Analytic models of magnetically enclosed spherical and solenoidal coils

Abstract

We provide analytic solutions of the net magnetic field generated by spherical and solenoidal coils enclosed in highly-permeable, coaxial magnetic shields. We consider both spherical and cylindrical shields in the case of the spherical coil and only cylindrical shields for the solenoidal coil. Comparisons of field homogeneity are made and we find that the solenoidal coil produces the more homogeneous field for a given number of windings. The models are useful as theoretical and conceptual guides for coil design, as well as for benchmarking finite-element analysis. We also demonstrate how the models can be generalized to explore field inhomogeneities related to winding misplacement.

arXiv comment29 pages, 11 figures

References in corpus (4)

• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• First ultracold neutrons produced at TRIUMF
• Comparison of magnetic field uniformities for discretized and finite-sized standard $\cos \theta$, solenoidal, and spherical coils
• A beamline for fundamental neutron physics at TRIUMF

Cited by in corpus (5)

• Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder
• Planar Coil Optimization in a Magnetically Shielded Cylinder
• Magnetic Field Design in a Cylindrical High-Permeability Shield: The Combination of Simple Building Blocks and a Genetic Algorithm
• Bespoke magnetic field design for a magnetically shielded cold atom interferometer
• A Three-step Model for Optimizing Coil Spacings Inside Cuboid-shaped Magnetic Shields