Coil Tolerances Motivated by Island Widths

Islands are inherent to stellarator equilibria and can negatively affect confinement and stability. In this presentation, we present a methodology that allows for the elimination of internal magnetic islands in new stellarator configurations. We optimize the island's width using shape gradients of coils which also allows us to determine the coil tolerances. A relationship exists between the island width and the island poloidal flux, which is the magnetic flux between the island's O and X points. Variations of the island poloidal flux due to variations of the coil magnetic field is given and allows the island width to be minimized. We first calculate shape gradients of the coils for the magnetic field. This allows us to calculate shape gradients of the coils for the island width. Using coil magnetic field shape gradients, we can derive shape gradients of the coils for the island widths. Since we solve for the coil shape gradients, we can also solve for coil tolerances by setting a maximum allowable island width. Since we derive an analytic equation for the coil tolerances, we can maximize the coil tolerances which will greatly reduce machine cost. Shape gradients are evaluated for a new stellarator configuration called, WISTELL-A. We demonstrate island width minimization and give coil tolerances. We also propose potential avenues for coil tolerance optimization.