Forbes, M.Robertson, W.S.P.Zander, A.C.Paulides, J.J.H.2025-10-092025-10-092025Journal of Magnetism and Magnetic Materials, 2025; 630:173416-1-173416-160304-88531873-4766https://hdl.handle.net/2440/147708In this article we highlight an Elemental Modelling Method, as an alternative to the standard Harmonic (or Fourier) Model, that can include variable permeability and non-periodic 3D geometry with superposition of boundary-free analytic magnetic field solutions. The methodology is demonstrated with an exhaustive parametric search to optimise a set of tubular double-sided Halbach slotless permanent magnet linear synchronous motor topologies, within a fixed volume constraint. The modelling method is computationally efficient, facilitating the search of close to 900,000 topologies with an axisymmetric-2D assumption, subsequently converted to a full 3D design. The aim of this study is to investigate the effect of strategic addition of iron within the topologies, against the trade-off of reducing permanent magnet volume — such an analysis is not simple, or possible, within the Harmonic Model. The elements of the model include coil filaments, permanent magnets, and iron segments inclusive of saturation effects from nonlinear permeability. A design with inset permanent magnets and surface iron found in the parametric search is shown to outperform the optimal Halbach topologies, with improved figures of merit for force and force ripple with low phase currents. Results are compared with Finite Element Analysis and performance of a design with non-unity relative permeability of the permanent magnets is assessed.en© 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Magnetic field modelling; Exact analytical solution; Magnetostatics; Linear synchronous motor; Nonlinear magnetic materials; Semi-analytic forcesJournal article10.1016/j.jmmm.2025.173416858774Forbes, M. [0000-0001-6605-0164]Robertson, W.S.P. [0000-0001-7351-8378]Zander, A.C. [0000-0003-4099-8146]