Improving the field homogeneity of fixed- and variable-diameter discrete Halbach magnet arrays for MRI via optimization of the angular magnetization distribution.

The aim of this work was to maximize the homogeneity of fixed- or variable-diameter Halbach array of discrete magnets by optimizing the angular rotation of individual magnets within each ring of the array. Numerical simulations have been performed for magnet arrays with various length:radius ratios (L/R) using a dipole-approximation model. These simulations used an uninformed random-search algorithm, with the initial state corresponding to the classical Halbach dipole configuration. Two different classes of systems were studied, one with magnet rings of constant radius, and the other in which the radius of the rings was allowed to vary to increase the homogeneity. Simulation results showed that for a fixed-diameter array optimization of the angular orientation of individual magnets increased the homogeneity by ~17% for very short magnets, with the improvement dropping to ~5% for L/R values greater than ~3:1, where the homogeneity was measured over a region-of-interest equal to one-half the diameter of the magnet array. An empirical formula was derived which allows easy estimation of the required magnetization angles for any L/R. For a 23-ring variable diameter magnet with L/R of ~4:1 the optimization procedure produces an increase in homogeneity of ~18%.