Multiscale structural assessment of toroidal field coils via reduced-order models

In a tokamak fusion reactor the confinement of the plasma is guaranteed primarily by a series of Toroidal Field Coils (TFC). The TFCs generate a toroidal magnetic field, and must typically withstand large electromagnetic forces. A constant-tension theoretical approach is commonly applied to define an ideal TFC profile, equilibrating in-plane load distributions without shear and bending effects. This paper focuses on the effectiveness of reduced-order models to analyse the TFC mechanical response when also non-ideal shapes are considered. Different beam models are introduced by referring to different treatments of shear and bending effects. A bottom-up homogenisation technique is employed in order to account for the subscale arrangement of TFC components, allowing also to deduce quantitative indications on average localisation effects. The considered beam theories have been specialised to quantify the discrepancies in the macro-micro TFC mechanical response when arc-based approximations are considered instead of the ideal TFC profile. The successful comparison with numerical benchmark solutions, defined by detailed three-dimensional Finite Element models, confirm that beam-like approaches may be considered reliable in a preliminary design stage.