In this paper we describe the results of a parameter survey of a 16 segmented Halbach cylinder in three dimensions in which the parameters internal radius, r_in, external radius, r_ex, and length, L, have been varied. Optimal values of r_ex and L were found for a Halbach cylinder with the least possible volume of magnets with a given mean flux density in the cylinder bore. The volume of the cylinder bore could also be significantly increase by only slightly increasing the volume of the magnets,

more »

... for a fixed mean flux density. Placing additional blocks of magnets on the end faces of the Halbach cylinder also improved the mean flux density in the cylinder bore, especially so for short Halbach cylinders with large r_ex. Moreover magnetic cooling as an application for Halbach cylinders was considered. A magnetic cooling quality parameter, Λ_cool, was introduced and results showed that this parameter was optimal for long Halbach cylinders with small r_ex. Using the previously mentioned additional blocks of magnets can improve the parameter by as much as 15 improve the homogeneity of the field in the cylinder bore.