Abstract: For designing magnetic fusion facilities, it is important to compute the magnetic field inside the electromagnetic coils due to superconducting quench limits. It is also necessary to compute the Lorentz force on coils to ensure a support structure is feasible. For both the internal field and force calculations, the coils cannot be approximated in the usual way as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables both the internal magnetic field vector and self-force to be computed rapidly and accurately within a 1D filament model. The method is obtained by rigorous analysis of the singularity, such that the filament model matches the true high-dimensional integrals for the field and force at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce direct finite-cross-section calculations for a non-planar coil of the HSX stellarator. Due to the efficiency of the model here, it is well suited for use inside optimization, such as in the optimization of stellarator coil shapes.
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