A numerical approach to magnetic field calculation in Hall thrusters considering nonlinear magnetic permeability with Aitken extrapolation for convergence acceleration

  • Jiasong Li orcid

    School of Physics, Dalian University of Technology, Dalian 116024, China
  • Yanbin Xi orcid

    School of Physics, Dalian University of Technology, Dalian 116024, China
  • Yue Liu orcid

    School of Physics, Dalian University of Technology, Dalian 116024, China
Article ID: 4172
DOI: https://doi.org/10.59400/adecp4172

(This article belongs to the Special Issue Numerical Technique and Analytical Theory of Differential-Integral Equation and the Interdisciplinary Meanings with Applied Physics Field)

Keywords: Hall thruster; magnetic field calculation; nonlinear magnetic permeability; finite difference method; nested iteration; Aitken extrapolation; convergence acceleration; magnetic circuit design

Abstract

This paper investigates the numerical computation of magnetic fields in a Hall thruster, a process governed by a nonlinear elliptic boundary value problem. The model rigorously accounts for the influence of ferromagnetic materials, where the relative permeability is defined as a magnetic field-dependent function exceeding unity in core regions and set to unity elsewhere. Consequently, the model equations are inherently nonlinear, and their coefficients exhibit discontinuity across material interfaces. To solve this complex system, the finite difference method is applied on a uniform staggered mesh to derive a system of nonlinear difference equations with discontinuous coefficients. An iterative algorithm featuring a nested loop structure is presented to tackle this nonlinearity: an inner loop computes the magnetic field for a fixed relative permeability, while an outer loop updates the permeability distribution based on the current field solution. A critical challenge in such simulations is the convergence difficulty under high excitation due to strong nonlinearity and magnetic saturation. To address this, we propose a robust nested iterative algorithm enhanced with Aitken extrapolation. The method is validated through numerical simulations on a miniature Hall thruster model across three distinct coil ampere-turn configurations. Results highlight a critical distinction: while the standard fixed-point iteration performs adequately under low-to-moderate excitation, it fails to converge under the high-excitation condition. In contrast, the proposed Aitken-accelerated algorithm achieves stable convergence across all test cases, successfully resolving the convergence bottleneck in high-field scenarios. This advancement provides a robust framework for the magnetic circuit design of high-power Hall thrusters.

Published
2026-06-03
How to Cite
Li, J., Xi, Y., & Liu, Y. (2026). A numerical approach to magnetic field calculation in Hall thrusters considering nonlinear magnetic permeability with Aitken extrapolation for convergence acceleration. Advances in Differential Equations and Control Processes, 33(2). https://doi.org/10.59400/adecp4172
Issue
Vol. 33 No. 2 (2026): In Progress
Section
Article

Copyright (c) 2026 Jiasong Li, Yanbin Xi, Yue Liu

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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