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The temporal characteristics of the Xe$^+$ ion axial Velocity DistributionFunction (VDF) were recorded in the course of low-frequency discharge currentoscillations ($\sim$~14 kHz) of the 5 kW-class PPS$\circledR$X000 Hallthruster. The evolution in time of the ion axial velocity component ismonitored by means of a laser induced fluorescence diagnostic tool with a timeresolution of 100 ns. As the number of fluorescence photons is very low duringsuch a short time period, a hom-made pulse-counting lock-in system was used toperform real-time discrimination between background photons and fluorescencephotons. The evolution in time of the ion VDF was observed at three locationsalong the thruster channel axis after a fast shut down of the thruster power.The anode discharge current is switched off at 2 kHz during 5 $\mu$s withoutany synchronization with the current oscillation cycle. This approach allows toexamine the temporal behavior of the ion VDF during decay and ignition of thedischarge as well as during forced and natural plasma oscillations.Measurements show that the distribution function of the axial component of theXe$^+$ ion does change periodically in time with a frequency close to thecurrent oscillation frequency in both forced and natural cases. The ion densityand the mean velocity are found to oscillate whereas the velocity dispersionstays constant, which indicates that ionization and acceleration layers haveidentical dynamics. Finally, variations over time of the electric field are forthe first time experimentally evidenced in a crossed-field discharge.

Time-evolution of the ion velocity distribution function in the discharge of a Hall effect thruster