A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate discharge current oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative value to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov-Poisson system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V HT simulation is performed through the hybrid Vlasov model. The ionization oscillation is analyzed. The oscillation amplitude and plasma density are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.