A novel magnet system—which enables uniformity of radial flux density by means of a parabolic yoke—applied in the Planck-Balance

Abstract

Abstract A uniform magnetic flux density that is effective in the movement range of the coil is essential for accurate Kibble balance experiments. By utilizing Hopkinson’s law and Kirchhoff’s circuit laws, basic formulas have been derived, providing a method to calculate the magnetic flux density distribution in the airgap of a cylindrical magnet system. A parabolic outer contour of the inner yoke has been found to be a suitable solution to achieve uniformity. Experiments show, that this approach results in a relative change of magnetic flux density in the order of 3 ⋅ 10 − 4 per 8 mm movement range, using a magnet system with a mass of only 2.3 kg. Therefore, the system will be integrated into the upgraded version of PTB’s Planck-Balance—a compact variant of a Kibble balance—aiming for sub 1 ⋅ 10 − 6 accuracy level determination of the geometric factor. The solution described provides a comparatively easy means to design a cylindrical magnet system, using only one permanent magnet disc, without the use of complex simulation software.