The spin exchange relaxation free (SERF) atomic magnetometer plays an important role in ultrahigh sensitive magnetic measurements. With the improvement of signal response and the reduction of sensor noise, the sensitivity of the SERF atomic magnetometer is limited mainly by environmental magnetic noise. In order to improve the performance of magnetic shielding, the models of a magnetic shielding cylinder with triangular holes were established in this paper, and the effect of aperture angle (θ) on the efficiency of shielding by a permalloy cylinder was investigated by the finite element analysis. The results showed that the shielding effectiveness decreases first and then increases with the augment of θ. The cylinder showed that the worst shielding effect at θ equals 60°, resulting from the magnetoresistance of leakage flux in the air dielectric. This research focuses on providing theoretical support for the design of magnetic shields and improvement of the magnetic shielding ability.
I. INTRODUCTION
The spin exchange relaxation free (SERF) atomic magnetometer1 has gained wide attention in biomedicine,2 military science,3 and other fields4 because of its ultra-high sensitivity. At present, the SERF atomic magnetometer with the highest theoretical sensitivity (0.01 fT/Hz1/2) and experimental testing sensitivity (0.16 fT/Hz1/2)5 is considered as the most promising magnetometer.
The SERF atomic magnetometer works in a weak magnetic environment below 10 nT. Isolating the interference from the external magnetic field (such as the Earth magnetic field) is crucial to implement an ultrahigh sensitive magnetic measurement.6 Passive magnetic shields frequently are used in the SERF atomic magnetometer. A few layers of nested shells, made from ferromagnetic material with high permeability, created a region in space that is magnetically isolated from the surroundings.7 The shapes of magnetic shielding include spherical,8 cylindrical,9 rectangular,10 and so forth.
The defects on the shielding cylinder is the main cause of magnetic flux leakage. Regular holes were designed on the surface of the magnetic shielding cylinder, providing a passage to laser and power cords of electronic equipment. The shielding cylinder is damaged to a certain extent due to external factors, such as aging of equipment and bump, resulting in irregular defects on the shielding cylinder. Therefore, it is necessary to research on the effect of defects on the magnetic shield performance.
The Harbin institute of technology first derived an analytical solution in terms of an infinite series for the case of a spherical magnetic shield out of infinite permeability material containing one circular aperture.11 Xuan et al. explored the relationship between the aperture diameter of the spherical magnetic shielding cylinder and the shielding factor.12 The shielding property of the cylinder with circular, square, and equilateral triangle holes was investigated by finite element analysis (FEA), proving that there is a critical area for holes. Cylinders with three shapes of holes obtain the same shielding property when the hole area is less than the critical area. The shielding performance of the magnetic shielding cylinder with triangular holes is better than that of the other two when the hole area exceeds the critical area.13 These researches mainly focus on the effect of regular and simple hole structures on the shielding performance. There are few studies on the effect of irregular defects on the shielding performance.
The angle is one of the significant characteristics of irregular defects. In this paper, the effect of aperture angle and aperture area of triangular holes on the magnetic shielding property was investigated by FEA. The central magnetic field intensity and surface magnetic field intensity of shielding cylinders were extracted and analyzed for the shielding efficiency. The influence of irregular defects on the shield was studied by exploring the influence of the triangle hole angle on the shield, which provided a critical theoretical basis for the study of irregular defects in the future.
II. SIMULATION METHOD
The SERF atomic magnetometer is mainly composed of an alkali metal atomic vapor cell, an electric heating chip, and a magnetic shielding cylinder, as shown in Fig. 1. The vapor cell, the electric heating chip, and the magnetic field compensation coil are situated inside the cylinder. The dimensional parameters of the shielding cylinder are designed according to the dimensions of the vapor cell and magnetic field compensation coil. The shielding cylinder adopts a multi-layer design in the structure. The parameters of the shielding cylinder are listed in Table I, including innermost axis length of the shielding cylinder (L), axial length difference between two adjacent layers (ΔL), innermost radius of the shielding cylinder (R), radius difference between two adjacent layers (ΔR), thickness of the layer (T), and number of layers (N). The values of L, ΔL, R, ΔR, T, and N are 250 mm, 20 mm, 65 mm, 10 mm, 0.4 mm, and 4, respectively.
Schematic diagram of the SERF atomic magnetometer (BE: beam expander, P: polarizer, BS: beam splitter, and D: detector).
Schematic diagram of the SERF atomic magnetometer (BE: beam expander, P: polarizer, BS: beam splitter, and D: detector).
Dimension parameters of the magnetic shielding cylinder.
| Parameter | Value |
|---|---|
| L | 250 mm |
| ΔL | 20 mm |
| R | 65 mm |
| ΔR | 10 mm |
| T | 0.4 mm |
| N | 4 |
| Parameter | Value |
|---|---|
| L | 250 mm |
| ΔL | 20 mm |
| R | 65 mm |
| ΔR | 10 mm |
| T | 0.4 mm |
| N | 4 |
Based on the FEA method, making use of simulation software, the influence of the opening angle of the shielding cylinder on the shielding effect was studied. Shielding cylinders with different opening angles were established by changing the parameters of the shielding cylinder and calculating the position of the hole, as shown in Fig. 2(a).
(a) Stereogram view of the shielding cylinder with hole. The top angle (θ) of the triangle hole increased from 10° to 150° on the cover, and the body of the cylinder is shown in (b) and (c).
(a) Stereogram view of the shielding cylinder with hole. The top angle (θ) of the triangle hole increased from 10° to 150° on the cover, and the body of the cylinder is shown in (b) and (c).
In order to explore the influence from the angle change on the shielding effect, isosceles triangular hole structures with different angles are designed on the surface of the magnetic shielding cylinder. Comparing the difference of the shielding effect in Y and Z directions, two isosceles triangular holes are designed at the center of the shielding tube cover and tube body (the center of the inscribed circle of the hole coincides with the center point). The three-dimensional model of the shielding cylinders with different vertex angles (θ) are established, as shown in Fig. 2(a). On the one hand, under the conditions of the same opening areas, the values of θ are 10°, 20°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, 65°, 70°, 75°, 80°, 85°, 90°, 100°, 110°, 120°, 130°, 140°, and 150°. 10°, 60°, and 150° are the three representative angles in θ, which can clearly show the changing process of the simulation results, as shown in Figs. 2(b) and 2(c). On the other hand, under the conditions of the same θ, three values of 350, 375, and 400 mm2 are selected for the opening areas to explore the influence of the change of the opening area on the shielding effect.
Permalloy is a known iron–nickel alloy with ultra-high permeability.14 Permalloy with a maximum permeability of 250 000 mH/m is chosen as the material for making magnetic shielding cylinders.15 The permeability of air is μ0 = 0.001 26 mH/m, and the permeability of permalloy is much higher than that of μ0. Permalloy exhibits ultra-low magnetoresistance, compared to air. Most of the geomagnetic field is conveyed through the magnetic shielding cylinder, reducing the magnetic field entering the cylinder.16
The magnetic field at the center of the magnetic shielding cylinder is called “the central residual magnetic field (Bθ).” The magnetic field strength on the outermost surface of the magnetic shield cylinder is called the “surface magnetic field strength.” The shielding coefficient (S) and shielding efficiency (SE) are used as the evaluation indices of the magnetic shielding cylinder. The definitions are given as follows:
where Bsh and Bush are the magnetic fields in the same position with and without the magnetic shield, respectively.
Owing to the structural heterogeneity of shielding cylinder in the X, Y, and Z directions, the shielding capacity of the shielding cylinder in different directions is different.17 The magnetic fields in X, Y, and Z directions are applied to the magnetic shielding cylinder to simulate the Earth’s magnetic field. The central magnetic field intensity and the surface magnetic field intensity of shielding cylinders with different holes are extracted from the results of simulation software and analyzed for the shielding efficiency SE. The magnetic field strength in the three directions are all 50 µT.
III. RESULTS AND DISCUSSION
The Bθ of the shielding cylinder with a hole area of 350 mm2 is simulated by software. Define BX(θ), BY(θ), and BZ(θ) as the Bθ of the shielding cylinder in the X, Y, and Z directions, respectively. BX(θ), BY(θ), and BZ(θ) as the functions of θ are described in Figs. 3(a)–3(c).
The change curves of Bθ with θ of shielding cylinders with different holes area in Y, Z, and X directions. The relationship of Bθ and θ on the condition of the hole area of 350, 375, and 400 mm2 is shown in (a)–(c), (d)–(f), and (g)–(i), respectively.
The change curves of Bθ with θ of shielding cylinders with different holes area in Y, Z, and X directions. The relationship of Bθ and θ on the condition of the hole area of 350, 375, and 400 mm2 is shown in (a)–(c), (d)–(f), and (g)–(i), respectively.
The entire process of BY(θ) and BZ(θ) can be divided into two stages: 10° < θ < 60° and 60° < θ < 150°. When 10° < θ < 60°, BY(θ) and BZ(θ) gradually increase with the variation of θ; when 60° < θ < 150°, BY(θ) and BZ(θ) gradually decrease with the variation of θ. The values of BY(θ) and BZ(θ) in the shielding cylinder increase first and then decrease with the increase of θ and reach their maximum value of 0.018 and 0.156 nT when θ is equal to 60°.
The SE at the center of the shielding cylinder in the Y and Z directions is diminished first and then raised. When θ is equal to 60°, SE reaches the minimum value of 128.87 and 110.12, and the shielding effect is the worst. The reduction of Bθ indicates that the geomagnetic field entering the cylinder is reduced; thereby, the influence on the working state of the SERF atomic magnetometer is smaller.
With the change of θ, BX(θ) is basically unchanged, as shown in Fig. 3(c). The value of BX(θ) is roughly equivalent to 1.16 × 10−4 nT, and the value of SE equals 172.69. Under the condition of the same θ, the relationship between BY(θ), BZ(θ), and BX(θ) is BX(θ) < BY(θ) < BZ(θ), and the order of SE in three directions is X > Y > Z. The shielding effect in the X direction is the best, followed by the Y direction, and the worst in the Z direction. There is not a hole in the X direction of cylinder, resulting in BX(θ) being the smallest. The cylinder structure results in a better shielding effect in the Y direction, and the conclusion was proved by Hao et al.13 and Fan et al.15
The area of the hole is also one of the important factors affecting the shielding effect of the shielding cylinder.18 On condition that the hole areas are 375 and 400 mm2, the function distribution of BX(θ), BY(θ), and BZ(θ) with respect to θ are shown in Figs. 3(d)–3(i).
Define BY2(θ), BY3(θ); BZ2(θ), BZ3(θ); and BX2(θ), BX3(θ) as BY(θ), BZ(θ), and BX(θ), respectively, of shielding cylinders with opening areas of 375 and 400 mm2. The orders are BY(θ) < BY2(θ) < BY3(θ), BZ(θ) < BZ2(θ) < BZ3(θ), and BX(θ) ≈ BX2(θ) ≈ BX3(θ) under the conditions of the same θ and directions. On the one hand, the values of Bθ in Y and Z directions increase with the augment of the opening area due to the augment of the magnetic leakage, and SE decreases.19 On the other hand, the values of Bθ in the X direction are basically unchanged with the augment of the opening area and are not affected with the various opening areas in Y and Z directions.
Three angles including θ = 10°, θ = 60°, and θ = 150° are selected, and the surface magnetic field distribution on the cover and body of the cylinder is shown in Figs. 4(a)–4(c) and 4(d)–4(f). The opening areas are all equal to 400 mm2. Three points named m, p, and n in Figs. 4(a)–4(f) show the same distance from the incenter of the isosceles triangular hole. Bm, Bp, and Bn represent the magnetic field at m, p, and n points.
Surface magnetic field distribution of the shielding cylinders with θ = 10°, θ = 60°, and θ = 150° on the condition of the hole area equal to 400 mm2. (a)–(c) and (d)–(f) are magnetic field diagrams on the cover and body of the cylinders, respectively.
Surface magnetic field distribution of the shielding cylinders with θ = 10°, θ = 60°, and θ = 150° on the condition of the hole area equal to 400 mm2. (a)–(c) and (d)–(f) are magnetic field diagrams on the cover and body of the cylinders, respectively.
On the condition of θ = 10°, θ = 60°, and θ = 150°, shown in Figs. 4(a)–4(c), the value of Bm, Bp, and Bn are equal to 73.9, 68.3, and 67.9; 63.9, 66.3, and 58.2; and 79.5, 76.6, and 96.7 µT, respectively. In Figs. 4(d)–4(f), the value of Bm, Bp, and Bn are equal to 70.7, 68.2, and 68.4; 67.6, 61.7, and 62.5; and 71.4, 69.3, and 69.2 µT, respectively. The maximum magnetic field intensity at m, p, and n points on the condition of θ = 150° show the best magnetic conduction effect. The minimum magnetic field intensity is on the condition of θ = 60°, indicating the worst conduction effect. There are the same results in the Y and Z directions.
Figure 5(a) is schematic diagram of the shielding cylinder with triangle holes whose values of θ are θ = 10°, θ = 60°, and θ = 150°. The red, blue, and black solid lines and dashed lines are the inscribed circles and radius (Rθ) of the triangular holes with θ = 10°, θ = 60°, and θ = 150°.
(a) Schematic diagram of the shielding cylinder with triangle holes whose values of θ were θ = 10°, θ = 60°, and θ = 150°. The values of Rθ with θ when the area of the triangle was 350, 375, and 400 mm2 are shown in (b)–(d).
(a) Schematic diagram of the shielding cylinder with triangle holes whose values of θ were θ = 10°, θ = 60°, and θ = 150°. The values of Rθ with θ when the area of the triangle was 350, 375, and 400 mm2 are shown in (b)–(d).
Magnetoresistance (Zm) of the isosceles triangle hole with various angles was expressed by the ratio of the magnetic potential difference (Um) and the magnetic flux (Φ),20
where L is the length of the magnetic circuit, B is the magnetic field strength on the magnetic circuit, and S is the hole area,
where a is the waist length of the isosceles triangle hole.
According to Eq. (7), the relationship between Rθ and θ under the condition of S = 350 mm2, S = 375 mm2, and S = 400 mm2 is shown in Figs. 5(b)–5(d), respectively. With the augment of θ from 10° to 60°, Rθ gradually increases first, and then Rθ decreases when θ increases from 60° to 150°. The biggest Rθ value is at θ = 60°.
According to Eq. (8), Rθ is proportional to Zm on the same S condition. Therefore, with the increase in θ from 10° to 60°, Zm gradually increases, resulting in the decrease in the magnetic field transmitting through the shielding cylinder and the augment of the magnetic field entering the cylinder. With the increase in θ from 60° to 150°, Zm gradually decreases, then the magnetic field transmitted through the shielding cylinder increases, and the magnetic field entering the cylinder decreases.
IV. CONCLUSION AND PERSPECTIVES
In this paper, the influence of a triangular hole angle on the shielding effect of the cylinder was investigated by using FEA software. With the augment of θ, the central residual magnetic field intensity (Bθ) increases first and then decreases. The value of Bθ reaches maximum when θ equals to 60°, and the cylinder shows the worst shielding effect resulting from magnetoresistance of leakage flux in the air dielectric. In addition, under the same θ conditions, three values of 350, 375, and 400 mm2 are selected for the opening areas to explore the influence of the change of the opening area on the shielding effect. Bθ increases with the increase in the area, and the shielding effect decreases with the increase in the opening area. This research focuses on providing a theoretical support for the design of magnetic shields and improvement on the magnetic shielding ability.
ACKNOWLEDGMENTS
This work was supported by the Beijing Natural Science Foundation (Grant Nos. 2214058 and 4214081), the National Natural Science Foundation of China (Grant Nos. 62105038 and 6210031543), and the Opened Fund of the State Key Laboratory of Integrated Optoelectronics (Grant No. IOSKL2020KF21).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Lei Wang: Data curation (equal); Formal analysis (equal); Investigation (lead); Software (equal); Writing – original draft (lead). Jing Zhu: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (lead). Lianqing Zhu: Funding acquisition (lead); Supervision (equal); Writing – review & editing (equal). Shuai Wang: Formal analysis (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
