We report the first direct observation using a retarding potential analyzer of time-resolved ion energy distribution functions (IDFs) in a Hall thruster (HT) on two distinct time scales corresponding to the breathing mode ($\sim \mathrm{kHz}$) and the ion transit time oscillation (ITTO, $\sim 100\mathrm{kHz}$). We combined the dynamic time warping technique with a calculation of the cumulative quadratic distance applied to measure weakly nonperiodic oscillations to achieve a previously inaccessible fine resolution of ion-acceleration dynamics driven by ITTOs and revealing the footprint of multiple ion bunches on the IDF in accordance with theory. The analysis demonstrates the significant role of high-frequency instabilities in shaping the IDF and explains fundamental mechanisms of axial wave-particle interactions and ion transport in HTs.

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• Particle acceleration in plasmas
• Plasma instabilities
• Plasma transport
• Wave-wave, wave-particle interactions