Planar Coil Optimization in a Magnetically Shielded Cylinder

Packer, M.; Hobson, P. J.; Holmes, N.; Leggett, J.; Glover, P.; Brookes, M. J.; Bowtell, R.; Fromhold, T. M.

Abstract

Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for various 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 biplanar hybrid active-passive systems, which generate a constant transverse field, B=x^, and a linear field gradient, B=(-xx^-yy^+2zz^), 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.

Citation

Packer, M., Hobson, P. J., Holmes, N., Leggett, J., Glover, P., Brookes, M. J., Bowtell, R., & Fromhold, T. M. (2021). Planar Coil Optimization in a Magnetically Shielded Cylinder. Physical Review Applied, 15(6), Article 064006. https://doi.org/10.1103/PhysRevApplied.15.064006

• Journal Article Type: Article
• Acceptance Date: May 13, 2021
• Online Publication Date: Jun 2, 2021
• Publication Date: Jun 1, 2021
• Deposit Date: Jul 15, 2021
• Publicly Available Date: Jul 15, 2021
• Journal: Physical Review Applied
• Electronic ISSN: 2331-7019
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 6
• Article Number: 064006
• DOI: https://doi.org/10.1103/PhysRevApplied.15.064006
• Public URL: https://nottingham-repository.worktribe.com/output/5786426
• Publisher URL: https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.064006
• Additional Information: © 2021 American Physical Society