An analytical algorithm for 3D magnetic field mapping of a watt balance magnet

TL;DR

This paper introduces an analytical algorithm to accurately model the 3D magnetic field of a watt balance magnet using only a single radial flux density measurement, improving field characterization and alignment analysis.

Contribution

It presents a novel analytical method that derives the full 3D magnetic field from a single vertical profile measurement, enhancing precision over previous approaches.

Findings

Provides a more accurate magnetic field model for watt balance magnets.

Reduces measurement requirements to a single flux density profile.

Improves alignment and profile analysis in watt balance experiments.

Abstract

A yoke-based permanent magnet, which has been employed in many watt balances at national metrology institutes, is supposed to generate strong and uniform magnetic field in an air gap in the radial direction. However, in reality the fringe effect due to the finite height of the air gap will introduce an undesired vertical magnetic component to the air gap, which should either be measured or modeled towards some optimizations of the watt balance. A recent publication, i.e., {\it Metrologia} 52(4) 445 [1], presented a full field mapping method, which in theory will supply useful information for profile characterization and misalignment analysis. This article is an additional material of [1], which develops a different analytical algorithm to represent the 3D magnetic field of a watt balance magnet based on only one measurement for the radial magnetic flux density along the vertical direction, $B_r(z)$. The new algorithm is based on the electromagnetic nature of the magnet, which has a much better accuracy.