A Three-step Model for Optimizing Coil Spacings Inside Cuboid-shaped Magnetic Shields

TL;DR

This paper introduces a three-step computational model for optimizing coil spacings inside cuboid-shaped magnetic shields, significantly reducing calculation time while maintaining accuracy, validated through FEM simulations and experimental measurements.

Contribution

The paper presents an improved mirror method with a reaction factor for fast magnetic field calculations inside cuboid shields, enabling efficient coil spacing optimization.

Findings

Model accurately predicts magnetic fields within shields.

Optimization reduces coil spacing errors by a factor of over 5.

Experimental results confirm model's effectiveness in real-world setups.

Abstract

A three-step model for calculating the magnetic field generated by coils inside cuboid-shaped shields like magnetically shielded rooms (MSRs) is presented. The shield is modelled as two parallel plates of infinite width and one tube of infinite height. We propose an improved mirror method which considers the effect of the parallel plates of finite thickness. A reaction factor is introduced to describe the influence of the vertical tube, which is obtained from finite element method (FEM) simulations. By applying the improved mirror method and then multiplying the result with the reaction factor, the magnetic flux density within the shielded volume can be determined in a fast computation. The three-step model is verified both with FEM and measurements of the field of a Helmholtz coil inside an MSR with a superconducting quantum interference device. The model allows a fast optimization of shield-coupled coil spacings compared to repetitive time-consuming FEM calculations. As an example, we optimize the distance between two parallel square coils attached to the MSR walls. Measurements of a coil prototype of 2.75~m in side length show a magnetic field change of 18~pT over the central 5~cm at the field strength of 2.7~\textmu T. This obtained relative field change of 6~ppm is a factor of 5.4 smaller than our previously used Helmholtz coil.