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Error fields are predominantly attributed to inevitable coil imperfections.Controlling error fields during coil fabrication and assembly is crucial forstellarators. Excessively tight coil tolerance increases time and cost, and, inpart, led to the cancellation of NCSX and delay of W7-X. In this paper, weimprove the recently proposed Hessian matrix method to rapidly identifyimportant coil deviations. Two of the most common figures of merit, magneticisland size and quasi-symmetry, are analytically differentiated over coilparameters. By extracting the eigenvectors of the Hessian matrix, we candirectly identify sensitive coil deviations in the order of the eigenvalues.The new method is applied to the upcoming CFQS configuration. Importantperturbations that enlarge n/m=4/11 islands and deteriorate quasi-axisymmetryof the magnetic field are successfully determined. The results suggest eachmodular coil should have separate tolerance and some certain perturbationcombinations will produce significant error fields. By relaxing unnecessarycoil tolerance, this method will hopefully lead to a substantial reduction intime and cost.

Identification of important error fields in stellarators using Hessian matrix method