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Hall thrusters are susceptible to large-amplitude plasma oscillations thatimpact thruster performance and lifetime and are also difficult to model.High-speed cameras are a popular tool to study these dynamics due to theirspatial resolution and are a popular, nonintrusive complement to in-situprobes. High-speed video of thruster oscillations can be isolated (decomposed)into coherent structures (modes) with algorithms that help us better understandthe evolution and interactions of each. This work provides an introduction,comparison, and step-by-step tutorial on established Fourier and newer ProperOrthogonal Decomposition (POD) algorithms as applied to high-speed video of theunshielded H6 6-kW laboratory model Hall thruster. From this dataset, both setsof algorithms identify and characterize $m=0$ and $m>0$ modes in the dischargechannel and cathode regions of the thruster plume, as well as mode hoppingbetween the $m=3$ and $m=4$ rotating spokes in the channel. The Fourier methodsare ideal for characterizing linear modal structures and also provide intuitivedispersion relationships. By contrast, the POD method tailors a basis set usingenergy minimization techniques that better captures the nonlinear nature ofthese structures and with a simpler implementation. Together, the Fourier andPOD methods provide a more complete toolkit for studying Hall thruster plasmainstabilities and mode dynamics. Specifically, we recommend first applying PODfirst to quickly identify the nature and location of global dynamics and thenusing Fourier methods to isolate dispersion plots and other wave-based physics.

A comparison of Fourier and POD mode decomposition methods for high-speed Hall thruster video