Correcting for background fields and multipole field errors in the localization of the magnetic axis in quadrupole magnets

The fiducial marker localization with respect to the magnetic axis of the magnet elements is a crucial step in the qualification of the magnets for particle accelerators. Background fields, such as the Earth's magnetic field and fringe fields from electrical sources may degrade the accuracy of this axis localization. In this paper, we discuss stretched-wire measurements, in static and vibrating operation modes, for the correction of stray fields in the quadrupole axis localization to an accuracy of 0.3 $\mu$m. Moreover, we present an analytical model to correct the magnetic axis position error due to higher-order multipole field errors in the magnet. This correction is particularly important for the static stretched-wire measurement because the wire movement must be large enough to obtain a sufficient signal-to-noise ratio.