Methodology and Historical Perspective of a Hall Thruster Efficiency Analysis

Abstract

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 farfield plume diagnostics, a case study is presented of low-discharge voltage operation from a 6 kW laboratory Hall thruster. Nomenclature A = spherical shell surface area element in the plume E 1 = voltage exchange parameter E 2 = mass exchange parameter F = thrust density vector in the plume F = Faraday constant, 96; 485 C=mol of charge f j = normalized ion mass flow fraction of jth ion species fv = velocity distribution function of ions and neutrals g = Earth's gravitational constant at sea level, 9:806 m=s 2 I Axial = axial component of beam current parallel to thruster centerline I Beam = integrated beam current I d = anode discharge current I sp = total specific impulse J = current density in the plume at angular position j = propellant charge state index, 0, 1, 2, 3, etc., for Xe 0 , Xe 1 , Xe 2 , Xe 3 M = molecular weight of propellant, Xe 0:1313 kg=mol _ m i = mass flow rate of ions, where P _ m j _ m i for j 1 to the jth ion species _ m j = mass flow rate of jth species _ m T = total mass flow rate to the anode and cathode, where P _ m j _ m T for j 0 to the jth ion species _ m = mass flux at angular position P d = discharge power to the anode P jet = jet power P loss = power lost to Joule heating processes P min = minimum power required to sustain ionization Q = average charge of propellant ions R = downst...

Conducting Wall Hall Thrusters

“…The original version of this thruster was a joint development between AFRL, JPL and the University of Michigan [23,[25][26][27][28]. The data collected on this thruster at JPL is used to validate plasma simulations [18,22,29] intended to evaluate thrusters being considered for NASA science missions.…”

Performance of a Helicon Hall Thruster Operating with Xenon, Argon, and Nitrogen

“…1,20 These components are determined by thruster telemetry, performance measurements, and probe diagnostics, and they can reveal the physical nature of thruster inefficiencies. This section outlines the efficiency architecture used to evaluate the performance of the HHT.…”

Magnetically Shielded Miniature Hall Thruster: Performance Assessment and Status Update

“…The scanning Faraday probe measured an ion current of 0.82 A, corrected for charge exchange collisions using the theory presented in [14]. A beam divergence half angle of approximately 43°, containing approximately 95% of the momentum-weighted ion current, was observed [15]. Figure 2 shows the uncorrected and corrected traces of the Faraday probe scan.…”

“…Xenon mass flow rates were identical to operation in jet mode: 12 sccm to the anode and 1 sccm to the cathode. The ion current reported by the scanning Faraday probe was 0.80 A, corrected for charge exchange collisions, with a divergence half angle of approximately 48° containing approximately 95% of the momentum-weighted ion current; the uncorrected and corrected scans for this operating mode are shown in Figure 5 [14,15]. The RPA recorded a most probable ion potential of 261 V. As shown in Figure 6, a beam species mix of approximately73.6% singly, 19.0% doubly, and 7.4% triply charged ions was measured by the ExB probe, again using Gaussian fits to the data.…”