Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder

TL;DR

This paper develops an inverse optimization method to design hybrid active-passive magnetic shielding systems that generate precise static magnetic fields over large volumes within cylindrical shields, improving field nulling accuracy.

Contribution

It formulates a new approach combining Green's functions and boundary conditions to optimize active-passive systems for accurate magnetic field shaping inside shields.

Findings

Successfully designs systems with high field accuracy over large volumes.

Simulates real-world shields with finite permeability and entry holes.

Demonstrates adaptability to arbitrary static magnetic fields.

Abstract

Magnetic shields that use both active and passive components to enable the generation of a tailored low-field environment are required for many applications in science, engineering, and medical imaging. Until now, accurate field nulling, or field generation, has only been possible over a small fraction of the overall volume of the shield. This is due to the interaction between the active field-generating components and the surrounding high-permeability passive shielding material. In this paper, we formulate the interaction between an arbitrary static current flow on a cylinder and an exterior closed high-permeability cylinder. We modify the Green's function for the magnetic vector potential and match boundary conditions on the shield's interior surface to calculate the total magnetic field generated by the system. We cast this formulation into an inverse optimization problem to design active--passive magnetic field shaping systems that accurately generate any physical static magnetic field in the interior of a closed cylindrical passive shield. We illustrate this method by designing hybrid systems that generate a range of magnetic field profiles to high accuracy over large interior volumes, and simulate them in real-world shields whose passive components have finite permeability, thickness, and axial entry holes. Our optimization procedure can be adapted to design active--passive magnetic field shaping systems that accurately generate any physical user-specified static magnetic field in the interior of a closed cylindrical shield of any length, enabling the development and miniaturization of systems that require accurate magnetic shielding and control.