∗ and Edgar Y. Choueiri † Princeton University, Princeton, NJ, 08544, USA A critical review of published thrust models for applied-field magnetoplasmadynamic thrusters is presented, along with a new model addressing shortcomings related to electrode and magnet geometry. While numerous theoretical thrust models have been presented in the literature, there has not been a comprehensive comparison to determine which best predicts thruster behavior across a large parameter space. In order to make this determi- nation, all thrust data available in the literature were collected into a single database and tested against each model. Unlike previous comparisons between prediction and measure- ment, only the regime in which the applied-field thrust component dominates is examined, allowing for a direct comparison without invoking models of self-field and gasdynamic components of thrust. The degree to which each model deviates from measurement is de- termined for each controllable parameter. It is found that the largest deviations are due to incorrect representation of the effects of electrode and solenoid geometries. In light of this comparative study, an improved empirical model is derived as a function of nondimensional parameters representing these geometric variables. The improved agreement is attributed to the effects of magnetic field topology near the anode, which sets the effective anode radius that controls the magnitude of the Lorentz force for certain electrode geometries. Nomenclature B A Applied magnetic field, T c s Sound speed, m/s F Force density, N/m 3 j Current density, A/m 2 J Current, A k Scaling constant k B Boltzmann constant, J/K l Axial length, m ˙ m Mass flow rate, kg/s M Atomic mass, u n Density, m -3 N A Avogadro’s number p b Background pressure, mTorr r Radius, m ¯ r Ratio of anode radius to cathode radius r * Characteristic length scale, m ˆ r Percentage distance between inner and outer surfaces ˆ r * Percentage distance at which ˆ s is minimized r B Average solenoid radius, m r Bi Inner solenoid radius, m r Bo Outer solenoid radius, m ˆ s Relative standard deviation T Thrust, N ¯ T Dimensionless thrust parameter ˆ ¯ T Normalized thrust parameter T Temperature, K u ex Exhaust velocity, m/s V Voltage, V ¯ Y Ionization factor z Distance from solenoid along thrust axis Z Charge number α Degree of ionization β Ratio of gasdynamic to magnetic pressure γ Adiabatic index ǫ i Ionization energy, eV ζ Detachment parameter, s 6 /m 9 κ Scaling constant * Graduate Student, MAE Dept., Princeton University, AIAA Student Member. † Chief Scientist, EPPDyL, Professor, Applied Physics Group, MAE Dept., Princeton University, AIAA Fellow. Copyright c  2017 by the American Institute of Aeronautics and Astronautics, Inc. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. 1 of 27 American Institute of Aeronautics and Astronautics Paper AIAA-2017-4723