Combining rotating-coil measurements of large-aperture accelerator magnets

The rotating coil is a widely used tool to measure the magnetic field and the field errors in accelerator magnets. The coil has a length that exceeds the entire magnetic field along the longitudinal dimension of the magnet and gives therefore a two-dimensional representation of the integrated field. Having a very good precision, the rotating coil lacks in versatility. The fixed dimensions make it impractical and inapplicable in situations, when the radial coil dimension is much smaller than the aperture or when the aperture is only little covered by the coil. That being the case for rectangular apertures with large aspect ratio, where a basic measurement by the rotating coil describes the field only in a small area of the magnet. A combination of several measurements at different positions is the topic of this work. Very important for a combination is the error distribution on the measured field harmonics. To preserve the good precision of the higher-order harmonics, the combination must not rely on the main field component that is measured with less precision. Considering that, a method is derived that computes the field harmonics at the central position by measurement data at displaced positions. The error propagation of the measurement error and the uncertainty of the position is studied for different cases. This is done for simulated fields but also for an actual measurement in the laboratory. It is shown that the precision of the computed field harmonics, in particular the higher-order ones, is improved with respect to a single measurement at one position. Finally, a coil design is presented that is adapted to the method and the measurement errors. Acquiring the used field harmonics with the highest sensitivity, improves the results of the computations. This work presents a method that improves the versatility of the rotating coil by combining measurements at several positions.