Thrust Efficiency, Energy Efficiency and Role of VDF in Hall Thruster Performance Analysis

Abstract

Abstract : A rocket power efficiency equation was written to explicitly account for the effect of the velocity distribution function (VDF) of the propellant jet on the conversion of anode electrical energy to jet kinetic energy. This enabled a mathematically rigorous distinction to be made between thrust efficiency and energy efficiency. In this approach anode thrust efficiency, the commonly reported figure of merit for Hall thrusters, is the product of three utilization efficiencies: (1) propellant utilization efficiency, (2) voltage utilization efficiency, and (3) current utilization efficiency, which are less than unity under all real operating conditions. Unit propellant utilization is characterized by 100 percent ionization to a single ionic species whose thrust vectors are all directed along the same thrust axis. Anode voltage utilization efficiency is unity when ion species are created at the anode and accelerated through the entire anode potential. Current utilization efficiency is the fraction of cathode electron flow utilized in neutralization of accelerated positive ions. It can never be unity because a portion of the electron flow must be recycled back to the anode to provide energy to ionize neutral propellant. The architecture of the efficiency analysis is such that energy efficiency becomes naturally expressed as a product of voltage and current utilization efficiencies, and is rigorously separated from propellant utilization efficiency. Thus, thrust efficiency is the product of propellant utilization efficiency and energy efficiency. The methodology is applied to analysis of data from systematic low and high power (0.2 to 50 kW) Hall thruster performance studies published in the open literature. The cited data includes measurement of thrust, propellant mass flow rate, anode voltage, and anode current coupled with various electrical and optical