An Approach for Restoring Magnetic Field Uniformity in Openable BIPM-Type Kibble Balance Magnets

TL;DR

This work identifies a splitting-gap–induced asymmetry in openable BIPM-type Kibble balance magnets that degrades magnetic-field uniformity. It introduces a two-step yoke compensation, combining a radial adjustment of the upper yoke inner radius Δr with fine-tuning of the splitting-gap height Δz, underpinned by a linear model ΔB_r(Δz,Δr) = αΔz + βΔr (with α>0, β<0). The method enables predictive compensation, and experimental validation using a gradient-coil setup confirms that sequentially adjusting Δr and Δz can restore symmetry and recover the target uniform-field range (~30 mm), achieving ΔB_r ≈ 0 where initially ΔB_r ≈ 5.5 mT. This provides a robust, practical strategy to improve magnetic-field quality in openable Kibble balance magnets, with direct benefits for Bl-based measurements and related precision metrology.

Abstract

The Kibble balance realizes the kilogram by linking mechanical and electrical quantities via a magnet system. In an improved BIPM-type magnet design by Tsinghua University, an open/close surface was incorporated, facilitating operation. However, an unavoidable mechanical air gap at the splitting plane introduces asymmetry in the magnetic flux density profile, degrading field uniformity. This study proposes a two-step yoke compensation method to restore symmetry by adjusting the upper outer yoke's inner radius and the splitting gap height. Finite element simulations show linear relationships between asymmetry and these parameters, enabling predictive compensation. Experimental results confirm that sequential tuning successfully eliminates asymmetry and recovers the designed uniform field range. The method provides an effective solution for enhancing magnetic field quality in openable Kibble balance magnets.

Figures (6)

• Figure 1: (a) Schematic of the modified BIPM magnet: permanent magnets (red), yoke (gray), and splitting plane (blue). Arrows indicate magnetization. The red circle highlights the inner yoke compensation structure (height $h_\mathrm{c}$, width $\delta_\mathrm{c}$) for improved field uniformity. (b) Photo of the magnet in open state. Splitting enables levitation and yields 92 N attraction when closed. (c) Magnetic field comparison: dotted curve (conventional design), dashed curve (with yoke compensation), solid curve (experimental result). The splitting gap causes a 5.5 mT intensification ($\Delta B_\mathrm{r}=B_{\rm{up}}-B_{\rm{dn}}$) above the plane, reducing uniformity. Red dashed lines indicate the open/close plane.
• Figure 2: Partial cross-sectional view of the magnet assembly showing geometric parameters $\Delta z$ and $\Delta r$. The splitting air gap $\Delta z$ and inner radius adjustment $\Delta r$ are indicated by dashed lines. Component labels identify the upper inner yoke (UIY), upper outer yoke (UOY), lower inner yoke (LIY), and lower outer yoke (LOY).
• Figure 3: Influence of key geometric parameters on magnetic field asymmetry. (a) Asymmetry $\Delta B_{\mathrm{r}}$ increases with splitting air gap height $\Delta z$. (b) Linear dependence $\Delta B_{\mathrm{r}}(\Delta z) = \alpha \Delta z$ is quantified, with $\alpha = 50.13$ mT/mm. (c) Increasing upper yoke radius adjustment $\Delta r$ reduces the peak field $B_\mathrm{up}$. (d) Corresponding linear relation $\Delta B_{\mathrm{r}}(\Delta r) = \beta \Delta r+\gamma$ is shown, where $\beta = -40.02$ mT/mm and $\gamma=5.45$ mT. (e) Combined influence of $\Delta z$ and $\Delta r$ on $\Delta B_\mathrm{r}$ is presented. Magnetic symmetry ($\Delta B_\mathrm{r}= 0$) defines a linear compensation line between $\Delta z$ and $\Delta r$.
• Figure 4: A photo of the experimental setup. A linear stage, PI M-413.2DG, is used to move the gradient coil up and down. Two DVMs, #1 and #2, are used to measure the induced voltage of one of the two coils and the differential voltage of two coils connected in opposite directions, respectively.
• Figure 5: The measured air-gap flux density following the adjustment of the upper outer yoke's inner diameter increment.