  Error fields are predominantly attributed to inevitable coil imperfections.
Controlling error fields during coil fabrication and assembly is crucial for
stellarators. Excessively tight coil tolerance increases time and cost, and, in
part, led to the cancellation of NCSX and delay of W7-X. In this paper, we
improve the recently proposed Hessian matrix method to rapidly identify
important coil deviations. Two of the most common figures of merit, magnetic
island size and quasi-symmetry, are analytically differentiated over coil
parameters. By extracting the eigenvectors of the Hessian matrix, we can
directly identify sensitive coil deviations in the order of the eigenvalues.
The new method is applied to the upcoming CFQS configuration. Important
perturbations that enlarge n/m=4/11 islands and deteriorate quasi-axisymmetry
of the magnetic field are successfully determined. The results suggest each
modular coil should have separate tolerance and some certain perturbation
combinations will produce significant error fields. By relaxing unnecessary
coil tolerance, this method will hopefully lead to a substantial reduction in
time and cost.
