A virtual Simons Hour Talk by Alessandro Geraldini
Note the time: 2:00pm EDT / 18:00 UTC

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Minimising the presence and size of magnetic islands in the core of stellarators is necessary to improve confinement. However, islands may be extremely sensitive to small magnetic field perturbations, which is undesirable and can lead to tight coil tolerances during construction. It is therefore also crucial to reliably and efficiently quantify the sensitivity of island size. To this end, I will present an adjoint approach to calculate the gradient of two quantities related to magnetic island size. The first quantity is the full radial width of an island calculated using a method developed by Cary & Hanson (1991), which relies on the island size being small compared to the system size and only requires finding the island center. The second quantity, known as Greene’s residue, can be calculated for any periodic field line, and for an island centre it is strongly correlated with the island width. Convergence tests for the gradients of island width and residue are presented. The result of a gradient-based optimisation of residues in a magnetic configuration produced by a pair of helical coils are presented. Furthermore, the shape gradient of the island width with respect to coils is calculated and numerically verified for a magnetic island in the NCSX configuration. A key advantage of the adjoint method relative to a finite difference calculation is that the island center need not be recomputed for every possible magnetic field perturbation.