Characterisation of X- and O-points in Wendelstein 7-X with respect to coil currents

This work analyses vacuum magnetic field topology in Wendelstein 7-X (W7-X) with respect to changes in the current in the superconducting coils. We develop a fast automated scheme to locate fixed points (such as X- and O-points) and calculate the trace of the Jacobian of the field line map for them ( $\mathrm{Tr}(\text{M})$ ), which represents several important properties of the fixed point. We perform two sets of coil current scans: (i) scans where each coil current is varied individually, using the ‘standard’, ‘high iota’ and ‘low iota’ configurations as starting points; (ii) a scan of over $2\times 10^5$ magnetic configurations in which the coil currents are randomly sampled. In both cases, we constrain the coil currents to the normal range of W7-X. We verify the principal roles of the non-planar, planar and control coils: the non-planar coils establish island chains with a certain phase; the planar coils modify the location of the island chain by both controlling the $\iota$ profile and shifting the configuration ‘inward’ and ‘outward’; the control coil affects the island size and phase. We also find that $\vert (\mathrm{Tr}(\text{M})-2)\vert$ (a quantity closely related to the magnitude of the Greene’s residue) tends to increase with the minor radius of the fixed points, and that $\mathrm{Tr}(\text{M})$ for X- and O-points can be very differently affected by the control coil current. Finally, we show that $\vert (\mathrm{Tr}(\text{M})-2)\vert$ serves as a proxy for island size for internal island chains, which may help identification of suitable experimental candidates.