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In this paper the smallest or optimal dimensions of a Halbach cylinder of afinite length for a given sample volume and desired flux density are determinedusing numerical modeling and parameter variation. A sample volume that iscentered in and shaped as the Halbach cylinder bore but with a possible shorterlength is considered. The external radius and the length of the Halbachcylinder with the smallest possible dimensions are found as a function of adesired internal radius, length of the sample volume and mean flux density. Itis shown that the optimal ratio between the outer and inner radius of theHalbach cylinder does not depend on the length of the sample volume. Finally,the efficiency of a finite length Halbach cylinder is considered and comparedwith the case of a cylinder of infinite length. The most efficient dimensionsfor a Halbach cylinder are found and it is shown that the efficiency increasesslowly with the length of the cylinder.

The ideal dimensions of a Halbach cylinder of finite length