An Evaluation of External Magnetic Flux Error in Magnet-Moving Kibble balances

Abstract

The magnet-moving measurement scheme in Kibble balances avoids displacing force-sensitive components, such as the weighing cell, and enables a broader magnetic profile measurement range during the velocity phase. However, this mechanism introduces the risk of asymmetry in the $Bl$ measurement due to external magnetic flux, leading to a potential systematic error in the final measurement results. Using the Tsinghua tabletop Kibble balance magnet as a case study, this paper investigates the error mechanism through finite element analysis and experimental investigations. An evaluation method combining external weak-field measurements with attenuation factor analysis is proposed to assess external magnetic flux errors in magnet-moving measurement schemes. The findings demonstrate that selecting an optimal weighing position can reduce the far-end flux effect to the order of $10^{-9}$. In contrast, the near-end flux effect can be quantified by monitoring the magnetic field surrounding the magnet system. In the Tsinghua Kibble balance system, we show that with proper control of external flux sources, the relative error can be reduced below $1 \times 10^{-8}$ without requiring additional magnetic shielding.