  An axial-azimuthal two-dimensional Hall thruster discharge model was
developed for analyzing gradient drift instability (GDI) and cross-field
electron transport enhancement induced solely by the GDI. A hybrid
particle-fluid model was used for the partially ionized plasma, where the
inertialess electron fluid in the quasineutral plasma was assumed. A
nonoscillatory numerical method was proposed for the potential solver in the
electron fluid model to avoid numerical instability and analyze the physics of
GDI accurately. A simulation is performed for a 1 kW-class anode-layer-type
Hall thruster, and the flow field with plasma instability is presented. Plasma
instability with vortex-like structures is observed in the acceleration and
plume regions. The generated plasma instability enhances the cross-field
electron transport in the axial direction around the channel exit and in the
plume region. Grid convergence is confirmed regarding the effect of electron
transport enhancement, which indicates that cross-field electron transport
enhancement is based on the plasma instability. Furthermore, the comparison
between the simulation results and linear perturbation analyses demonstrates
that the simulated plasma instability reflects the theory of GDI. Thus, it is
concluded that the hybrid model is useful for the analyses of GDI, and the GDI
can enhance the cross-field electron transport in Hall thrusters.
