Planar Coil Optimization in a Magnetically Shielded Cylinder

TL;DR

This paper presents a new method for designing planar coils within high-permeability cylindrical shields to generate precise magnetic fields, accounting for the interaction between active and passive components.

Contribution

It introduces a modified Green's function approach for inverse optimization of planar coils coupled with high-permeability shields, validated through two practical examples.

Findings

Optimized coil designs accurately produce desired magnetic fields.

Method effectively accounts for passive shield interactions.

Designs are suitable for miniaturized, high-performance applications.

Abstract

Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for a variety of technologies and experiments that require precision-controlled magnetic field environments. However, the fields generated by the active components interact with the passive magnetic shield, distorting the desired field profiles. Consequently, optimization of the active components needed to generate user-specified target fields must include coupling to the high-permeability passive components. Here, we consider the optimization of planar active systems, on which an arbitrary static current flows, coupled to a closed high-permeability cylindrical shield. We modify the Green's function for the magnetic vector potential to match boundary conditions on the shield's interior surface, enabling us to construct an inverse optimization problem to design planar coils that generate user-specified magnetic fields inside high-permeability shields. We validate our methodology by designing two bi-planar hybrid active--passive systems, which generate a constant transverse field, $\mathbf{B}=\mathbf{\hat{x}}$, and a linear field gradient, $\mathbf{B}=(-x~\mathbf{\hat{x}}-y~\mathbf{\hat{y}}+2z~\mathbf{\hat{z}})$, respectively. For both systems, the inverse-optimized magnetic field profiles agree well with forward numerical simulations. Our design methodology is accurate and flexible, facilitating the miniaturization of high-performance hybrid magnetic field generating technologies with strict design constraints and spatial limitations.