Optimization of passive superconducting coil arrays

Inverse magnetostatic optimization of coils is an important problem across scientific fields; a desired magnetic field is prescribed, and a distribution of steady currents is computed to produce that target field. Here we consider the novel problem of optimizing a large set of passive superconducting coils (PSCs) with currents induced by a background external field instead of using power supplies. In the nuclear fusion literature, such passive coils have been proposed to produce the 3D magnetic fields for stellarators (reducing the complexity of toroidal field coils), generate advantageous magnetic field perturbations in tokamaks, and provide passive stabilization. However, optimization has not been previously performed to test the feasibility of these applications. In this work, we formalize the large-scale optimization of PSCs with respect to the orientation of each coil, and demonstrate the advantages of this approach for stellarator optimization. Optimization of energized, window-pane coils can reuse much of the present work. We conclude by generating passive coil designs for a vacuum QH and a finite-beta QA stellarator.