It will be appreciated that a solid magnet ring piece can be magnetized in an azimuthal repetitive manner so as to create repeating segments, with each segment magnetized with a different magnetization direction and/or strength. In the present context, such a magnet piece will be considered an MPMR where the phases share common material composition but differ in their magnetization states, even though mechanically there is no actual segmentation of the magnet ring. The same holds, for instance, for a solid magnet ring created with different material compositions where the composition changes in an azimuthal repetitive way. In such a case, different magnetic compositions areas will be considered as different phases. The same holds for a solid magnet piece which has its axial thickness and/or radial thickness and/or cross section geometry vary azimuthally in a repetitive way. In this case the ring will be considered an MPMR with phases which differ by their geometry but share a common composition and magnetic state, even though there is no segmentation mechanically.

For a given weight of an asymmetric magnet ring array, using two or more phase-dissimilar MPMRs will result in a level of field uniformity inside the inner volume that is substantially higher than that achieved by the asymmetric array incorporating only one MPMR or several phase-similar MPMRs.