Abstract
Magnetic shields that use both active and passive components to enable the generation of a tailored low-field 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.
Highlights
Regions of space that require precisely controlled magnetic field environments are essential for a wide range of experiments, devices, and applications
To construct practical current sources from these current density maps, we define the streamfunction of the current continuum and discretize it into a set of closed-loop current-carrying wire geometries. Using this formulation, we present two example coil designs optimized in the interior of a closed cylindrical magnetic shield of finite length and high permeability, μr 1, and show that our analytical model agrees well with Finite element methods (FEMs) simulations performed for the optimized current flow patterns
We show that our design methodology can be used in a real-world situation where the cylindrical magnetic shield has finite thickness and permeability as well as axial entry holes in the end caps to allow experimental access. Using this formulation, we transform the performance of systems designed to generate user-specified magnetic field profiles in the magnetostatic regime, finding globally optimal solutions required for practical, low size, weight, power, and cost technologies for the applications listed above
Summary
Regions of space that require precisely controlled magnetic field environments are essential for a wide range of experiments, devices, and applications. To construct practical current sources from these current density maps, we define the streamfunction of the current continuum and discretize it into a set of closed-loop current-carrying wire geometries Using this formulation, we present two example coil designs optimized in the interior of a closed cylindrical magnetic shield of finite length and high permeability, μr 1, and show that our analytical model agrees well with FEM simulations performed for the optimized current flow patterns. We show that our design methodology can be used in a real-world situation where the cylindrical magnetic shield has finite thickness and permeability as well as axial entry holes in the end caps to allow experimental access Using this formulation, we transform the performance of systems designed to generate user-specified magnetic field profiles in the magnetostatic regime, finding globally optimal solutions required for practical, low size, weight, power, and cost technologies for the applications listed above
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