Implementation of Maxwell's equations in the reconstruction of the magnetic field in the $g-2$ storage ring

TL;DR

This paper introduces an efficient method using toroidal-harmonic solutions of Laplace's equation to incorporate Maxwell's equations constraints into magnetic field measurements in the $g-2$ muon storage ring, enabling fast and accurate field reconstructions.

Contribution

The paper presents a novel linear-algebra-based algorithm that efficiently enforces Maxwell's equations constraints in magnetic field fitting for the $g-2$ experiment.

Findings

Able to process 10^5 data points with 10^4 harmonics in under an hour

Improved accuracy in magnetic field reconstruction in the $g-2$ storage ring

Method successfully applied to preliminary measurement data

Abstract

We present a method for implementing the constraints that are implied by Maxwell's equations in fits to measurements of the magnetic field in the muon storage ring of the $g-2$ experiment. The method that we use makes use of toroidal-harmonic solutions of Laplace's equation. We point out that the fitting problem can be approximated well as a linear-algebra problem. We have devised an efficient algorithm for the linear-algebra problem that makes it possible to find a solution for $10^5$ data points and $10^4$ harmonics in less than an hour on a present-day desktop computer. We illustrate our method by applying it to some preliminary measurements of the magnetic field in the $g-2$ storage ring.