Azimuthal Spoke Propagation in Hall Effect Thrusters

Abstract

Spokes are azimuthally propagating perturbations in the plasma discharge of Hall effect thrusters (HETs) that travel in the E x B direction. The mechanisms for spoke formation are unknown, but their presence has been associated with improved thruster performance in some thrusters motivating a detailed investigation. The propagation of azimuthal spokes are investigated in a 6 kW HET by using high-speed imaging and azimuthally spaced probes. The spoke velocity is determined from high-speed image analysis using three methods with similar results. The spoke velocity for three discharge voltages (300, 400, and 450 V) and three anode mass flow rates (14.7, 19.5, and 25.2 mg/s) are between 1500 and 2200 m/s across a range of magnetic field settings. The spoke velocity is inversely dependent on magnetic field strength for lower B-fields and asymptotes at higher B-fields. Spoke velocities calculated from the probes are consistently higher by 30% or more. An empirically approximated dispersion relation of ω <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> = v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">θ</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> - ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ch</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> where α ≥ 1 yields a characteristic velocity that matches the ion acoustic speed for N5 eV electrons which exist in the near-anode and near-field plume regions of the discharge.