Dimensionality reduction of Poisson's equation with application to particle-in-cell simulations of Hall thrusters

TL;DR

This paper presents a new dimensionality reduction method for Poisson's equation that significantly decreases computational costs in particle-in-cell simulations of Hall thrusters while maintaining accuracy in plasma parameter distributions.

Contribution

The authors introduce a novel reduced-order particle-in-cell scheme for Poisson's equation, enabling efficient and accurate simulations of Hall thrusters with lower computational requirements.

Findings

Accurately resolves axial plasma distributions in quasi-2D simulations.

Replicates azimuthal instability characteristics consistent with literature.

Demonstrates reduced computational cost compared to traditional methods.

Abstract

In this article, we introduce a novel dimensionality reduction formulation for the Poisson's equation in the Vlasov-Poisson system that yields a reduced-order particle-in-cell scheme. This scheme allows a remarkable reduction in the computational cost of self-consistent kinetic simulations of Hall thrusters. The formulation of the dimensionality reduction approach, together with its verification for a general Poisson's problem, is presented. Moreover, we show the results of several "quasi-2D" axial-azimuthal simulations we performed with the conditions of a well-established 2D3V reference case. Comparison between the results of the quasi-2D simulations and the reference case revealed that our method is able to resolve accurately the axial distributions of the intensive plasma parameters. In addition, the characteristics of the azimuthal instabilities observed from the quasi-2D simulation are shown to be closely in line with those reported in the literature. Accordingly, the reduced-order PIC scheme is verified as a viable, low-computational-cost alternative to the traditional multi-dimensional particle-in-cell simulations of Hall thrusters.