Inference of Plasma Wave Dispersion Relation from Transfer-Function Laser-Induced Fluorescence

Hall thrusters are annular ExB plasma devices which are widely used to accelerate ions to high speeds and provide efficient in-space propulsion. These devices are rich with so-called "non-classical" particle transport which presents a difficulty to predictive modeling and improved design. In many cases, this anomalous motion of particles, especially electrons, has been attributed to various plasma wave structures, which can exchange energy and momentum with both electrons and ions. In order to better understand and model the operation of Hall thrusters, it is necessary to experimentally characterize this plasma wave environment throughout the discharge.

We present a novel technique for determining the dispersion relation of low-frequency plasma waves propagating in a low-density plasma such as the Hall thruster plume. We apply laser-induced fluorescence to measure the velocity distribution of ions in the hollow cathode plume of this device with temporal resolution up to 100 kHz. Synchronized acquisitions spaced 1 mm apart allow for the statistical estimation of the wavenumber and phase at each frequency and velocity, providing the dispersion relation and growth rate of the measured waves. We use this technique to characterize rotational waves in the hollow cathode plume.