Two MPMRs are said to be phase-similar if there is a one-to-one correspondence between the phases of the two rings for which (a) the volumetric ratios of corresponding phases are the same, (b) the magnetic permeabilities of corresponding non-permanent magnet phases are the same, and (c) the magnetization vectors of corresponding phases differ at most by a rotation through a constant angle in the r-Z plane common for all phases, and by a constant scaling factor in the magnetization magnitudes common for all phases.

Thus, when two MPMRs are phase-dissimilar, the relative contribution of each individual phase in a given ring to the total magnetic field of that ring is different for the two rings. For example, with the aid of computerized magnetic field simulation tools, the phases of at least two MPMRs which are phase-dissimilar, and the magnetic moment directions of their permanent magnet phases, can be adjusted, or “tuned,” so as to optimize the uniformity of the total magnetic field inside an inner volume. These extra degrees of freedom are most advantageous when the array is subject to various geometric constraints (such as position of the rings, radial/axial thickness), which commonly arouse from mechanical r or manufactural limitations.