Passive magnetic shielding in static gradient fields

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.

Sensitivity of fields generated within magnetically shielded volumes to changes in magnetic permeability

“…The differences are small, suggesting that the ideal spherical model of Ref. [26] and the high-µ approximation of Eq. 2 provide valuable insight for the design and analysis of shield-coupled coils.…”

“…The solid curve is the exact calculation for the ideal spherical coil and shield from Ref. [26]; the dashed curve is the approximation of Eq. 2.…”

“…For closed objects, such as spherical shells [26,27], the shielding factor approaches infinity as µ → ∞, and | µ The simulations differed slightly in their results, dependent on whether OPERA or FEMM was used, and whether the solenoidal coil or loop coil were used. Based on the simulations, the result is | µ Bs dBs dµ | = 0.42 − 0.50 for the solenoidal coil, with the lower value being given by FEMM and the upper value being given by a 3D OPERA simulation, for identical geometries.…”

How the Minuscule Can Contribute to the Big Picture: The Neutron Electric Dipole Moment Project at TRIUMF

“…A multilayer magnetically shielded room will create an ideal low-field magnetic environment, which the neutrons enter from the side: four high permeability metal layers with a large DC and low-frequency shielding factor for magnetic fields and gradients [38] and an aluminum layer serving to shield high frequencies take the approach of [17] one step further. A self shielded B 0 coil [39] will minimize the interaction of the internal field with external disturbances such as temperature changes of the mu metal.…”

Self-Shielded Uniform Magnetic Field Coil Design for Miniature Atomic Sensors Using a Particle Swarm Optimization Algorithm

“…[5]- [8] The coupling between the coil and the high permeability alloy layers often amplifies the coil magnetic field. [9], [10] and also affects the distribution of the magnetic field. Some researchers adjusted the current distribution of the coil to obtain a coil with better uniformity within the magnetic shielding layers.…”