  The temporal characteristics of the Xe$^+$ ion axial Velocity Distribution
Function (VDF) were recorded in the course of low-frequency discharge current
oscillations ($\sim$~14 kHz) of the 5 kW-class PPS$\circledR$X000 Hall
thruster. The evolution in time of the ion axial velocity component is
monitored by means of a laser induced fluorescence diagnostic tool with a time
resolution of 100 ns. As the number of fluorescence photons is very low during
such a short time period, a hom-made pulse-counting lock-in system was used to
perform real-time discrimination between background photons and fluorescence
photons. The evolution in time of the ion VDF was observed at three locations
along 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 without
any synchronization with the current oscillation cycle. This approach allows to
examine the temporal behavior of the ion VDF during decay and ignition of the
discharge as well as during forced and natural plasma oscillations.
Measurements show that the distribution function of the axial component of the
Xe$^+$ ion does change periodically in time with a frequency close to the
current oscillation frequency in both forced and natural cases. The ion density
and the mean velocity are found to oscillate whereas the velocity dispersion
stays constant, which indicates that ionization and acceleration layers have
identical dynamics. Finally, variations over time of the electric field are for
the first time experimentally evidenced in a crossed-field discharge.

Plasma Physics