A Reduced-Order Equivalent-Dipole Model for DC Stray Magnetic Fields

Accurate characterization of stray magnetic fields is essential in high-field devices, where external fields may affect diagnostics and personnel safety. Although finite-element models provide high-fidelity solutions, they may require extensive preprocessing and discretization of large source-free regions, making repeated evaluations costly when the magnetic source is unchanged. This paper proposes a reduced-order equivalent-dipole model that provides an analytical representation of the three-dimensional background stray field after one-time offline calibration. Dipoles are placed at Gauss–Legendre nodes within an auxiliary volume, while symmetry and anti-symmetry conditions are embedded in the source mapping. Their effective moments are identified from magnetic-flux-density data through a regularized linear inverse problem. The method is assessed for the SHiP spectrometer magnet at CERN against a high-fidelity finite-element reference. A controlled comparison of five model orders selects the 125-dipole configuration, reducing the relative vector 𝐿2 error on a common three-dimensional evaluation grid from 21.2% for 27 dipoles to 4.59%. An independently generated dense three-dimensional post-selection dataset confirms the accuracy of the selected model, giving a relative vector 𝐿2 error of 1.77% for 𝑑aux≥0.50 m. The complementary dense mid-plane assessment gives 0.95% over the same validity region.