Preparation for High-Frequency Wave Dispersion Relation Measurements Using LIF, and Comparison of Ion Velocities in Stand-Alone Cathode Testing versus Hall Thruster Operation

Ion heating by waves in the lower hybrid frequency range that are driven unstable by density gradients and cross-field ion flow has been identified as a likely driver of front pole erosion in NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS). To validate this proposed mechanism's inclusion in thruster life simulations carried out with the Hall2De code, we are pursuing non-invasive measurements of the relevant wave dispersion relations using laser-induced fluorescence (LIF). This paper presents the derivations of the first-order perturbed ion velocity distribution function (IVDF) and the phase-sensitive detection steps that are needed to complete these measurements. A demonstration of our capability to resolve high-frequency electrostatic waves will first be carried out in a stand-alone hollow cathode test setup. We have also measured time-averaged ion velocities in the cathode plume, with two different cylindrical anode diameters. In this paper, the velocity vectors are compared with those previously measured in the cathode plume during thruster operation, and they are shown to be in reasonably good agreement for both anode sizes. We find that the mean radial ion velocities at the edge of the cathode plume are smaller in the thruster than in the stand-alone cathode configurations due to the presence of a secondary ion population streaming radially inwards from the region in front of the inner pole.