Minimizing Magnetic Island Width Sensitivity to Multi-Filament Coil Shape Perturbations

Stellarator coil optimization attempts to reconstruct magnetic fields from fixed-boundary equilibria. These reconstructions are typically not perfect and there will be differences between the fixed and free-boundary equilibria. Resonant error fields can induce considerable magnetic islands, even if the magnitude of the error fields is small. These islands typically degrade energy confinement times. Methodologies for minimizing island widths have been implemented with respect to NCSX and CTH. Here we introduce a new method to minimize the island width by targeting the island's helical flux. However, optimizing for island widths alone is insufficient due to the islands being extremely sensitive to magnetic field perturbations, therefore we must consider the island widths' sensitivity to coil shape perturbations. Due to the high island width sensitivity, we optimize realistic coil windings (multi-filament coils). We calculate the island width sensitivity to coil shape perturbations and two methodologies for minimizing island width sensitivity are presented. The first method is to target the magnitude of the coil shape gradient for the helical flux. We also demonstrate a more robust method, that is, a stochastic optimization of the helical flux.