Passive Magnetic Shielding in Gradient Fields

TL;DR

This paper investigates how passive magnetic shields made of high permeability materials can effectively reduce magnetic field gradients, improving internal field uniformity, and provides formulas for optimizing shield design and active compensation systems.

Contribution

It offers a quantitative analysis of magnetic shielding effectiveness for multipole fields and introduces design considerations for internal coils and active stabilization.

Findings

Higher order multipoles are shielded more effectively.

Coupling of coils to the innermost shield improves field uniformity.

Provides formulas for shield optimization and active compensation.

Abstract

The effect of passive magnetic shielding on dc magnetic field gradients imposed by both external and internal sources is studied. It is found that for concentric cylindrical or spherical shells of high permeability material, higher order multipoles in the magnetic field are shielded progressively better, by a factor related to the order of the multipole. In regard to the design of internal coil systems for the generation of uniform internal fields, we show how one can take advantage of the coupling of the coils to the innermost magnetic shield to further optimize the uniformity of the field. These results demonstrate quantitatively a phenomenon that was previously well-known qualitatively: that the resultant magnetic field within a passively magnetically shielded region can be much more uniform than the applied magnetic field itself. Furthermore we provide formulae relevant to active magnetic compensation systems which attempt to stabilize the interior fields by sensing and cancelling the exterior fields close to the outermost magnetic shielding layer. Overall this work provides a comprehensive framework needed to analyze and optimize dc magnetic shields, serving as a theoretical and conceptual design guide as well as a starting point and benchmark for finite-element analysis.