Reduced-order particle-in-cell scheme for computationally efficient kinetic plasma modelling

Existing high-fidelity kinetic plasma simulations, such as particle-in-cell (PIC) method, can provide valuable insights into the physics of the E×B discharges unachievable with other numerical methods. However, their enormous computational cost does not allow for extensive parametric investigations and prohibits fully kinetic 3-dimensional simulations needed to properly study the multi-dimensional, multi-scale physics in real-size devices over real-world timescales. The reduced-order PIC (RO-PIC) scheme, developed in this work and extensively verified in various E×B plasma configurations, serves as a promising computational tool, realizing self-consistent multi-dimensional kinetic modeling of plasma at a drastically reduced computational cost (up to several orders of magnitude) compared to the conventional PIC simulations. The verified RO-PIC is used for extensive parametric investigations in 2D radial-azimuthal and axial-azimuthal Hall-thrusters-representative discharge settings. These studies demonstrated the RO-PIC’s utility for investigating plasma phenomena across a broad parameter space of both fundamental and applied significance. Also, they have provided unique aggregated insights into the variations in the plasma instabilities, the electrons’ cross-field transport, and the macroscopic plasma behavior with the changes in the system’s operational and physical parameters. In radial-azimuthal geometry, the studies reveal the dominance of various instabilities including Electron Cyclotron Instability (ECDI) and Modified Two Stream Instability (MTSI) with distinct consequences on plasma, under different electromagnetic field intensities and magnetic field curvatures. Along axial-azimuthal coordinates, the variation trends in plasma behavior and instabilities including Ion Acoustic Instability (IAI) and Transit Time Instability (ITTI) across diverse operating conditions are observed. The application of RO-PIC as a predictive engineering tool is demonstrated through a first-of-its-kind attempt to self-consistently simulate an industrial 20-kW-class Hall thruster kinetically within practical timeframes, obtaining predictions of the experimental performance parameters with accuracies of 70-80% across three simulated operating conditions. Finally, future directions for further advancing the RO-PIC, including its extension to 3D, are outlined.