Velocity distribution functions (VDFs) in a Hall thruster are known to be non-Maxwellian. For instance, the acceleration and ionization occur simultaneously inside the channel so that the ions have a bi-Maxwellian VDF. In order to model the behavior of the plasma, two main methods have been developed: fluid and particle methods. Fluid models assume near-Maxwellian VDFs and particle methods, although nonequilibrium phenomena are captured, suffer from statistical noise. By comparison, a direct

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... ulation method which solves the Vlasov equation coupled with collision terms can achieve better resolution of VDFs. In this study, a one-dimensional direct Vlasov simulation using a bounded upwind scheme is developed and applied for a plasma simulation in a Hall thruster channel. Results obtained from the hybrid-Vlasov simulation show good agreement with hybrid-PIC results and experimental data. Low frequency plasma oscillations, often referred to as the breathing mode, are observed. Using the Vlasov simulation, an improved resolution of VDFs with less statistical noise is obtained in comparison to the particle simulation.