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The velocity-distribution function (VDF) of metastable Xe+ ions was measured along the channel axis of the 5-kW-class PPSX000 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: 1) The broadening of the VDF 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 kinetic-energy dispersion increases with the discharge voltage; it reaches up to 200 eV at 700 V. 2) Most of the acceleration potential 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, i.e., the fraction of potential inside the channel increases with the voltage. On the contrary, the electric field is shifted downstream when the gas flow rate increases. The magnetic field has a little impact on the potential distribution. 3) A nonnegligible amount of very fast (kinetic energy higher than the applied potential) and very slow 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 both kinetic and hybrid models.