Concept of the generalized reduced-order particle-in-cell scheme and verification in an axial-azimuthal Hall thruster configuration

Abstract

The reduced-order particle-in-cell (PIC) scheme is a novel modeling approach that enables computationally efficient electrostatic kinetic simulations of plasma. In our previous publications, we demonstrated that a proof-of-concept implementation of this novel PIC scheme resolves the multi-dimensional plasma processes and their interactions in a Hall thruster in a manner close to traditional electrostatic PIC codes. In this work, we extend our efforts on this topic and present a mathematically mature formulation for the dimensionality reduction of Poisson’s equation in the Vlasov-Poisson system, which enables the generalized reduced-order ‘quasi-multi-dimensional’ PIC scheme. The applicability of the dimensionality-reduction approach to solve general 2D Poisson problems is numerically verified. Next, we present several reduced-order quasi-2D (Q2D) simulations of a well-defined axial-azimuthal simulation case from the literature using approximation orders of the 2D problem whose computational costs are 2%-15% of a full-2D simulation. It is shown that these reduced-order simulations allow us to recover the same characteristics, behaviors and effects reported in the literature regarding the azimuthal instabilities in Hall thrusters. Moreover, in terms of the time-averaged plasma properties, it was found that, when increasing the approximation order, the error associated with the Q2D simulations’ predictions decreases from 15% to 4% for the electric field and from 20% to 2% for the ion number density. We have additionally discussed a series of sensitivity analysis results, including the influence of the initial number of macroparticles per cell on the predictions of the Q2D simulations. According to the detailed results and analyses presented, we conclude that the generalized reduced-order PIC scheme serves as a rigorous foundation for eventual cost-effective and comprehensive three-dimensional kinetic studies of the physics in Hall thrusters and similar electrostatic plasma technologies.