Coil-current effect in Kibble balances: analysis, measurement, and optimization

The Kibble balance is expected to become an important instrument in the near future for realizing the unit of mass, the kilogram, in the revised international system of units (SI). The Kibble balance assumes an equality of two magnetic profiles measured in the weighing and velocity phases. A recent study conducted in the Kibble balance group at the Bureau International des Poids et Mesures (BIPM) showed that the coil current could significantly affect the magnetic profile, which should be carefully taken into account in the Kibble balance experiment. This paper gives a deeper understanding and investigation of the effect, and discusses the magnetic profile change due to the coil current, for both the classical two-mode and the one-mode Kibble balances. The coil current effect has been theoretically and experimentally investigated based on a typical magnet design with an air gap. One important conclusion found in the one-mode Kibble balance is that the magnetic profile change measured in the velocity phase is twice the change in the weighing phase. A compensation suggestion, to minimize the profile change due to the coil current in a BIPM-type magnet, is presented.