Improving magnet designs with high and low field regions
  A general scheme for increasing the difference in magnetic flux density between a high and a low magnetic field region by removing unnecessary magnet material is presented. This is important in, e.g., magnetic refrigeration where magnet arrays has to deliver high field regions in close proximity to low field regions. Also, a general way to replace magnet material with a high permeability soft magnetic material where appropriate is discussed. As an example these schemes are applied to a two dimensional concentric Halbach cylinder design resulting in a reduction of the amount of magnet material used by 42% while increasing the difference in flux density between a high and a low field region by 45%. 
R. Bj{\o}rk, C. R. H. Bahl, A. Smith and N. Pryds
physics.ins-det physics.class-ph