Correlation and causation and time-lagged phase portrait analysis of discharge current and plume ion flux in a hall thruster as a function of facility operating pressure

We characterize discharge current and plume ion flux oscillations of the H9 Hall effect thruster (HET) at the 6-kW, 300 V, and 20 A operating condition, using krypton propellant. Initial time and frequency domain analyses show similarities between discharge current and ion flux. We then use the extended convergent cross mapping (eCCM) technique to validate the discharge current and ion flux dataset by determining their correlation and causation at background vacuum chamber pressures of 6.236, 14.03, 21.83, 28.06, 32.74, and 38.98 µTorr-Kr. We construct time-lagged phase portraits (TLPPs) to provide a unique representation of the H9 HET as a function of the operating pressure and to assess the similarity between discharge current and ion flux. The results show a high, positive correlation between discharge current and ion flux that decreases with increasing operating pressure, with a maximum correlation of 0.9547. Additionally, the discharge current influences the ion flux; this observation matches what one would expect, as ion flux originates within the thruster cavity where electron density oscillations are generated. The correlation results show that the eCCM technique can determine causality in thruster measurements. Furthermore, the TLPPs represent a fingerprint of a HET that can allow one to determine the operating state of the thruster as a function of operating pressure using the Earth mover’s distance (EMD) metric. From the lowest pressure, used as the reference, to the highest pressure, the EMD values are 0, 1.092, 1.672, 1.753, 1.871, and 2.023, showing that each TLPP is indeed distinct.