Among the advantages of Halbach magnet arrays is the fact that the magnetic
field behind the array is very small, and the magnets act as a natural flu
x guide. This paper discusses an optimization index that proves useful for
objectively examining any magnet array used in induction applications. Mult
ivariate spline tensor analysis and variable metric methods with a boundary
element solver are used to predict the index of performance for these arra
ys and competing alternatives. The results show that steel based magnet arr
ays will out-perform conventional Halbach arrays.