A review of 3D particle-in-cell simulations for electron drift instability in Hall thrusters

This review summarizes how three-dimensional particle-in-cell (PIC) simulations are used to investigate the electron drift instability (EDI) in Hall thrusters and its link to anomalous cross-field electron transport, with emphasis on transport closures and computational feasibility. EDI dynamics are intrinsically three-dimensional, owing to their strong coupling to axial ion acceleration and radial plasma wall/sheath interactions; consequently, reduced dimensionality (1D/2D) PIC models tend to bias the mode structure and the inferred transport, motivating fully 3D PIC simulations. The review traces the evolution of 3D PIC modeling from early cost-driven reduced or scaled studies to high-fidelity channel--plume simulations enabling quantitative characterization. Advances from our group are also summarized, spanning WarpX-based investigations and the in-house PMSL code, with a focus on convergence acceleration, realistic field configurations, and transport-resolving diagnostics. Finally, representative computational workloads and wall-clock costs are compiled, and practical strategies for reducing time-to-solution while strengthening verification and enhancing the credibility of 3D PIC predictions are outlined.