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Permanent magnets together with yokes to concentrate the magnetic flux into acylindrical air-gap are widely employed in Kibble balances. These experimentsrequire a uniform magnetic flux density along a vertical path, typically asubstantial fraction of the length of the air-gap. Fringe fields that arepresent at both ends of the air-gap limit the region where the flux densitydoes not change more than a certain relative fraction (here: $5\times 10^{-4}$)of the flux density in the center of the magnet system. By simply adding aniron ring with a rectangular cross-section to the inner yoke at each end of theair gap, the effects of the fringe fields can be counteracted, and, hence, thelength of the region, where the flux density remains within a given toleranceband is increased. Compared to the alternative, employing a taller magnet, theproposed method yields a magnet system with an extended region of a uniformfield without significantly increasing the mass of the magnet system. Potentialapplications include compact and table-top Kibble balances. We investigatepossible adverse effects on the performance of the magnet system caused by theadditional rings: magnetic field strength, coil-current effect, and adependence of the radial field on the radial position in the field. Nosubstantial disadvantage was found. Instead, the method presented hereoutperformed previously suggested methods to improve the radial dependence ofthe radial field, e.g., shorter outer yoke. In summary, adding rings to theinner yoke improves the uniformity of the field without a detrimental effect tofunction, cost, and form factor of the magnet system.

A Simple Improvement for Permanent Magnet Systems for Kibble Balances: More Flat Field at Almost No Cost