Field representation of a watt balance magnet by partial profile measurements

TL;DR

This paper introduces an algorithm that reconstructs the full magnetic field of a watt balance magnet from limited radial field measurements, aiding in precise alignment and correction.

Contribution

The novel algorithm estimates the entire magnetic field from a few radial profiles using polynomial fitting and Maxwell's equations, verified by FEM simulations.

Findings

Accurately reconstructs 3D magnetic fields from limited measurements

Provides essential parameters for magnet alignment corrections

Validated by finite element method simulations

Abstract

Permanent magnets with high-permeability yokes have been widely used in watt balances for supplying a robust and strong magnetic field at the coil position. Subjected to the mechanical realization, only several $B_r(z)$ (radial magnetic field along the vertical direction) profiles can be measured by coils for field characterization. In this article, we present an algorithm that can construct the global magnetic field of the air gap based on $N(N\geq1)$ additional measurements of $B_r(z)$ profiles. The proposed algorithm is realized by polynomially estimating the $B_z(r)$ function with analysis of basic relations between two magnetic components in air gap, i.e., $B_r(r,z)$ and $B_z(r,z)$, following the Maxwell's equations. The algorithm, verified by FEM simulations, can characterize the three-dimensional contribution of the magnetic field for a watt balance magnet with acceptable accuracy, which would supply basic field parameters for alignment and misalignment corrections.