  Permanent magnets together with yokes to concentrate the magnetic flux into a
cylindrical air-gap are widely employed in Kibble balances. These experiments
require a uniform magnetic flux density along a vertical path, typically a
substantial fraction of the length of the air-gap. Fringe fields that are
present at both ends of the air-gap limit the region where the flux density
does 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 an
iron ring with a rectangular cross-section to the inner yoke at each end of the
air gap, the effects of the fringe fields can be counteracted, and, hence, the
length of the region, where the flux density remains within a given tolerance
band is increased. Compared to the alternative, employing a taller magnet, the
proposed method yields a magnet system with an extended region of a uniform
field without significantly increasing the mass of the magnet system. Potential
applications include compact and table-top Kibble balances. We investigate
possible adverse effects on the performance of the magnet system caused by the
additional rings: magnetic field strength, coil-current effect, and a
dependence of the radial field on the radial position in the field. No
substantial disadvantage was found. Instead, the method presented here
outperformed previously suggested methods to improve the radial dependence of
the radial field, e.g., shorter outer yoke. In summary, adding rings to the
inner yoke improves the uniformity of the field without a detrimental effect to
function, cost, and form factor of the magnet system.
