Methodology and Historical Perspective of a Hall Thruster Efficiency Analysis

A Hall thruster performance architecture was developed based on separation of the total thrust directed along thruster centerline into mass-weighted and momentum-weighted terms. With this formulation, the total thruster efficiency equation was analytically decomposed to explicitly account for the effects of energy conversion losses, plume divergence, and the velocity distribution function of the propellant jet. Thruster efficiency is defined as the product of 1) energy efficiency, 2) propellant efficiency, and 3) beam efficiency. Energy efficiency comprises losses due to ionization processes and losses that manifest as Joule heating, and contains no information about the vector properties of the jet. Propellant efficiency incorporates losses from dispersion in the jet composition and is unity for 100% ionization to a single ion species. The effect of neutrals on dispersion of the jet velocity distribution function in propellant efficiency is introduced in the neutral-gain utilization. The beam efficiency accounts for divergence of the jet and is ideal when the ion velocity vectors are parallel to the thrust axis. Plume divergence is defined as a momentum-weighted term, and the approximation as a charge-weighted term is characterized. The efficiency architecture is derived from first principles and is applicable to all propulsion employing electrostatic acceleration, including Hall thrusters and ion thrusters. Distinctions and similarities to several past methodologies are discussed, including past ion thruster analyses, early Russian performance studies, and contemporary architectures. To illustrate the potential for enhanced understanding of loss mechanisms and ionization processes with an array of far-field plume diagnostics, a case study is presented of low-discharge voltage operation from a 6 kW laboratory Hall thruster.