Non-invasive time-resolved measurements of anomalous collision frequency in a Hall thruster

Abstract

The time-resolved cross-field electron anomalous collision frequency in a Hall thruster is inferred from minimally invasive laser-based measurements. This diagnostic is employed to characterize the relationship between the dominant low-frequency “breathing” oscillations and anomalous electron transport mechanisms. The ion Boltzmann equation combined with a generalized Ohm's law is used to infer key quantities including the ionization rate and axial electric field strength which are necessary in computing the total electron cross-field collision frequency. This is accomplished by numerically integrating functions of velocity moments of the ion velocity distribution function measured with laser-induced fluorescence, in conjunction with current density measurements at a spatial boundary. Estimates of neutral density are used to compute the classical collision frequency profile and the difference in the total collision frequency, and this quantity describes the anomalous collision frequency. This technique reveals the anticipated trends in electron transport: few collisions in the acceleration region but a collision frequency approaching the cyclotron frequency farther downstream. The time-resolved transport profiles indicate that the anomalous collision frequency fluctuates by several orders of magnitude during a breathing cycle. At troughs in the discharge current, classical collisions may dominate; at peaks in the discharge current, anomalous collisions dominate. These results show that the breathing mode and electron transport are directly correlated. This finding is discussed with regard to existing numerical models for the breathing mode and interpretations of anomalous electron transport.