[en] The Velocity Distribution Function (VDF) of metastable Xe⁺ ions was measured along the channel axis of the 5 kW-class PPS registered X000 Hall effect thruster by means of Laser Induced Fluorescence spectroscopy at 834.72 nm for various voltages, magnetic fields and mass flow rates. Axial velocity and dispersion profiles are compared to on-axis profiles obtained with the 1.5 kW-class PPS100 thruster. Outcomes of the comparison are threefold. (i) The broadening of the FDV across the region of strong magnetic field is a general feature for Hall thrusters. It originates in the overlap between ionization and acceleration layers. The velocity dispersion increases with the discharge voltage; it reaches up to 200 eV in unit of kinetic energy at 700 V. (ii) Most of the acceleration potential (≅70%) is localized outside the thruster channel whatever the thruster size and operating conditions. The electric field moves upstream when the applied voltage is ramped up; in other words the fraction of potential inside the channel increases with the voltage; (iii) A non negligible amount of very slow and very fast (kinetic energy higher than the applied potential) Xe⁺ ions are always observed. Such ions may find their origin in space and temporal oscillations of the electric field as suggested by numerical simulations carried out with a hybrid model