# A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances

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## Abstract

**:**

## 1. Introduction

## 2. Analytical Model

#### 2.1. Analytical Formula

#### 2.2. The Commonly Used FEM Method

#### 2.3. The FEM Method Combined with the JA Model

## 3. Experiment

## 4. The Simulation Model of the JA Model Method

## 5. Results

#### 5.1. The Shielding Factors When the External Fields Are Sine Waves

#### 5.2. The Internal Wave When the External Field Is a Triangle Wave

#### 5.3. The Internal Waves When the External Fields Are Arbitrary

^{−1}for different rates of field changes. The basic shape of the internal waveform simulated by the JA model method fits the experimental result. The differences between the simulation and the experiment is reasonable because the simulation did not take the complexity of the MSR structure, e.g., holes, air gaps and doors, which has influences on the real shielding performance.

## 6. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Geometry and meshing of the model. (

**a**) The 2D geometry model of the MSR at HIT. (

**b**) The meshing details of the model.

**Figure 3.**The shielding factors of the MSR at HIT when the magnitude of the external field is 50 $\mathsf{\mu}$T.

**Figure 4.**The shielding factors of the MSR at HIT when the frequency of the external field is 0.01 Hz.

**Figure 5.**The internal wave of the MSR at HIT when the external field is a 0.01 Hz, 50 $\mathsf{\mu}$T triangular wave.

Layer | Material | Thickness | Side Length | Door Size |
---|---|---|---|---|

1 | Permalloy | 2 mm | 2.6 m | 2.2 m × 2.5 m |

2 | Aluminum | 8 mm | 2.43 m | / |

3 | Permalloy | 2 mm | 2.25 m | 0.8 m × 1.80 m |

4 | Permalloy | 2 mm | 1.85 m | 0.8 m × 1.76 m |

Items | Material |
---|---|

Ms | $8\times {10}^{5}$ A/m |

a | 3.75 A/m |

$\alpha $ | $1.5\times {10}^{-5}$ |

k | 2.4 A/m |

c | 0.35 |

$\sigma $ | $1.8\times {10}^{6}$ S/m |

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**MDPI and ACS Style**

Zhao, Y.; Sun, Z.; Pan, D.; Lin, S.; Jin, Y.; Li, L. A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances. *Energies* **2019**, *12*, 2048.
https://doi.org/10.3390/en12112048

**AMA Style**

Zhao Y, Sun Z, Pan D, Lin S, Jin Y, Li L. A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances. *Energies*. 2019; 12(11):2048.
https://doi.org/10.3390/en12112048

**Chicago/Turabian Style**

Zhao, Yiyang, Zhiyin Sun, Donghua Pan, Shengxin Lin, Yinxi Jin, and Liyi Li. 2019. "A New Approach to Calculate the Shielding Factor of Magnetic Shields Comprising Nonlinear Ferromagnetic Materials under Arbitrary Disturbances" *Energies* 12, no. 11: 2048.
https://doi.org/10.3390/en12112048