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For designing high-field electromagnets, the Lorentz force on coils must becomputed to ensure a support structure is feasible, and the inductance shouldbe computed to evaluate the stored energy. Also, the magnetic field and itsvariation inside the conductor is of interest for computing stress and strain,and due to superconducting quench limits. For these force, inductance, energy,and internal field calculations, the coils cannot be naively approximated asinfinitesimally thin filaments due to divergences when the source andevaluation points coincide, so more computationally demanding calculations areusually required, resolving the finite cross-section of the conductors. Here,we present a new alternative method that enables the internal magnetic fieldvector, self-force, and self-inductance to be computed rapidly and accuratelywithin a 1D filament model. The method is applicable to coils for which thecurve center-line can have general noncircular shape, as long as the conductorwidth is small compared to the radius of curvature. This paper extends aprevious calculation for circular-cross-section conductors [Hurwitz et al,arXiv:2310.09313 (2023)] to consider the case of rectangular cross-section. Thereduced model is derived by rigorous analysis of the singularity, regularizingthe filament integrals such that they match the true high-dimensional integralsat high coil aspect ratio. The new filament model exactly recovers analyticresults for a circular coil, and is shown to accurately reproduce fullfinite-cross-section calculations for a non-planar coil of a stellaratormagnetic fusion device. Due to the efficiency of the model here, it is wellsuited for use inside design optimization.

Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils. II. Rectangular cross-section