Abstract
The effect of passive magnetic shielding on dc magnetic field gradients imposed by both external and internal sources is studied for two idealized shield models: concentric spherical and infinitely-long cylindrical shells of linear material. It is found that higher-order multipoles of an externally applied magnetic field are always shielded progressively better for either geometry by a factor related to the order of the multipole. In regard to the design of internal coil systems, we determine reaction factors for the general multipole field and provide examples of how one can take advantage of the coupling of the coils to the innermost shell to optimize the uniformity of the field. Furthermore, we provide formulae relevant to active magnetic compensation systems which attempt to stabilize the interior fields by sensing and cancelling the exterior fields close to the outermost shell. Overall this work provides a comprehensive framework that is useful for the analysis and optimization of dc magnetic shields, serving as a theoretical and conceptual design guide as well as a starting point and benchmark for finite-element analysis.
Highlights
Passive magnetic shielding systems typically use a concentric arrangement of thin shells of a high permeability material to divert magnetic field lines around a region of interest
The effect of passive magnetic shielding on dc magnetic field gradients imposed by both external and internal sources is studied for two idealized shield models: concentric spherical and infinitely-long cylindrical shells of linear material
While magnetic shielding is useful for a variety of applications, the most stringent requirements are found in high precision experiments where the limits of magnetometry technology are experienced or are themselves being studied
Summary
Passive magnetic shielding systems typically use a concentric arrangement of thin shells of a high permeability material to divert magnetic field lines around a region of interest. The field external to the shield is calculated, and is useful for designing active magnetic compensation systems This field is typically dominated by the response of the outermost layer (provided it is not near saturation) and the analysis is restricted to a single shell only. R We report static shielding factors, interior reaction factors, and exterior response fields for single layer, infinitely-long cylindrical magnetic shields, exposed to general multipole transverse dc fields This extends the work of Ref. 23 from spherical to cylindrical geometries. As is commonly done to achieve analytic solutions for passive shielding problems, we restrict our analysis to shields of linear, homogeneous media, carrying no free current Under such conditions, the response of a permeable object to an applied magnetic field can be recast in terms of bound current on the surfaces of the object. The typical means of solution using the magnetic scalar potential (e.g. Ref. 38) gives a set of 4M simultaneous equations, albeit resulting in a sparser matrix
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