High-energy tail formation in an ion energy distribution function in the cylindrical Hall thruster plasma

Ion energy distribution functions (IEDFs) of individual ion species having different charge states (i.e. Xe$^{+}$, Xe$^{2+}$, Xe$^{3+}$, etc.) in the Hall thruster plasma are obtained from the measured E $\times$ B probe spectrum by a novel inversion technique using the iterative Tikhonov regularization method. The obtained IEDFs show the existence of a high-energy tail in the cylindrical Hall thruster plasmas that is mainly due to Xe$^{+}$ ions despite the presence of Xe$^{2+}$ and Xe$^{3+}$ ions with a large fraction. Ion dynamics inside the plasma was numerically investigated to demonstrate that the high-energy tail is due to nonlinear ion acceleration in the plasma oscillating at typically 100 to 500 kHz. We found that this oscillation driven by transit-time instability is responsible for the shift of the IEDF of the Xe$^{+}$ ions toward the high-energy side, showing the formation of high-energy tail in the overall IEDF. It was also found that the Xe flow rate raised from 4 to 10 sccm increases the oscillation strength at the same frequency of 360 kHz, which can be applied to control of the shape of the IEDF.