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The levitation characteristics of the magnetic substances using trapped HTS bulk annuli with various magnetic field distributions
Physica C 494 (2013) 270–275
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The levitation characteristics of the magnetic substances using trapped HTS bulk annuli with various magnetic field distributions S.B. Kim a,⇑, T. Ikegami a, J. Matsunaga a, Y. Fujii a, H. Onodera b a b
Graduate School of Natural Science and Technology, Okayama University, 3-1-1, Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan Japan Science and Technology Agency–Core Research for Evolutional Science and Technology (JST–CREST), Tokyo 102-0076, Japan
a r t i c l e
i n f o
Article history: Accepted 21 May 2013 Available online 29 May 2013 Keywords: Magnetic levitation HTS bulk Spherical solenoid magnet Reapplied field method
a b s t r a c t We have been investigating the levitation system without any mechanical contact which is composed of a field-cooled ring-shaped high temperature superconducting (HTS) bulks [1]. In this proposed levitation system, the trapped magnetic field distributions of stacked HTS bulk are very important. In this paper, the spherical solenoid magnet composed of seven solenoid coils with different inner and outer diameters was designed and fabricated as a new magnetic source. The fabricated spherical solenoid magnet can easily make a homogeneous and various magnetic field distributions in inner space of stacked HTS bulk annuli by controlling the emerging currents of each coil. By using this spherical solenoid magnet, we tried to make a large magnetic field gradient in inner space of HTS bulk annuli, and it is very important on the levitation of magnetic substances. In order to improve the levitation properties of magnetic substances with various sizes, the external fields were reapplied to the initially trapped HTS bulk magnets. We could generate a large magnetic field gradient along the axial direction in inner space of HTS bulk annuli, and obtain the improved levitation height of samples by the proposed reapplied field method. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Because the non-contact levitation system does not have a mechanical friction, there is no energy loss and the maintenance is rarely needed. The trapped HTS bulks by FC method have a trapped magnetic field and exhibit diamagnetic behaviors, so those trapped HTS bulks were expected to be used for superconducting permanent magnets and magnetic levitation system [1]. The levitation systems to levitate the ferromagnetic samples using the trapped HTS bulks are very similar to the levitation principle of Mixed-m system composed of the ferromagnetic substance, diamagnetic material and the superconducting magnet [2–5]. In the Mixed-m system, the ferromagnetic substance suffers two forces, attractive force by the superconducting magnet and repulsive force by the diamagnetic material, and levitates. The diamagnetism is the property of an object which causes it to create a magnetic field in opposition to apply magnetic field, and it is generally quite a weak in most materials. However, HTS materials have a strong diamagnetism and pinning force to trap the magnetic flux. By using these characteristics, the ferromagnetic substance which dropped to inner space of HTS bulk annuli suffers attractive force and repulsive force and levitates. It means that the HTS bulk plays the roles ⇑ Corresponding author. Address: Department of Electrical and Electronic Engineering, Okayama University, 3-1-1, Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan. Tel.: +81 862518116; fax: +81 862518259. E-mail address: [email protected] (S.B. Kim). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.05.020
of the diamagnetic substance and the superconducting magnet at the same time [6,7]. We have been developing the levitation system using trapped HTS bulk annuli magnetized by FC method, and we confirmed that the good homogeneity along the radial direction and large magnetic gradient along the axial direction were very effective for the levitation of the ferromagnetic samples with various sizes. In this paper, the reapplied field method that the external fields were reapplied to the initially trapped HTS bulks was proposed in order to improve the levitation height and force. 2. Magnetic levitation system using trapped HTS bulk annuli and the spherical solenoid magnet In our levitation system, the three-stacked HTS bulks annuli with 20 mm ID, 60 mm OD and 15–20 mm thickness are prepared as shown in Fig. 1. The three-stacked HTS bulks annuli were fixed by installing bakelite in the upper and lower sides in experiment. The three-stacked HTS bulks annuli fixed were put into the room temperature bore of the superconducting magnet, and then it was magnetized by the superconducting magnet with FC method (LN2). The trapped magnetic fields of stacked HTS bulks annuli were used for the levitation system after pulling out of the superconducting magnet, and stacked HTS bulks annuli were still placed in liquid nitrogen to keep the superconducting state during experiment. The levitation height of iron samples as the ferromagnetic substances was measured after dropping a sample to inner space of HTS bulk annuli as shown in Fig. 1c.
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composed of seven solenoid coils with different inner and outer diameters as shown in Fig. 2. The fabricated spherical solenoid magnet can easily make the homogeneous and various magnetic
60 mm
HTS bulk
20 mm 15 mm
32
SUS ring (2mm thickness)
Magnetic flux density Bz (mT)
20 mm
15 mm
(a) Bakelite
30
HTS bulks amounted region
28
26
24
60 mm
22
0
20
40
60
80
z -axis(mm)
(a) (b) Magnetized HTS bulks
30.5
Magnetic flux density Bz (mT)
Iron sample
(c)
LN2
Fig. 1. (a) Photographs of the three-stacked HTS bulks annuli, (b) stacked HTS bulks annuli fixed by two bakelites and (c) schematic drawing of levitation system for the ferromagnetic substance using stacked HTS bulk annuli.
30.4 HTS bulks amounted region
30.3 1.7 G
30.2
30.1
30.0
0
10
20
30
40
x -axis (mm)
(b)
z 19mm 14mm CoilNo.1
10mm
11.4
3mm 9mm
18mm
Measured value
11.2
2mm
60mm
CoilNo.3
20mm
22mm 3mm
CoilNo.4
6mm
13mm x
50mm
CoilNo.5 Three stacked HTS bulks annuli
CoilNo.6
CoilNo.7
Magnetic flux density Bz (mT)
CoilNo.2
Calculated value
11.0 10.8 10.6 10.4 10.2 10.0
Fig. 2. To-scaled schematic drawing of fabricated spherical solenoid magnet composed of seven solenoid coils, and the 3-stacked HTS bulk annuli.
9.8 -80
-60
-40
-20
0
20
40
60
80
z -axis (mm) In the proposed magnetic levitation system, the magnetic field gradients in axial and radial directions were very important. So, we designed and fabricated the spherical solenoid magnet as a new magnetic source instead of superconducting magnet, and it
(c) Fig. 3. Calculated Bz profiles (a) along the axial direction, (b) along the radial direction, and (c) measured and calculated values.
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70
Magnetic flux density Bz (mT)
65 A
60 55
Initial trapping patterns
50 45 40
D
35
B
30 C
25 20 15
E -20
-10
0
10
20
z-axis (mm)
(a) initial applied field
(a)
30
Magnetic flux density Bz (mT)
B 28 Initial trapping patterns 26
C
24 D 22 20 E 18 16
-20
-10
0
10
20
z-axis (mm)
(b) Fig. 5. (a) Calculated magnetic field distributions along the axial direction of 5 trapping patterns, and (b) the enlarged profiles of the patterns B–E excluding the pattern A.
reapplied field
(b) Fig. 4. The schematic drawing of supercurrent distributions in the HTS bulk (a) by initially applied magnetic field and (b) reapplied magnetic fields.
Table 1 The initial trapping patterns with various coil currents and the reapplied field patterns. Patterns
Initial applied process
Reapplied process
A B C
Coil Coil Coil Coil Coil Coil Coil
Coil No. 4: 3 A Coil No. 1 and 7: 3 A
D E
No. No. No. No. No. No. No.
1 – 7: 3 A 4: 3 A 2 and 6: 2 A 4: 3 A 2 and 6: 1 A 1 – 7: 1 A 4: 3 A
radial directions by series connected coils with operating current at 1.35 A. From Fig. 3b, the calculated attenuation value of Bz along the radial direction seems to be large, but actual attenuation value is less than 1.7 G. Fig. 3c shows the measured and calculated Bz profiles along the axial direction of spherical magnet, it shows a good agreement. We know that the fabricated spherical solenoid magnet generates homogeneous Bz distributions at the region of HTS bulks annuli (z = 0–25 mm, x = 0–30 mm). This spherical solenoid magnet can easily make the various magnetic field distributions in the axial direction by controlling each solenoid coils current.
Coil No. 2 and 6: 3 A Coil No. 3 and 5: 3 A Coil No. 1 – 7: 3 A
field distributions at inner space of HTS bulk annuli. The internal space of the spherical solenoid magnet was designed taking into account the size of the stacked HTS bulk annuli. Fig. 3a and b shows the calculated magnetic flux density Bz profiles along the axial and
3. Reapplied field method to improve the levitation force In order to improve the magnetic field gradient along the vertical direction with keeping the homogeneous magnetic field along the radial direction, the external fields were reapplied to the initially trapped HTS bulk annuli. Fig. 4a and b shows the schematic drawing of supercurrent distributions in the HTS bulk by initially applied magnetic field and reapplied magnetic field, respectively. By the initial trapping process, the supercurrent which generates
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33
Initial trapping pattern A
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
68 67 66
A
65
B Reapplied patterns
64
C D
63
E 62 -20
-10
0
10
32 31 30
A B
29 Reapplied patterns
C D
28
E
27
20
Initial trapping pattern B
-20
-10
0
10
20
z-axis (mm)
z-axis (mm)
(a)
(b) Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
28 27 Initial trapping pattern C 26 25 A
24
B 23
Reapplied patterns
22
C D E
21
-20
-10
0
10
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
Reapplied patterns
17
C D E
31
0
10
10
B Reapplied patterns
E
-20
-10
0
10
(f)
B
26 Reapplied patterns
C
24
D
23
E
22 21 0
z -axis (mm)
(g)
10
20
20
Initial trapping pattern C
26
A
27
C D
(e)
28
20
A
z-axis (mm)
29
-10
0
Initial trapping pattern A
68 67 66 65 64 63 62 61 60 59 58 57 56
20
Initial trapping pattern B
-20
-10
z -axis (mm)
30
25
21 -20
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
B
-10
22
(d)
A
-20
E
(c)
19
C D
23
z-axis (mm)
20
16
B Reapplied patterns
24
20
Initial trapping pattern E
18
A
25
z-axis (mm)
22 21
Initial trapping pattern D
26
24 A
22
B 20
Reapplied patterns
C D
18
E 16 -20
-10
0
10
20
z -axis (mm)
(h)
Fig. 6. Calculated magnetic field distributions along the axial direction by reapplied field method (patterns A–E) at each initial trapping patterns A–E (colored plots; reapplied field was applied the same direction of an initial magnetization, and uncolored plots; the opposite direction field to the initial magnetization was applied). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Initial trapping pattern E
21
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
23 22 Initial trapping pattern D
21 20
A
19
B C
Reapplied patterns
18
D
17
E
16 15
-20
-10
0
10
20
20 19 18 17
A
16
B
15
Reapplied patterns
14
C D
13
E
12 11 10
-20
-10
0
z-axis (mm)
z -axis (mm)
(i)
(j)
10
20
Fig. 6 (continued)
-2
Magnetic field gradient (10 T/m)
4.5
Initial trapping patterns A B C D E
4.0 3.5 3.0
Initial trapping patterns A + Bex B + Bex C + Bex D + Bex E + Bex
2.5 2.0 1.5 1.0 0.5
A
B
C
D
E
Reapplied magnetic field patterns Fig. 7. Calculated magnetic field gradient along +5 mm axial direction from the center of stacked HTS bulks at initial trapped and reapplied field with opposite direction to the initial magnetization.
Table 2 Cylindrical iron samples with various size and volume. Size (mm)
Volume (mm3)
u 1.0 H 10 u 1.2 H 10 u 1.4 H 10 u 1.6 H 10 u 1.8 H 10 u 2.0 H 10
31.416 45.239 61.575 80.425 101.788 125.664
the magnetic field in the same direction as the applied external field flew in the HTS bulks as shown in Fig. 4a. Then, the shielding currents flowed into the opposite direction of the initial supercurrent in the most outer side of HTS bulk by the reapplied field, and those shielding currents flow into the inner side of HTS bulk proportional to the strength of the reapplied field due to Meissner effect as shown in Fig. 4b. 3.1. Analysis results Table 1 shows the 5 trapping patterns with various coil currents used to FC method process, and these patterns were used in
reapplied field method, also. Fig. 5 shows the calculated magnetic field distributions along the axial direction of 5 trapping patterns and the enlarged profiles of the patterns B–E excluding the pattern A. The maximum operating current of copper winding wire is 3 A, it can flow in the coil while preventing the Joule’s heating, and the highest magnetic field was generated in pattern A. The strength and distribution of magnetic field in internal space of HTS bulk annuli could change by control the energizing currents of each coil as shown in Fig. 5. Fig. 6 shows the calculated magnetic field distributions along the axial direction by reapplied field method (patterns A–E) at each initial trapping patterns A–E (colored plots; reapplied field was applied the same direction of an initial magnetization, and uncolored plots; the opposite direction field to the initial magnetization was applied). The strength of the reapplied field by the spherical solenoid magnet is very weak. From this reason, when reapplying external magnetic field to magnetized HTS bulks, the shielding currents in the most outer side of HTS bulk due to Meissner effect were weak, and it affects slightly in the central part. In the case of the reapplied field with the same direction of the initial magnetization, the magnetic field intensity should be reduced in the central part since the shielding currents with opposite direction to initial magnetization, and field homogeneity should be increased as shown in Fig. 6. However, because we wanted make a large magnetic field gradient along the axial direction with homogeneous radial field distributions. We reapplied the external magnetic field with opposite direction to the initial magnetization. The magnetic field gradients greater than the initially trapped magnetic field were obtained by the reapplied field method with opposite direction to the initial magnetization at each pattern as shown in Fig. 6. In our levitation experiments, iron samples (u 1–2 mm H 10 mm) were used as a magnetic substance, so, the magnetic field gradients along + 5 mm axial direction from the center of stacked HTS bulks at initial trapped and reapplied field with opposite direction were calculated as shown in Fig. 7. In all patterns, the magnetic field gradients with the reapplied field method were higher than the initial value, and the reapplied pattern A generated the highest field gradient. Therefore, we chose the reapplied pattern A in the experiment. 3.2. Experimental results Table 2 shows the size and volume of cylindrical iron samples. The levitation height of iron samples were measured when the reapplied pattern A with opposite direction to the initial magnetization for all initial trapping processes. Fig. 8 shows the measured magnetic field distributions (Bz) along the axial and radial directions in inner space of HTS bulk annuli as a function of the initial
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170
70
Magnetic flux density Bz (mT)
65
160
A
140
60 150 55
Initial trapping patterns
50
140
45
130
40
D
110
C
25
15
100
100 A
-10
0
10
A 60 Initial trapping patterns 50
40
D B
30 C 20
E
-2
0
2
4
6
x -axis (mm)
(b) Fig. 8. Measured magnetic field distributions Bz along the axial and radial directions in inner space of HTS bulk annuli as a function of initial trapping process at the reapplied field pattern A (colored plots; after initial trapping process, and uncolored plots; after reapplied field process with pattern A). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
-9 Initial trapping patterns A B C D E
-10 -11 -12 -13 -14
D
E
Fig. 10. The variation rate of magnetic field gradient and levitation height before and after the reapplied field process.
70
-4
C
20
(a)
10 -6
B
Initial magnetization patterns
E -20
z -axis (mm)
Magnetic flux density Bz (mT)
120
110
B
30
130
120
35
20
Levitation height (mm)
150
Initial trapping patterns A + Bex B + Bex C + Bex D + Bex E + Bex
-15
trapping process for the reapplied field pattern A (colored plots; after initial trapping process, and uncolored plots; after reapplied field process with pattern A). In all cases of initial trapping patterns, the measured magnetic field gradients along the axial direction were improved by the reapplied field process, but the field distributions along the radial direction were not changed. Fig. 9 shows the measured levitation height as a function of the volume of samples and the initial trapping patterns with/without the reapplied field pattern A. The levitation height of the iron sample corresponds to the distance from the center of the iron sample to the center of HTS bulks, and the levitation heights were higher in the turn of the initial trapping patterns E, C, B, and D. In addition, the levitation height of the iron sample improved about 0.5–1 mm at all patterns by the reapplied field method. Fig. 10 shows the variation rate of the magnetic field gradient and levitation height before and after reapplied field process. From Fig. 10, we found that the shape of variation rate of the magnetic field gradient was similar to the shape of the variation rate of the levitation height. We expected that the variation rate of the levitation height of iron sample depended on the variation rate of magnetic field gradient. 4. Conclusion In this paper, we investigated the improvement of the levitation performance of the iron samples as a ferromagnetic substance by the reapplied field method using the spherical solenoid magnet composed of seven solenoid coils with different inner and outer diameters. The fabricated spherical solenoid magnet can easily make a homogeneous and various magnetic field distributions in inner space of HTS bulk annuli by controlling each of coil currents. We could generate a large magnetic gradient along the axial direction at inner space of HTS bulks with the homogeneous radial field distributions using the reapplied field process after the initially magnetized HTS bulks, and the improved levitation height of samples were obtained by the proposed reapplied field method.
-16 -17
References
-18 -19 -20 -21 40
60
80
Volume of sample
100
120
(mm 3 )
Fig. 9. Measured levitation height as functions of the volume of samples and initial trapping patterns with/without reapplied field pattern A.
[1] S.B. Kim, J. Mataunaga, A. Doi, T. Ikegami, H. Onodera, Physica C (2013) 316– 320. [2] Y. Fukasawa, H. Ohsaki, IEEE Trans. Appl. Supercond. 9 (2) (1999). June. [3] T. Takao, S. Kameyama, T. Doi, N. Tanoue, H. Kamijo, IEEE Trans. Appl. Supercond. 21 (3) (2011) 1543–1546. June. [4] M. Ghodsi, T. Ueno, H. Tesima, H. Hirano, T. Higuchi, Physica C (2006) 343–346. [5] T. Kashiwagi, M. Kubota, E. Suzuki, T. Matsuda, M. Hirakawa, H. Nakashima, H. Ohsaki, T. Mizuno, Physica C (2003) 654–658. [6] Y. Iwasa, H. Lee, Cryogenics 37 (1997) 807–816. [7] M. Tsuda, H. Lee, S. Noguchi, Y. Iwasa, Cryogenics 39 (1999) 893–903.
Contents lists available at SciVerse ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The levitation characteristics of the magnetic substances using trapped HTS bulk annuli with various magnetic field distributions S.B. Kim a,⇑, T. Ikegami a, J. Matsunaga a, Y. Fujii a, H. Onodera b a b
Graduate School of Natural Science and Technology, Okayama University, 3-1-1, Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan Japan Science and Technology Agency–Core Research for Evolutional Science and Technology (JST–CREST), Tokyo 102-0076, Japan
a r t i c l e
i n f o
Article history: Accepted 21 May 2013 Available online 29 May 2013 Keywords: Magnetic levitation HTS bulk Spherical solenoid magnet Reapplied field method
a b s t r a c t We have been investigating the levitation system without any mechanical contact which is composed of a field-cooled ring-shaped high temperature superconducting (HTS) bulks [1]. In this proposed levitation system, the trapped magnetic field distributions of stacked HTS bulk are very important. In this paper, the spherical solenoid magnet composed of seven solenoid coils with different inner and outer diameters was designed and fabricated as a new magnetic source. The fabricated spherical solenoid magnet can easily make a homogeneous and various magnetic field distributions in inner space of stacked HTS bulk annuli by controlling the emerging currents of each coil. By using this spherical solenoid magnet, we tried to make a large magnetic field gradient in inner space of HTS bulk annuli, and it is very important on the levitation of magnetic substances. In order to improve the levitation properties of magnetic substances with various sizes, the external fields were reapplied to the initially trapped HTS bulk magnets. We could generate a large magnetic field gradient along the axial direction in inner space of HTS bulk annuli, and obtain the improved levitation height of samples by the proposed reapplied field method. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Because the non-contact levitation system does not have a mechanical friction, there is no energy loss and the maintenance is rarely needed. The trapped HTS bulks by FC method have a trapped magnetic field and exhibit diamagnetic behaviors, so those trapped HTS bulks were expected to be used for superconducting permanent magnets and magnetic levitation system [1]. The levitation systems to levitate the ferromagnetic samples using the trapped HTS bulks are very similar to the levitation principle of Mixed-m system composed of the ferromagnetic substance, diamagnetic material and the superconducting magnet [2–5]. In the Mixed-m system, the ferromagnetic substance suffers two forces, attractive force by the superconducting magnet and repulsive force by the diamagnetic material, and levitates. The diamagnetism is the property of an object which causes it to create a magnetic field in opposition to apply magnetic field, and it is generally quite a weak in most materials. However, HTS materials have a strong diamagnetism and pinning force to trap the magnetic flux. By using these characteristics, the ferromagnetic substance which dropped to inner space of HTS bulk annuli suffers attractive force and repulsive force and levitates. It means that the HTS bulk plays the roles ⇑ Corresponding author. Address: Department of Electrical and Electronic Engineering, Okayama University, 3-1-1, Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan. Tel.: +81 862518116; fax: +81 862518259. E-mail address: [email protected] (S.B. Kim). 0921-4534/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2013.05.020
of the diamagnetic substance and the superconducting magnet at the same time [6,7]. We have been developing the levitation system using trapped HTS bulk annuli magnetized by FC method, and we confirmed that the good homogeneity along the radial direction and large magnetic gradient along the axial direction were very effective for the levitation of the ferromagnetic samples with various sizes. In this paper, the reapplied field method that the external fields were reapplied to the initially trapped HTS bulks was proposed in order to improve the levitation height and force. 2. Magnetic levitation system using trapped HTS bulk annuli and the spherical solenoid magnet In our levitation system, the three-stacked HTS bulks annuli with 20 mm ID, 60 mm OD and 15–20 mm thickness are prepared as shown in Fig. 1. The three-stacked HTS bulks annuli were fixed by installing bakelite in the upper and lower sides in experiment. The three-stacked HTS bulks annuli fixed were put into the room temperature bore of the superconducting magnet, and then it was magnetized by the superconducting magnet with FC method (LN2). The trapped magnetic fields of stacked HTS bulks annuli were used for the levitation system after pulling out of the superconducting magnet, and stacked HTS bulks annuli were still placed in liquid nitrogen to keep the superconducting state during experiment. The levitation height of iron samples as the ferromagnetic substances was measured after dropping a sample to inner space of HTS bulk annuli as shown in Fig. 1c.
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composed of seven solenoid coils with different inner and outer diameters as shown in Fig. 2. The fabricated spherical solenoid magnet can easily make the homogeneous and various magnetic
60 mm
HTS bulk
20 mm 15 mm
32
SUS ring (2mm thickness)
Magnetic flux density Bz (mT)
20 mm
15 mm
(a) Bakelite
30
HTS bulks amounted region
28
26
24
60 mm
22
0
20
40
60
80
z -axis(mm)
(a) (b) Magnetized HTS bulks
30.5
Magnetic flux density Bz (mT)
Iron sample
(c)
LN2
Fig. 1. (a) Photographs of the three-stacked HTS bulks annuli, (b) stacked HTS bulks annuli fixed by two bakelites and (c) schematic drawing of levitation system for the ferromagnetic substance using stacked HTS bulk annuli.
30.4 HTS bulks amounted region
30.3 1.7 G
30.2
30.1
30.0
0
10
20
30
40
x -axis (mm)
(b)
z 19mm 14mm CoilNo.1
10mm
11.4
3mm 9mm
18mm
Measured value
11.2
2mm
60mm
CoilNo.3
20mm
22mm 3mm
CoilNo.4
6mm
13mm x
50mm
CoilNo.5 Three stacked HTS bulks annuli
CoilNo.6
CoilNo.7
Magnetic flux density Bz (mT)
CoilNo.2
Calculated value
11.0 10.8 10.6 10.4 10.2 10.0
Fig. 2. To-scaled schematic drawing of fabricated spherical solenoid magnet composed of seven solenoid coils, and the 3-stacked HTS bulk annuli.
9.8 -80
-60
-40
-20
0
20
40
60
80
z -axis (mm) In the proposed magnetic levitation system, the magnetic field gradients in axial and radial directions were very important. So, we designed and fabricated the spherical solenoid magnet as a new magnetic source instead of superconducting magnet, and it
(c) Fig. 3. Calculated Bz profiles (a) along the axial direction, (b) along the radial direction, and (c) measured and calculated values.
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S.B. Kim et al. / Physica C 494 (2013) 270–275
70
Magnetic flux density Bz (mT)
65 A
60 55
Initial trapping patterns
50 45 40
D
35
B
30 C
25 20 15
E -20
-10
0
10
20
z-axis (mm)
(a) initial applied field
(a)
30
Magnetic flux density Bz (mT)
B 28 Initial trapping patterns 26
C
24 D 22 20 E 18 16
-20
-10
0
10
20
z-axis (mm)
(b) Fig. 5. (a) Calculated magnetic field distributions along the axial direction of 5 trapping patterns, and (b) the enlarged profiles of the patterns B–E excluding the pattern A.
reapplied field
(b) Fig. 4. The schematic drawing of supercurrent distributions in the HTS bulk (a) by initially applied magnetic field and (b) reapplied magnetic fields.
Table 1 The initial trapping patterns with various coil currents and the reapplied field patterns. Patterns
Initial applied process
Reapplied process
A B C
Coil Coil Coil Coil Coil Coil Coil
Coil No. 4: 3 A Coil No. 1 and 7: 3 A
D E
No. No. No. No. No. No. No.
1 – 7: 3 A 4: 3 A 2 and 6: 2 A 4: 3 A 2 and 6: 1 A 1 – 7: 1 A 4: 3 A
radial directions by series connected coils with operating current at 1.35 A. From Fig. 3b, the calculated attenuation value of Bz along the radial direction seems to be large, but actual attenuation value is less than 1.7 G. Fig. 3c shows the measured and calculated Bz profiles along the axial direction of spherical magnet, it shows a good agreement. We know that the fabricated spherical solenoid magnet generates homogeneous Bz distributions at the region of HTS bulks annuli (z = 0–25 mm, x = 0–30 mm). This spherical solenoid magnet can easily make the various magnetic field distributions in the axial direction by controlling each solenoid coils current.
Coil No. 2 and 6: 3 A Coil No. 3 and 5: 3 A Coil No. 1 – 7: 3 A
field distributions at inner space of HTS bulk annuli. The internal space of the spherical solenoid magnet was designed taking into account the size of the stacked HTS bulk annuli. Fig. 3a and b shows the calculated magnetic flux density Bz profiles along the axial and
3. Reapplied field method to improve the levitation force In order to improve the magnetic field gradient along the vertical direction with keeping the homogeneous magnetic field along the radial direction, the external fields were reapplied to the initially trapped HTS bulk annuli. Fig. 4a and b shows the schematic drawing of supercurrent distributions in the HTS bulk by initially applied magnetic field and reapplied magnetic field, respectively. By the initial trapping process, the supercurrent which generates
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33
Initial trapping pattern A
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
68 67 66
A
65
B Reapplied patterns
64
C D
63
E 62 -20
-10
0
10
32 31 30
A B
29 Reapplied patterns
C D
28
E
27
20
Initial trapping pattern B
-20
-10
0
10
20
z-axis (mm)
z-axis (mm)
(a)
(b) Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
28 27 Initial trapping pattern C 26 25 A
24
B 23
Reapplied patterns
22
C D E
21
-20
-10
0
10
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
Reapplied patterns
17
C D E
31
0
10
10
B Reapplied patterns
E
-20
-10
0
10
(f)
B
26 Reapplied patterns
C
24
D
23
E
22 21 0
z -axis (mm)
(g)
10
20
20
Initial trapping pattern C
26
A
27
C D
(e)
28
20
A
z-axis (mm)
29
-10
0
Initial trapping pattern A
68 67 66 65 64 63 62 61 60 59 58 57 56
20
Initial trapping pattern B
-20
-10
z -axis (mm)
30
25
21 -20
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
B
-10
22
(d)
A
-20
E
(c)
19
C D
23
z-axis (mm)
20
16
B Reapplied patterns
24
20
Initial trapping pattern E
18
A
25
z-axis (mm)
22 21
Initial trapping pattern D
26
24 A
22
B 20
Reapplied patterns
C D
18
E 16 -20
-10
0
10
20
z -axis (mm)
(h)
Fig. 6. Calculated magnetic field distributions along the axial direction by reapplied field method (patterns A–E) at each initial trapping patterns A–E (colored plots; reapplied field was applied the same direction of an initial magnetization, and uncolored plots; the opposite direction field to the initial magnetization was applied). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Initial trapping pattern E
21
Magnetic flux density Bz (mT)
Magnetic flux density Bz (mT)
23 22 Initial trapping pattern D
21 20
A
19
B C
Reapplied patterns
18
D
17
E
16 15
-20
-10
0
10
20
20 19 18 17
A
16
B
15
Reapplied patterns
14
C D
13
E
12 11 10
-20
-10
0
z-axis (mm)
z -axis (mm)
(i)
(j)
10
20
Fig. 6 (continued)
-2
Magnetic field gradient (10 T/m)
4.5
Initial trapping patterns A B C D E
4.0 3.5 3.0
Initial trapping patterns A + Bex B + Bex C + Bex D + Bex E + Bex
2.5 2.0 1.5 1.0 0.5
A
B
C
D
E
Reapplied magnetic field patterns Fig. 7. Calculated magnetic field gradient along +5 mm axial direction from the center of stacked HTS bulks at initial trapped and reapplied field with opposite direction to the initial magnetization.
Table 2 Cylindrical iron samples with various size and volume. Size (mm)
Volume (mm3)
u 1.0 H 10 u 1.2 H 10 u 1.4 H 10 u 1.6 H 10 u 1.8 H 10 u 2.0 H 10
31.416 45.239 61.575 80.425 101.788 125.664
the magnetic field in the same direction as the applied external field flew in the HTS bulks as shown in Fig. 4a. Then, the shielding currents flowed into the opposite direction of the initial supercurrent in the most outer side of HTS bulk by the reapplied field, and those shielding currents flow into the inner side of HTS bulk proportional to the strength of the reapplied field due to Meissner effect as shown in Fig. 4b. 3.1. Analysis results Table 1 shows the 5 trapping patterns with various coil currents used to FC method process, and these patterns were used in
reapplied field method, also. Fig. 5 shows the calculated magnetic field distributions along the axial direction of 5 trapping patterns and the enlarged profiles of the patterns B–E excluding the pattern A. The maximum operating current of copper winding wire is 3 A, it can flow in the coil while preventing the Joule’s heating, and the highest magnetic field was generated in pattern A. The strength and distribution of magnetic field in internal space of HTS bulk annuli could change by control the energizing currents of each coil as shown in Fig. 5. Fig. 6 shows the calculated magnetic field distributions along the axial direction by reapplied field method (patterns A–E) at each initial trapping patterns A–E (colored plots; reapplied field was applied the same direction of an initial magnetization, and uncolored plots; the opposite direction field to the initial magnetization was applied). The strength of the reapplied field by the spherical solenoid magnet is very weak. From this reason, when reapplying external magnetic field to magnetized HTS bulks, the shielding currents in the most outer side of HTS bulk due to Meissner effect were weak, and it affects slightly in the central part. In the case of the reapplied field with the same direction of the initial magnetization, the magnetic field intensity should be reduced in the central part since the shielding currents with opposite direction to initial magnetization, and field homogeneity should be increased as shown in Fig. 6. However, because we wanted make a large magnetic field gradient along the axial direction with homogeneous radial field distributions. We reapplied the external magnetic field with opposite direction to the initial magnetization. The magnetic field gradients greater than the initially trapped magnetic field were obtained by the reapplied field method with opposite direction to the initial magnetization at each pattern as shown in Fig. 6. In our levitation experiments, iron samples (u 1–2 mm H 10 mm) were used as a magnetic substance, so, the magnetic field gradients along + 5 mm axial direction from the center of stacked HTS bulks at initial trapped and reapplied field with opposite direction were calculated as shown in Fig. 7. In all patterns, the magnetic field gradients with the reapplied field method were higher than the initial value, and the reapplied pattern A generated the highest field gradient. Therefore, we chose the reapplied pattern A in the experiment. 3.2. Experimental results Table 2 shows the size and volume of cylindrical iron samples. The levitation height of iron samples were measured when the reapplied pattern A with opposite direction to the initial magnetization for all initial trapping processes. Fig. 8 shows the measured magnetic field distributions (Bz) along the axial and radial directions in inner space of HTS bulk annuli as a function of the initial
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170
70
Magnetic flux density Bz (mT)
65
160
A
140
60 150 55
Initial trapping patterns
50
140
45
130
40
D
110
C
25
15
100
100 A
-10
0
10
A 60 Initial trapping patterns 50
40
D B
30 C 20
E
-2
0
2
4
6
x -axis (mm)
(b) Fig. 8. Measured magnetic field distributions Bz along the axial and radial directions in inner space of HTS bulk annuli as a function of initial trapping process at the reapplied field pattern A (colored plots; after initial trapping process, and uncolored plots; after reapplied field process with pattern A). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
-9 Initial trapping patterns A B C D E
-10 -11 -12 -13 -14
D
E
Fig. 10. The variation rate of magnetic field gradient and levitation height before and after the reapplied field process.
70
-4
C
20
(a)
10 -6
B
Initial magnetization patterns
E -20
z -axis (mm)
Magnetic flux density Bz (mT)
120
110
B
30
130
120
35
20
Levitation height (mm)
150
Initial trapping patterns A + Bex B + Bex C + Bex D + Bex E + Bex
-15
trapping process for the reapplied field pattern A (colored plots; after initial trapping process, and uncolored plots; after reapplied field process with pattern A). In all cases of initial trapping patterns, the measured magnetic field gradients along the axial direction were improved by the reapplied field process, but the field distributions along the radial direction were not changed. Fig. 9 shows the measured levitation height as a function of the volume of samples and the initial trapping patterns with/without the reapplied field pattern A. The levitation height of the iron sample corresponds to the distance from the center of the iron sample to the center of HTS bulks, and the levitation heights were higher in the turn of the initial trapping patterns E, C, B, and D. In addition, the levitation height of the iron sample improved about 0.5–1 mm at all patterns by the reapplied field method. Fig. 10 shows the variation rate of the magnetic field gradient and levitation height before and after reapplied field process. From Fig. 10, we found that the shape of variation rate of the magnetic field gradient was similar to the shape of the variation rate of the levitation height. We expected that the variation rate of the levitation height of iron sample depended on the variation rate of magnetic field gradient. 4. Conclusion In this paper, we investigated the improvement of the levitation performance of the iron samples as a ferromagnetic substance by the reapplied field method using the spherical solenoid magnet composed of seven solenoid coils with different inner and outer diameters. The fabricated spherical solenoid magnet can easily make a homogeneous and various magnetic field distributions in inner space of HTS bulk annuli by controlling each of coil currents. We could generate a large magnetic gradient along the axial direction at inner space of HTS bulks with the homogeneous radial field distributions using the reapplied field process after the initially magnetized HTS bulks, and the improved levitation height of samples were obtained by the proposed reapplied field method.
-16 -17
References
-18 -19 -20 -21 40
60
80
Volume of sample
100
120
(mm 3 )
Fig. 9. Measured levitation height as functions of the volume of samples and initial trapping patterns with/without reapplied field pattern A.
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