Magnetically-sensitive experiments and newly-developed quantum technologies
with integrated high-permeability magnetic shields require increasing control
of their magnetic field environment and reductions in size, weight, power and
cost. However, magnetic fields generated by active components are distorted by
high-permeability magnetic shielding, particularly when they are close to the
shield's surface. Here, we present an efficient design methodology for creating
desired static magnetic field profiles by using discrete coils
electromagnetically-coupled to a cylindrical passive magnetic shield. We
utilize a modified Green's function solution that accounts for the interior
boundary conditions on a closed finite-length high-permeability cylindrical
magnetic shield, and determine simplified expressions when a cylindrical coil
approaches the interior surface of the shield. We use an analytic formulation
of simple discrete building blocks to provide a complete discrete coil basis to
generate any physically-attainable magnetic field inside the shield. We then
use a genetic algorithm to find optimized discrete coil structures composed of
this basis. We use our methodology to generate an improved linear axial
gradient field, dBz/dz, and transverse bias field, Bx.
These optimized structures increase, by a factor of seven and three compared to
the standard configurations, the volume in which the desired and achieved
fields agree within 1% accuracy, respectively. This coil design method can
be used to optimize active--passive magnetic field shaping systems that are
compact and simple to manufacture, enabling accurate magnetic field control in
spatially-confined experiments at low cost.Comment: The authors M. Packer and P. J. Hobson have contributed equally to
this work. 24 pages, 16 figure