Planar Coil Optimization in a Magnetically Shielded Cylinder

Hybrid magnetic shields with both active field generating components and high-permeability magnetic shielding are increasingly needed for various technologies and experiments that require precisioncontrolled 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 highpermeability 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 - y y + 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.

Automated summary

Hybrid magnetic shields combining active field generating components and high-permeability magnetic shielding are needed for precision-controlled magnetic field environments. Optimization of active components interacting with passive magnetic shield is crucial to generate user-specified target fields effectively. Methods involving modified Green's function and inverse optimization can design planar coils producing desired magnetic fields within high-permeability shields accurately and flexibly.