Optimizing the differential connection schemes for detecting 3D magnetic perturbations in DIII-D

Optimizing the differential pair connection scheme (i.e., the set of pairs) of a toroidal array of magnetic sensors dedicated to measuring slowly rotating asymmetric fields can enhance the mode number detection capability and failure-resilience. In this work, the condition number obtained from singular value decomposition of the design matrix is used as a metric to evaluate the quality of a connection scheme. A large number of possible pair connections are usually available, so evaluating all of them may require extensive use of computational resources and can be very time-consuming. Alternative methods to reduce the number of pairs evaluated without losing the capabilities of toroidal mode detection are presented in this paper. Three examples of the applications of such analysis for the 3D magnetic diagnostic system of DIII-D are also presented: the addition of two new toroidal arrays with n > 3 detection capabilities, the modification of an existing toroidal array in the low field side of the machine to accommodate the addition of a helicon antenna, and the design of changes in several toroidal arrays in the high field side to accommodate the addition of a lower hybrid current drive antenna on the center post.