Analytic models of magnetically enclosed spherical and solenoidal coils

Liu, C.-Y.; Andalib, T.; Ostapchuk, David Cecil Murphy; Bidinosti, Christopher

doi:10.1016/j.nima.2019.162837

Cited by 27 publications

(14 citation statements)

References 16 publications

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“…We now analyze our theoretical model by designing and testing hybrid active-passive magnetic field-generating systems. Regarding the validation of our calculations, we first note that, as expected from previous work [36][37][38] and shown in Appendix B, our calculations confirm that the optimal coil design for generating a constant axial field inside a closed cylindrical perfect magnetic shield is a perfect solenoid that runs along the full length of the cylindrical shield.…”

Section: Resultssupporting

confidence: 83%

“…As shown in previous work [36][37][38], a solenoid of the same length as the high-permeability cylinder provides the most optimal solution for generating a constant axial field. Because of the image currents, the finite solenoid effectively acts as one of infinite extension, resulting in the most homogeneously possible magnetic field in the z direction.…”

Section: Appendix B: Solenoidal Coilmentioning

confidence: 57%

“…Analytical formulations of the magnetic field generated by hybrid active-passive systems have the distinct advantage that optimal solutions can be calculated at a range of target points with minimal computation [35]. Currently, analytical solutions for coils in high-permeability cylindrical magnetic shields have only been formulated in the specific cases of magnetically shielded solenoids and discrete current loops [36][37][38]. The geometric parameters of the active structure in these systems, such as the separation distances of wire loops, are adapted to account for the interaction between the active and passive systems.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder

et al. 2020

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Magnetic shields that use both active and passive components to enable the generation of a tailored lowfield environment are required for many applications in science, engineering, and medical imaging. Until now, accurate field nulling, or field generation, has only been possible over a small fraction of the overall volume of the shield. This is due to the interaction between the active field-generating components and the surrounding high-permeability passive shielding material. In this paper, we formulate the interaction between an arbitrary static current flow on a cylinder and an exterior closed high-permeability cylinder. We modify the Green's function for the magnetic vector potential and match boundary conditions on the shield's interior surface to calculate the total magnetic field generated by the system. We cast this formulation into an inverse optimization problem to design active-passive magnetic field shaping systems that accurately generate any physical static magnetic field in the interior of a closed cylindrical passive shield. We illustrate this method by designing hybrid systems that generate a range of magnetic field profiles to high accuracy over large interior volumes, and simulate them in real-world shields whose passive components have finite permeability, thickness, and axial entry holes. Our optimization procedure can be adapted to design active-passive magnetic field shaping systems that accurately generate any physical user-specified static magnetic field in the interior of a closed cylindrical shield of any length, enabling the development and miniaturization of systems that require accurate magnetic shielding and control.

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Section: Resultssupporting

confidence: 83%

Section: Appendix B: Solenoidal Coilmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

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Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder

et al. 2020

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“…Currently, analytical models for hybrid active-passive systems are restricted to a limited number of scenarios. Simple discrete coil geometries have been formulated in cylindrical high-permeability magnetic shields, where the magnetic field is decomposed into azimuthal Fourier modes [23][24][25] and matched at the shield boundary.…”

Section: Introductionmentioning

confidence: 99%

Planar Coil Optimization in a Magnetically Shielded Cylinder

et al. 2021

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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 − yŷ + 2zẑ), 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.

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“…Currently, however, analytical models for hybrid active-passive systems are restricted to a limited number of scenarios. Simple discrete coil geometries have been formulated in cylindrical high-permeability magnetic shields, where the magnetic field is decomposed into azimuthal Fourier modes [23][24][25] and matched at the shield boundary. Planar highpermeability materials have been incorporated into optimization procedures using the method of mirror images [26,27] to determine the total magnetic field generated by a static current source inside a magnetically shielded room [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Planar Coil Optimization in a Magnetically Shielded Cylinder

Packer,

Hobson,

Holmes

et al. 2021

Preprint

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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 bi-planar hybrid active-passive systems, which generate a constant transverse field, B = x, and a linear field gradient, B = (−x x − y ŷ + 2z ẑ), 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.

show abstract

Analytic models of magnetically enclosed spherical and solenoidal coils

Cited by 27 publications

References 16 publications

Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder

Optimal Inverse Design of Magnetic Field Profiles in a Magnetically Shielded Cylinder

Planar Coil Optimization in a Magnetically Shielded Cylinder

Planar Coil Optimization in a Magnetically Shielded Cylinder

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