Generalized reduced-order particle-in-cell scheme for Hall thruster modeling: concept and in-depth verification in the axial-azimuthal configuration

TL;DR

This paper introduces a mathematically rigorous reduced-order particle-in-cell scheme for Hall thruster modeling, demonstrating its accuracy and efficiency in quasi-2D simulations with potential for 3D applications.

Contribution

The paper develops a generalized quasi-multi-dimensional PIC scheme with proven convergence, validated through simulations that match full 2D results at reduced computational costs.

Findings

The reduced-order PIC scheme accurately reproduces full 2D simulation results.

Higher order approximations recover azimuthal instabilities in Hall thrusters.

The approach significantly reduces computational costs while maintaining predictive accuracy.

Abstract

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 the potentials of a preliminary implementation of this PIC scheme to resolve the multi-dimensional plasma processes in a Hall thruster in a manner close to traditional multi-dimensional PIC simulations. In this work, we first introduce a mathematically mature formulation for the dimensionality reduction of Poisson's equation, which enables the generalized "quasi-multi-dimensional" PIC scheme. We present the proof that the dimensionally reduced Poisson's equation converges to the multi-dimensional one in the limit. A reduced-dimension Poisson solver incorporating the dimensionality-reduction formulation is then verified for general 2D Poisson problems. Next, we present the results of several quasi-2D axial-azimuthal simulations performed using the generalized reduced-order electrostatic PIC scheme. We show that the improvements in the formulation of the reduced-order PIC notably augments its predictive capability, enabling the approach to reproduce quite accurately the results from reference full-2D PIC simulations in several conditions using low-order approximations of the 2D problem. Moreover, higher order approximations allow us to recover the same characteristics and behaviors reported in the literature regarding the azimuthal instabilities in Hall thrusters with simulations offering several factors reduction in computational cost. Finally, we discuss a series of sensitivity analyses, including the influence of the cathode boundary condition and the azimuthal domain length on the quasi-2D simulations' predictions. Accordingly, we outline in the conclusions the ongoing activities on the reduced-order scheme toward cost-effective three-dimensional studies of Hall thrusters' physics.