Shim coil design by Fourier synthesis

A new method of creating “shims”, i.e. spherically harmonic fields, is proposed. The technique relies on a direct correspondence between the spatial frequency of sinusoidal azimuthal currents on the surface of an axially aligned cylinder and the degree of the spherically harmonic, axial magnetic fields they create. The sinusoidal current waveform is sampled at at least twice the maximum desired degree/frequency, and the current samples are then applied to the same number of identical conducting arcs, at the same axial position, evenly distributed in a ring. Repetition of this building block at differing axial positions and with appropriate sinusoidal current amplitudes is then used to allow a mix of harmonics of any degree less than or equal to the maximum; the maximum order is determined by the number of axial positions. Calculations are analytical, apart from numerical minimisation of power consumption or mean square current, and correction of minor end effects. Access to the author's Mathematica Notebooks that may help with concepts and calculations is provided. The design holds the promise of more accurate generation of higher orders and degrees than is currently normal, and of easy fabrication with either foil or ribbon cable; the complexity usually associated with construction is essentially transferred to exterior electronics. A novel, conceptual current driver with high efficiency and compliance is also mentioned.