Magnetic Shielding
Magnetic Shielding: Theoretical Foundations
Principles of Magnetic Shielding
Professor, how does magnetic shielding work?
By surrounding an area with a high-permeability material (such as permalloy or silicon steel), magnetic flux is diverted, attenuating the internal magnetic field. Shielding Effectiveness (SE):
Theoretical formula for a single-layer spherical shell shield:
$t$: shield thickness, $r$: shield radius, $\mu_r$: relative permeability.
So, higher permeability and greater thickness increase shielding effectiveness.
Correct. However, permalloy ($\mu_r \sim 80,000$) has a low saturation flux density ($B_s \approx 0.75$ T). Under strong magnetic fields, it saturates and its effectiveness drops, making multilayer shields (outer layer: low-carbon steel, inner layer: permalloy) effective.
Summary
- Divert magnetic flux with high-permeability materials — Basic principle
- $SE \propto \mu_r \cdot t/r$ — Permeability × thickness / radius
- Multilayer structure — For strong fields, prevent saturation with an outer layer and finish with an inner layer
Static Magnetic Field Shielding — The Mechanism of "Permalloy Diverting Magnetic Fields"
Low-frequency and DC magnetic field shielding functions via a completely different mechanism than electromagnetic shielding. High-permeability materials (permalloy, μ-metal) "suck in" magnetic flux and divert it around the interior, reducing the magnetic field inside the shield. Shielding effectiveness can be approximated by SE=1+μr×t/(2r) (spherical shell approximation), with higher permeability μr yielding greater effectiveness. However, there is a "saturation problem": when ferromagnetic materials saturate under strong external fields, their permeability drastically decreases, and shielding effectiveness is lost. In magnetic shield design for MRI and electron microscopes, multilayer shields that consider this saturation limit are used.
Computational Methods for Magnetic Shielding
Shielding Analysis with FEM
Are there any points to note when using FEM for shield analysis?
When the shield material is thin, the aspect ratio of volume elements deteriorates. Countermeasures:
- Thin shell elements (Shell elements): Supported by JMAG, Maxwell. Treat thickness direction via shell attributes
- Impedance boundary condition: Model only the surface to reduce computational cost
- Nonlinear analysis: Essential because permalloy's $\mu_r$ strongly depends on B
It becomes an open-space problem, right?
The area outside the shield is infinite space. Model using BEM (Boundary Element Method), infinite elements, or a sufficiently large air domain. COMSOL's Infinite Element Domain is convenient.
Summary
- Thin shell elements or impedance boundary — Mesh countermeasure for thin shields
- Nonlinear analysis — Consider saturation
- Open space handling — BEM or infinite elements
Numerical Analysis of Magnetic Shielding — FEM and "Finite Element Approximation of Magnetic Reluctance"
In FEM analysis of magnetic shielding, the "modeling" of high-permeability thin plates directly affects accuracy. Realistically modeling a 1 mm thick permalloy plate can create an element size difference of over 1000 times compared to the surrounding air region. Instead, a thin plate boundary condition (SHIE element) that equivalently treats it as a "surface magnetic reluctance sheet" is used, significantly reducing the number of elements while accurately reproducing the magnetic flux diversion effect. ANSYS and COMSOL support this thin magnetic shell element as standard, enabling rapid FEM design of magnetic shields with arbitrary shapes.
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