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Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields
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Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields Jing Jiang , Yuhang Li , Ju wang , Lifeng Zhao , Yong Zhang , Yong Zhao PII: DOI: Reference:
S0921-4534(19)30241-2 https://doi.org/10.1016/j.physc.2019.1353582 PHYSC 1353582
To appear in:
Physica C: Superconductivity and its applications
Received date: Revised date: Accepted date:
3 July 2019 24 October 2019 2 December 2019
Please cite this article as: Jing Jiang , Yuhang Li , Ju wang , Lifeng Zhao , Yong Zhang , Yong Zhao , Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields, Physica C: Superconductivity and its applications (2019), doi: https://doi.org/10.1016/j.physc.2019.1353582
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Highlights
In this paper, we studied the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the superconducting magnet(SM). We think the research results are interesting and novel. The results showed that the direction variation of the induced shielding current (Is) in the HTS which was kept in the intensity considerable varying magnetic field directly resulted in the positive and negative values of the force, so that the forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character. Moreover, when the full penetration behavior happened in the HTS, the variation tendency of the force with the external magnetic field displayed two different segments, whatever in the field increase or decrease process. In the aspect of the relaxation properties, we found that the magnetic field (Bz) and the magnetic field gradient (dBz/dz) of the SM were bigger, the attenuation of the forces were larger.
1
Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields Jing Jiang 1, Yuhang Li 1, Ju wang1, Lifeng Zhao1,Yong Zhang 1, Yong Zhao 2 1
Superconductivity and New Energy R&D Center (SRDC), Key Laboratory of Magnetic Levitation
Technologies and Maglev Trains, Ministry of Education of China, Southwest Jiaotong University, Chengdu 610031, China 2
School of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, 351007, China
Corresponding author: Jing Jiang, Superconductivity and New Energy R&D Center (SRDC), Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Southwest Jiaotong University, Chengdu 610031, China, E-mail: [email protected] Yong Zhao, School of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, 351007, China, E-mail: [email protected] Acknowledgments This work was supported by the National Magnetic Confinement Fusion Science Program (Nos. 2013 GB114003-1, 2013GB110001), the 863 Program (No. 2014AA032701), the Sichuan Province Science Foundation (Nos. 2017JY0057, 2018JY0003)
2
Abstract Because the intensity and distribution of the external magnetic field are limited, the levitation characteristics of a high-Tc superconductor (HTS) are also remarkably restricted on the present magnetic levitation system. Based on the unique features of the magnetic field distribution and gradient of the superconducting magnet (SM), the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the SM were investigated in this paper. The results showed that the force and the hysteresis loss of the bulk both increased with increasing the external magnetic fields, when the HTS was placed in the gradient varying magnetic field. The influence of the moving times on the levitation force could be neglected, with increasing the HTS's moving times. Furthermore, the direction variation of the induced shielding current (Is) in the HTS which was kept in the intensity considerable varying magnetic field directly resulted in the positive and negative values of the force, so that the forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character. When the full penetration behavior happened in the HTS, the variation tendency of the force with the external magnetic field displayed two different segments, whatever in the field increase or decrease process. In the aspect of the relaxation properties, it can be found that the magnetic field (Bz) and the magnetic field gradient (dBz/dz) of the SM were bigger, the attenuation of the forces were larger. The field-cooling (FC) method was beneficial to improve the relaxation performance of the HTS.
Keywords: High-Tc superconductor; Levitation forces; Relaxation properties; gradient varying magnetic field; intensity varying magnetic field
1 Introduction We know that the levitation characteristics of the high-Tc superconducting magnetic levitation system are mainly determined by the distribution and intensity of the external magnetic fields, when the high-Tc superconductor (HTS) utilized in the system is definitized. At present, large numbers of experimental and theoretical researches about the levitation system's static and dynamic levitation performance have already been carried out in the external magnetic field of the permanent magnet (PM) and permanent magnet guideway (PMG) [1-9]. Nevertheless, the levitation characteristics of the HTS are remarkably restricted on the present magnetic levitation system, due to the limitation of the intensity and distribution of the external magnetic field. With the development of the superconducting magnet (SM) [10-12], the exploration of the HTS's 3
levitation performances in a varying magnetic field of the SM is beneficial to deepen the understanding of the interaction between the HTS and the external magnetic field [13-16]. Although T. Suzuki et al. found that the levitation force trended to be saturated in the conventional SM system in the case that the external magnetic field exceeded 3T. The variation tendency of the levitation force in a further high magnetic field has rarely been reported [17]. The investigations executed in the field of the SM are promising to promote wider applications of the high-Tc superconducting magnetic levitation system in the future. Because of the unique characteristic of the magnetic field distribution and gradient of the SM, the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the SM were both investigated, under the zero-field-cooling (ZFC) and field-cooling (FC) condition. Moreover, whether the HTS's moving times in the low magnetic field of the SM would affect the levitation force was also clearly discussed. Finally, the influences of the magnetic field gradient, FC method and intensity of the magnetic field on the relaxation properties of the HTS were also studied in this paper.
2 Experimental 2.1 Experimental apparatus The all experiments in this paper were carried out on the high magnetic field (HMF) levitation characteristic measurement system. The schematic illustration of the measurement system is shown in Fig. 1(a). The magnetic source of this system is provided by a NbTi conduction-cooled SM with a Ф 50mm room temperature bore. The magnetic field generated from the SM can be easily varied by controlling the exciting current ( Ie ) of the SM. It must be mentioned that the magnetic field of the SM in this paper is the Z-component of the magnetic field (Bz) which is measured by a two-dimensional hall probe. The maximum value of the Bz can be up to 6.35T at the center of the SM, when the Ie changes from 0A to 150A. In terms of the measured values of the Bz, the magnetic field gradient (dBz/dz) and magnetic force field (Bz×dBz/dz) [18,19] of the SM at different Ie were calculated. In order to confirm the position of the HTS in the whole experimental process, the top surface of the SM’s flange was set as the measurement zero position. As is shown in Fig. 1(a), the distance between the seed-crystal surface of the bulk and the top surface of the flange is defined as the moving distance of the HTS. In contrast to a positive value, the location of the HTS is a negative value, when the distance is below the zero position. The center of the SM where the maximum value of the Bz can be obtained is at the location of -394mm. A cylindrical shape liquid nitrogen vessel (LNV) which is directly connected to the SM is coaxially placed in the room temperature bore of the SM. The YBCO bulk with 30mm diameter and 18mm height can move along the Z-coordinate and can stop at any position in the LNV under the control of the motor. 4
Motor Supporting pole
Top plate Nylon rod
position
position -394mm
Distance
B
3
4
Bz=-0.02344+0.02916Ie
1 0
Bz=6.75235E-5+0.0058Ie 0
30
60
90
120
0
0.6
Bz -4
dBz/dz Bz×dBz/dz
Z 200
300
400
500
600
700
0.3
0.0 800
Z ( mm )
X
Liquid nitrogen
0.9
150
Ie ( A )
-8
Superconducting magnet coil
1.2
2
Fig. 1. (a) Schematic illustration of the HMF levitation characteristic measurement system (b) The Bz, dBz/dz and Bz×dBz/dz of the SM at 30A
Fig.1 (b) displays the distribution of the Bz, dBz/dz and Bz×dBz/dz between -150mm to -550mm along the Z-axis direction of the SM at 30A. We can see that the Bz exhibits a normal distribution along the center of the SM. However, the dBz/dz and Bz×dBz/dz both trend to be qusi-sinusoidal distribution. It should be noticed that the position where the dBz/dz and Bz×dBz/dz are zero values is just at the center of the SM. In addition, it can be found that the value of the Bz, dBz/dz and Bz×dBz/dz are all increased between the range from -200mm to -300mm, where the bulk is moved in the LNV along the Z-coordinate in our experiment. From the relationship between the Bz and Ie of the SM at the position of -200mm and -300mm in the insert of Fig.1 (b), we can see that the Bz both increase with increasing the Ie at the two different positions. The two straight lines are the fitted lines of the measured values. The fitted equations can be denoted as Bz=6.75235E-5+0.0058Ie and Bz= -0.02344+0.02916Ie, respectively. According to the slope of the fitted equation, it can be found that the variation of the Bz with the Ie at the position of -300mm is faster than that at -200mm. Table 1 The values of the Bz ( mT ) at the position of -200mm and -300mm Ie ( A )
5
10
15
20
25
30
-200mm
30
60
90
110
140
160
-300mm
150
300
450
570
710
850
When the levitation forces of the HTS moved in the low magnetic field were studied, six different exciting currents were employed, i. e., 5A, 10A, 15A, 20A, 25A and 30A. The low magnetic fields generated from the SM at these six different exciting currents are presented in Table 1.
2.2 Experimental process During the process of investigating the levitation performances of the HTS, two FC methods were 5
Bz ( T )
Zero
-200mm -300mm Fitted line of -200mm Fitted line of -300mm
4
30A Bz ( T )
YBCO bulk
8
2
Liquid nitrogen vessel
dBz/dz ( T/m ), Bz×dBz/dz (T /m)
Force sensor
adopted in our experiments, i. e., ZFC and FC conditions. In the ZFC case, the HTS was firstly cooled to the superconducting state by the liquid nitrogen without any external magnetic fields, then the SM was excited by the Ie. On the contrary, the SM was firstly excited by the Ie, after that the HTS was cooled in a constant magnetic field of the SM during the FC process. In order to ensure the HTS was completely transformed to the superconducting state, the cooling-time of the two different FC methods were both set to 5mins. When the HTS moved in the gradient varying low magnetic field, the bulk was firstly placed at the location of -200mm to complete the FC procedure. Then the YBCO bulk was moved up and down along the Z-coordinate within the range of -200mm and -300mm, meanwhile, the levitation force acted on the bulk was measured simultaneously. When the effect of moving times on the levitation force was studied, the bulk was moved up and down three times from -200mm to -300mm in the gradient varying low magnetic field. In order to study the variation of the levitation force with the intensity varying magnetic field, the HTS was kept at -300mm in the whole experimental process and the ZFC method was adopted. The Ie of the SM was firstly increased from 0A to 150A, then kept at 150A for about 5mins and finally decreased from 150A to 0A. During the process that the Ie increased from 0A to 150A and then decreased to 0A, the magnetic field generated from the SM at -300mm correspondingly changed from 0T to 4.47T and then decreased to 0T. In the aspect of the relaxation properties, the HTS was separately placed at the position of -260mm and -300mm in the ZFC and FC cases, then the effect of the magnetic field gradient and FC method on the relaxation properties were studied, while the Ie was kept at 50A. Moreover, in order to investigate the influence of the magnetic field intensity on the relaxation performances, the relaxation properties of the HTS at four different moments that corresponded to four different external magnetic fields during the whole field increase process were also discussed, meanwhile the HTS was kept at the position of -300mm.
3 Results and discussion 3.1 Characteristics of the levitation force When the HTS is magnetized in a gradient varying magnetic field of the SM, the levitation force ( FL ) which is caused by the coupled-action of the magnetization and magnetic field gradient, can be expressed by the following equation:
FL V 1 0 Bz dBz dz
(1)
Where V is the volume of the bulk, 0 is the vacuum permeability, is the susceptibility, dBz/dz is the magnetic field gradient and BzdBz/dz is the magnetic force field of the SM along the Z-coordinate. From the equation (1), we can see that the FL acted on the HTS placed in a gradient varying magnetic field is mainly determined by the BdB/dz, in the case that the superconducting bulk used in the 6
experiment maintains unchanged. 40
FCH=-200mm 5A 10A 15A 20A 25A 30A
Levitation Force ( N )
30
20
10
0
-10 0 300
20 280
40 260
60 240
80 220
100 200
Distance Z ( mm )
Fig. 2 The levitation forces of the HTS moving in the low magnetic fields of the SM at different exciting currents
From the calculated results above mentioned, the values of the BdB/dz are increased between the range from -200mm to -300mm of the SM. The experimental results show that the levitation force exerted on the bulk also gradually increases, during the process that the HTS moving from -200mm to -300mm. As is shown in Fig.2, the maximum value of the levitation forces are obtained at the position of -300mm and the specific values are 2.8N、8.5N、12N、20.7N、28.2N and 33.9N separately. On the contrary, the force acted on the bulk decreases by degrees, during the ascent process of the HTS moving from -300mm to -200mm. Moreover, we can find that the forces are all positive values in the whole moving process, when the exciting currents are 5A and 10A. Moreover, the hysteresis phenomenon almost cannot be found in the case that the Ie is 5A. Whereas, with the increasing of the Ie, the hysteresis phenomenon becomes more and more obvious in the whole moving process. In another words, the Ie is bigger, the hysteresis loss becomes higher. 30
25
FC-20A ZFC-20A
Levitation Force ( N )
20
Levitation Force ( N )
25 20 15
15 10 5 0 -5 0 300
20 280
10
40
260
60 240
80
220
100
200
Distance Z ( mm )
5 0
FC-25A First time Second time Third time
-5 0 300
20 280
40 260
60 240
80 220
100 200
Distance Z ( mm )
Fig. 3 The effect of moving times on the levitation force at 25A
Considering the HTS may move repeatedly in the practical applications, the effect of moving times on the levitation force was researched. From Fig.3, we can find that the force measured in the first time is obviously larger than those very close values which were obtained in the latter two times, when the bulk moves downwards. Whereas, the forces measured in the three times are almost equivalent, during 7
the ascent processes. From the above experimental results, we can conclude that with the increase of the moving times, the influence of the moving times on the levitation force can be neglected. The insert in Fig.3 shows that the force measured in the FC case is smaller than that measured in the ZFC case, during the whole ascent and descent process. It implies that ZFC method is helpful to enhance the value of the levitation force. Besides the levitation force of the HTS moved in the gradient varying low magnetic field was studied, the force of the bulk placed in the intensity varying magnetic field was also investigated. Considering the penetration depth (dr) of the induced shielding current (Is) in the bulk, the electromagnetic force (Fz) acted on the HTS can be given by equation (2) [13, 19]. 4
dr Rd B 2 Fz Bz z Lcyl . Rd , t , dr z 2
(2)
Where Rd is the radius of the bulk, Lcyl . is the self-inductance of the Is, t is the thickness of the bulk. 80
B C
A
60
ZFC
-300mm Force
Levitation Force ( N )
40
D
field increase
20
M
0
N -20
field decrease -40 -60 -10
0
10
20
30
40
50
60
70
Time( min )
Fig.4 The levitation forces of the HTS placed in the intensity varying magnetic field of the SM at -300mm
The insert at the left-bottom corner of the Fig.4 shows the Is flows around the peripheral penetration layer of the bulk. We know that the increase of the external magnetic field will result in the increase of the Is in the HTS, which is placed in the intensity varying magnetic field. Then, the levitation force acted on the bulk will also increase. Whereas, the interior induced Is will attain a maximum value, in the case that the external magnetic field penetrates the bulk fully. After that the force acted on the bulk will no longer increase, but decrease with further increase the external magnetic field, which may be caused by the increase of the energy loss and the decrease of the critical current density of the bulk [20, 21]. As is shown in Fig.4, the levitation forces measured in the field increase and decrease process exhibit an approximate anti-symmetrical character. The forces obtained in the field increase process are all positive values, i.e., the forces acted on the HTS are levitation forces. On the contrary, the forces 8
measured in the whole field decrease process are all attractive forces. In addition, the variation of the force represents two different segments, no matter in the whole field increase or decrease process. It can be clearly found that the levitation forces firstly increase with increasing the field, and the maximum value of the levitation force is 65.8N. Then, the levitation force decreases from 65.8N to 13.5N with further increasing the field. The similar variation tendency can also be found in the whole field decrease process, and the maximum attractive force obtained in the field decrease process is about 53.8N. Finally, the attractive forces become to 0N with decreasing the Ie to 0A. During the process that the Ie kept at 150A, an obvious relaxation property of the bulk can be found. From Fig.4, a large force attenuation from point D to point M can be seen. In addition to the decrease in the critical current density of the bulk, the rapid fall down to zero of the force can also be originated from the penetration depth is too small in that field. Moreover, it should be notable that a large force attenuation also appears at the moment that the field directly switches to the decrease process (i. e. from point M to point N), which may be caused by the rapid transformation of the interior magnetic flux of the HTS bulk in the process of the external magnetic field variation.
3.2 Relaxation properties of the HTS The effect of Bz, dBz/dz and different FC methods on the relaxation performance were compared in this paper. Moreover, the relaxation properties of the bulk superconductor in four different external magnetic fields were also investigated. 2.0
50A
dBz/dz ( T/m )
10
1.5
0
1.0
-10
0.9
Bz ( T )
20
1.0
0.5
Bz dBz/dz
-20
0.0
F/Fmax
150
200
250 300 Z ( mm )
350
400
0.8
0.7
-260mm-FC -260mm-ZFC -300mm-FC -300mm-ZFC
0.6 0.0
0.5
1.0
1.5
2.0
ln ( t+1)
Fig. 5 The relaxation properties of the HTS at the position of -260mm and -300mm
It can be seen from the Fig. 5, the attenuation of the force at -300mm is evidently larger than that at -260mm, no matter the HTS cooled by FC or ZFC method. The insert in Fig. 5 is the distribution of the Bz and dBz/dz of the SM between the distance range from -150mm to -395mm, when the exciting current is 50A. We can find that the values of the Bz and dBz/dz at the position of -300mm are both larger than that at -260mm. From the above experimental results and our former research results [16] we can conclude that the Bz and especially the dBz/dz are bigger, the attenuation of the forces are larger. 9
Simultaneously, it can be found that the force reduction of the bulk cooled by ZFC method is faster than that cooled by FC method, in another words, the FC method is beneficial to improve the relaxation performance of the HTS. 1.0 0.9 0.8
point A point B point C point D
0.6 80
0.5 0.4 0.3 0.2
B
70
Levitation Force ( N )
F/Fmax
0.7
A
60 50
C ZFC -300mm
Force
40 30
D
20
field increase
10 0 -5
0
5
10
15
20
25
30
35
Time ( min )
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ln ( t+1 )
Fig.6 The influence of the magnetic field intensity on the relaxation performances
From the insert of Fig.6, we can find that the point B and D are the moments that the maximum and minimum values of the levitation force are obtained, during the whole field increase process. The point A and C are just the moments that the levitation forces attain an identical value. From the measured Bz values of the SM, the Bz at point A, B, C and D are 1.39T, 2.17T, 2.81T and 4.47T, separately. Fig. 6 shows that the force attenuation at point A is the smallest, and that at point D is the largest. Moreover, we can see that although the force obtained at point A and C are identical, the force attenuation at point C is larger than that at point A. Combined with the magnetic field of the four different points, it can be conclude that the external magnetic field is stronger, the force attenuation of the bulk is larger. The factor to impact the relaxation properties of the HTS bulk is mainly determined by the magnetic field intensity, but not the force acted on the bulk.
4 Conclusion In the gradient varying low magnetic field, the forces exerted on the bulk all increased with increasing the external magnetic fields and vice versa. With the increasing of the Ie, the hysteresis loss of the bulk also became more and more obvious. Moreover, the influence of the moving times on the levitation force could be neglected, in the case that the HTS's moving times increased. In the intensity varying magnetic field, the levitation forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character, due to the direction of the induced Is in the HTS changed. Moreover, because of the full penetration of the external magnetic field in the bulk, the variation tendency of the force clearly displayed two different segments, no matter in the field increase or decrease process. The Bz and especially the dBz/dz of the SM were bigger, the attenuation of the forces were larger. Because of the rapid transformation or jumping behavior of the interior magnetic flux of the HTS bulk, 10
a large force attenuation was found in the high magnetic field. Moreover, the FC method was verified to be helpful to improve the relaxation performance of the HTS. The factor to impact the relaxation properties of the HTS bulk is mainly determined by the magnetic field intensity, but not the force acted on the bulk.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields Jing Jiang , Yuhang Li , Ju wang , Lifeng Zhao , Yong Zhang , Yong Zhao PII: DOI: Reference:
S0921-4534(19)30241-2 https://doi.org/10.1016/j.physc.2019.1353582 PHYSC 1353582
To appear in:
Physica C: Superconductivity and its applications
Received date: Revised date: Accepted date:
3 July 2019 24 October 2019 2 December 2019
Please cite this article as: Jing Jiang , Yuhang Li , Ju wang , Lifeng Zhao , Yong Zhang , Yong Zhao , Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields, Physica C: Superconductivity and its applications (2019), doi: https://doi.org/10.1016/j.physc.2019.1353582
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Highlights
In this paper, we studied the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the superconducting magnet(SM). We think the research results are interesting and novel. The results showed that the direction variation of the induced shielding current (Is) in the HTS which was kept in the intensity considerable varying magnetic field directly resulted in the positive and negative values of the force, so that the forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character. Moreover, when the full penetration behavior happened in the HTS, the variation tendency of the force with the external magnetic field displayed two different segments, whatever in the field increase or decrease process. In the aspect of the relaxation properties, we found that the magnetic field (Bz) and the magnetic field gradient (dBz/dz) of the SM were bigger, the attenuation of the forces were larger.
1
Levitation forces and relaxation properties of a high-Tc superconductor in varying external magnetic fields Jing Jiang 1, Yuhang Li 1, Ju wang1, Lifeng Zhao1,Yong Zhang 1, Yong Zhao 2 1
Superconductivity and New Energy R&D Center (SRDC), Key Laboratory of Magnetic Levitation
Technologies and Maglev Trains, Ministry of Education of China, Southwest Jiaotong University, Chengdu 610031, China 2
School of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, 351007, China
Corresponding author: Jing Jiang, Superconductivity and New Energy R&D Center (SRDC), Key Laboratory of Magnetic Levitation Technologies and Maglev Trains, Ministry of Education of China, Southwest Jiaotong University, Chengdu 610031, China, E-mail: [email protected] Yong Zhao, School of Physics and Energy, Fujian Normal University, Fuzhou, Fujian, 351007, China, E-mail: [email protected] Acknowledgments This work was supported by the National Magnetic Confinement Fusion Science Program (Nos. 2013 GB114003-1, 2013GB110001), the 863 Program (No. 2014AA032701), the Sichuan Province Science Foundation (Nos. 2017JY0057, 2018JY0003)
2
Abstract Because the intensity and distribution of the external magnetic field are limited, the levitation characteristics of a high-Tc superconductor (HTS) are also remarkably restricted on the present magnetic levitation system. Based on the unique features of the magnetic field distribution and gradient of the superconducting magnet (SM), the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the SM were investigated in this paper. The results showed that the force and the hysteresis loss of the bulk both increased with increasing the external magnetic fields, when the HTS was placed in the gradient varying magnetic field. The influence of the moving times on the levitation force could be neglected, with increasing the HTS's moving times. Furthermore, the direction variation of the induced shielding current (Is) in the HTS which was kept in the intensity considerable varying magnetic field directly resulted in the positive and negative values of the force, so that the forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character. When the full penetration behavior happened in the HTS, the variation tendency of the force with the external magnetic field displayed two different segments, whatever in the field increase or decrease process. In the aspect of the relaxation properties, it can be found that the magnetic field (Bz) and the magnetic field gradient (dBz/dz) of the SM were bigger, the attenuation of the forces were larger. The field-cooling (FC) method was beneficial to improve the relaxation performance of the HTS.
Keywords: High-Tc superconductor; Levitation forces; Relaxation properties; gradient varying magnetic field; intensity varying magnetic field
1 Introduction We know that the levitation characteristics of the high-Tc superconducting magnetic levitation system are mainly determined by the distribution and intensity of the external magnetic fields, when the high-Tc superconductor (HTS) utilized in the system is definitized. At present, large numbers of experimental and theoretical researches about the levitation system's static and dynamic levitation performance have already been carried out in the external magnetic field of the permanent magnet (PM) and permanent magnet guideway (PMG) [1-9]. Nevertheless, the levitation characteristics of the HTS are remarkably restricted on the present magnetic levitation system, due to the limitation of the intensity and distribution of the external magnetic field. With the development of the superconducting magnet (SM) [10-12], the exploration of the HTS's 3
levitation performances in a varying magnetic field of the SM is beneficial to deepen the understanding of the interaction between the HTS and the external magnetic field [13-16]. Although T. Suzuki et al. found that the levitation force trended to be saturated in the conventional SM system in the case that the external magnetic field exceeded 3T. The variation tendency of the levitation force in a further high magnetic field has rarely been reported [17]. The investigations executed in the field of the SM are promising to promote wider applications of the high-Tc superconducting magnetic levitation system in the future. Because of the unique characteristic of the magnetic field distribution and gradient of the SM, the levitation forces of the HTS in a gradient varying low magnetic field and an intensity considerable varying magnetic field of the SM were both investigated, under the zero-field-cooling (ZFC) and field-cooling (FC) condition. Moreover, whether the HTS's moving times in the low magnetic field of the SM would affect the levitation force was also clearly discussed. Finally, the influences of the magnetic field gradient, FC method and intensity of the magnetic field on the relaxation properties of the HTS were also studied in this paper.
2 Experimental 2.1 Experimental apparatus The all experiments in this paper were carried out on the high magnetic field (HMF) levitation characteristic measurement system. The schematic illustration of the measurement system is shown in Fig. 1(a). The magnetic source of this system is provided by a NbTi conduction-cooled SM with a Ф 50mm room temperature bore. The magnetic field generated from the SM can be easily varied by controlling the exciting current ( Ie ) of the SM. It must be mentioned that the magnetic field of the SM in this paper is the Z-component of the magnetic field (Bz) which is measured by a two-dimensional hall probe. The maximum value of the Bz can be up to 6.35T at the center of the SM, when the Ie changes from 0A to 150A. In terms of the measured values of the Bz, the magnetic field gradient (dBz/dz) and magnetic force field (Bz×dBz/dz) [18,19] of the SM at different Ie were calculated. In order to confirm the position of the HTS in the whole experimental process, the top surface of the SM’s flange was set as the measurement zero position. As is shown in Fig. 1(a), the distance between the seed-crystal surface of the bulk and the top surface of the flange is defined as the moving distance of the HTS. In contrast to a positive value, the location of the HTS is a negative value, when the distance is below the zero position. The center of the SM where the maximum value of the Bz can be obtained is at the location of -394mm. A cylindrical shape liquid nitrogen vessel (LNV) which is directly connected to the SM is coaxially placed in the room temperature bore of the SM. The YBCO bulk with 30mm diameter and 18mm height can move along the Z-coordinate and can stop at any position in the LNV under the control of the motor. 4
Motor Supporting pole
Top plate Nylon rod
position
position -394mm
Distance
B
3
4
Bz=-0.02344+0.02916Ie
1 0
Bz=6.75235E-5+0.0058Ie 0
30
60
90
120
0
0.6
Bz -4
dBz/dz Bz×dBz/dz
Z 200
300
400
500
600
700
0.3
0.0 800
Z ( mm )
X
Liquid nitrogen
0.9
150
Ie ( A )
-8
Superconducting magnet coil
1.2
2
Fig. 1. (a) Schematic illustration of the HMF levitation characteristic measurement system (b) The Bz, dBz/dz and Bz×dBz/dz of the SM at 30A
Fig.1 (b) displays the distribution of the Bz, dBz/dz and Bz×dBz/dz between -150mm to -550mm along the Z-axis direction of the SM at 30A. We can see that the Bz exhibits a normal distribution along the center of the SM. However, the dBz/dz and Bz×dBz/dz both trend to be qusi-sinusoidal distribution. It should be noticed that the position where the dBz/dz and Bz×dBz/dz are zero values is just at the center of the SM. In addition, it can be found that the value of the Bz, dBz/dz and Bz×dBz/dz are all increased between the range from -200mm to -300mm, where the bulk is moved in the LNV along the Z-coordinate in our experiment. From the relationship between the Bz and Ie of the SM at the position of -200mm and -300mm in the insert of Fig.1 (b), we can see that the Bz both increase with increasing the Ie at the two different positions. The two straight lines are the fitted lines of the measured values. The fitted equations can be denoted as Bz=6.75235E-5+0.0058Ie and Bz= -0.02344+0.02916Ie, respectively. According to the slope of the fitted equation, it can be found that the variation of the Bz with the Ie at the position of -300mm is faster than that at -200mm. Table 1 The values of the Bz ( mT ) at the position of -200mm and -300mm Ie ( A )
5
10
15
20
25
30
-200mm
30
60
90
110
140
160
-300mm
150
300
450
570
710
850
When the levitation forces of the HTS moved in the low magnetic field were studied, six different exciting currents were employed, i. e., 5A, 10A, 15A, 20A, 25A and 30A. The low magnetic fields generated from the SM at these six different exciting currents are presented in Table 1.
2.2 Experimental process During the process of investigating the levitation performances of the HTS, two FC methods were 5
Bz ( T )
Zero
-200mm -300mm Fitted line of -200mm Fitted line of -300mm
4
30A Bz ( T )
YBCO bulk
8
2
Liquid nitrogen vessel
dBz/dz ( T/m ), Bz×dBz/dz (T /m)
Force sensor
adopted in our experiments, i. e., ZFC and FC conditions. In the ZFC case, the HTS was firstly cooled to the superconducting state by the liquid nitrogen without any external magnetic fields, then the SM was excited by the Ie. On the contrary, the SM was firstly excited by the Ie, after that the HTS was cooled in a constant magnetic field of the SM during the FC process. In order to ensure the HTS was completely transformed to the superconducting state, the cooling-time of the two different FC methods were both set to 5mins. When the HTS moved in the gradient varying low magnetic field, the bulk was firstly placed at the location of -200mm to complete the FC procedure. Then the YBCO bulk was moved up and down along the Z-coordinate within the range of -200mm and -300mm, meanwhile, the levitation force acted on the bulk was measured simultaneously. When the effect of moving times on the levitation force was studied, the bulk was moved up and down three times from -200mm to -300mm in the gradient varying low magnetic field. In order to study the variation of the levitation force with the intensity varying magnetic field, the HTS was kept at -300mm in the whole experimental process and the ZFC method was adopted. The Ie of the SM was firstly increased from 0A to 150A, then kept at 150A for about 5mins and finally decreased from 150A to 0A. During the process that the Ie increased from 0A to 150A and then decreased to 0A, the magnetic field generated from the SM at -300mm correspondingly changed from 0T to 4.47T and then decreased to 0T. In the aspect of the relaxation properties, the HTS was separately placed at the position of -260mm and -300mm in the ZFC and FC cases, then the effect of the magnetic field gradient and FC method on the relaxation properties were studied, while the Ie was kept at 50A. Moreover, in order to investigate the influence of the magnetic field intensity on the relaxation performances, the relaxation properties of the HTS at four different moments that corresponded to four different external magnetic fields during the whole field increase process were also discussed, meanwhile the HTS was kept at the position of -300mm.
3 Results and discussion 3.1 Characteristics of the levitation force When the HTS is magnetized in a gradient varying magnetic field of the SM, the levitation force ( FL ) which is caused by the coupled-action of the magnetization and magnetic field gradient, can be expressed by the following equation:
FL V 1 0 Bz dBz dz
(1)
Where V is the volume of the bulk, 0 is the vacuum permeability, is the susceptibility, dBz/dz is the magnetic field gradient and BzdBz/dz is the magnetic force field of the SM along the Z-coordinate. From the equation (1), we can see that the FL acted on the HTS placed in a gradient varying magnetic field is mainly determined by the BdB/dz, in the case that the superconducting bulk used in the 6
experiment maintains unchanged. 40
FCH=-200mm 5A 10A 15A 20A 25A 30A
Levitation Force ( N )
30
20
10
0
-10 0 300
20 280
40 260
60 240
80 220
100 200
Distance Z ( mm )
Fig. 2 The levitation forces of the HTS moving in the low magnetic fields of the SM at different exciting currents
From the calculated results above mentioned, the values of the BdB/dz are increased between the range from -200mm to -300mm of the SM. The experimental results show that the levitation force exerted on the bulk also gradually increases, during the process that the HTS moving from -200mm to -300mm. As is shown in Fig.2, the maximum value of the levitation forces are obtained at the position of -300mm and the specific values are 2.8N、8.5N、12N、20.7N、28.2N and 33.9N separately. On the contrary, the force acted on the bulk decreases by degrees, during the ascent process of the HTS moving from -300mm to -200mm. Moreover, we can find that the forces are all positive values in the whole moving process, when the exciting currents are 5A and 10A. Moreover, the hysteresis phenomenon almost cannot be found in the case that the Ie is 5A. Whereas, with the increasing of the Ie, the hysteresis phenomenon becomes more and more obvious in the whole moving process. In another words, the Ie is bigger, the hysteresis loss becomes higher. 30
25
FC-20A ZFC-20A
Levitation Force ( N )
20
Levitation Force ( N )
25 20 15
15 10 5 0 -5 0 300
20 280
10
40
260
60 240
80
220
100
200
Distance Z ( mm )
5 0
FC-25A First time Second time Third time
-5 0 300
20 280
40 260
60 240
80 220
100 200
Distance Z ( mm )
Fig. 3 The effect of moving times on the levitation force at 25A
Considering the HTS may move repeatedly in the practical applications, the effect of moving times on the levitation force was researched. From Fig.3, we can find that the force measured in the first time is obviously larger than those very close values which were obtained in the latter two times, when the bulk moves downwards. Whereas, the forces measured in the three times are almost equivalent, during 7
the ascent processes. From the above experimental results, we can conclude that with the increase of the moving times, the influence of the moving times on the levitation force can be neglected. The insert in Fig.3 shows that the force measured in the FC case is smaller than that measured in the ZFC case, during the whole ascent and descent process. It implies that ZFC method is helpful to enhance the value of the levitation force. Besides the levitation force of the HTS moved in the gradient varying low magnetic field was studied, the force of the bulk placed in the intensity varying magnetic field was also investigated. Considering the penetration depth (dr) of the induced shielding current (Is) in the bulk, the electromagnetic force (Fz) acted on the HTS can be given by equation (2) [13, 19]. 4
dr Rd B 2 Fz Bz z Lcyl . Rd , t , dr z 2
(2)
Where Rd is the radius of the bulk, Lcyl . is the self-inductance of the Is, t is the thickness of the bulk. 80
B C
A
60
ZFC
-300mm Force
Levitation Force ( N )
40
D
field increase
20
M
0
N -20
field decrease -40 -60 -10
0
10
20
30
40
50
60
70
Time( min )
Fig.4 The levitation forces of the HTS placed in the intensity varying magnetic field of the SM at -300mm
The insert at the left-bottom corner of the Fig.4 shows the Is flows around the peripheral penetration layer of the bulk. We know that the increase of the external magnetic field will result in the increase of the Is in the HTS, which is placed in the intensity varying magnetic field. Then, the levitation force acted on the bulk will also increase. Whereas, the interior induced Is will attain a maximum value, in the case that the external magnetic field penetrates the bulk fully. After that the force acted on the bulk will no longer increase, but decrease with further increase the external magnetic field, which may be caused by the increase of the energy loss and the decrease of the critical current density of the bulk [20, 21]. As is shown in Fig.4, the levitation forces measured in the field increase and decrease process exhibit an approximate anti-symmetrical character. The forces obtained in the field increase process are all positive values, i.e., the forces acted on the HTS are levitation forces. On the contrary, the forces 8
measured in the whole field decrease process are all attractive forces. In addition, the variation of the force represents two different segments, no matter in the whole field increase or decrease process. It can be clearly found that the levitation forces firstly increase with increasing the field, and the maximum value of the levitation force is 65.8N. Then, the levitation force decreases from 65.8N to 13.5N with further increasing the field. The similar variation tendency can also be found in the whole field decrease process, and the maximum attractive force obtained in the field decrease process is about 53.8N. Finally, the attractive forces become to 0N with decreasing the Ie to 0A. During the process that the Ie kept at 150A, an obvious relaxation property of the bulk can be found. From Fig.4, a large force attenuation from point D to point M can be seen. In addition to the decrease in the critical current density of the bulk, the rapid fall down to zero of the force can also be originated from the penetration depth is too small in that field. Moreover, it should be notable that a large force attenuation also appears at the moment that the field directly switches to the decrease process (i. e. from point M to point N), which may be caused by the rapid transformation of the interior magnetic flux of the HTS bulk in the process of the external magnetic field variation.
3.2 Relaxation properties of the HTS The effect of Bz, dBz/dz and different FC methods on the relaxation performance were compared in this paper. Moreover, the relaxation properties of the bulk superconductor in four different external magnetic fields were also investigated. 2.0
50A
dBz/dz ( T/m )
10
1.5
0
1.0
-10
0.9
Bz ( T )
20
1.0
0.5
Bz dBz/dz
-20
0.0
F/Fmax
150
200
250 300 Z ( mm )
350
400
0.8
0.7
-260mm-FC -260mm-ZFC -300mm-FC -300mm-ZFC
0.6 0.0
0.5
1.0
1.5
2.0
ln ( t+1)
Fig. 5 The relaxation properties of the HTS at the position of -260mm and -300mm
It can be seen from the Fig. 5, the attenuation of the force at -300mm is evidently larger than that at -260mm, no matter the HTS cooled by FC or ZFC method. The insert in Fig. 5 is the distribution of the Bz and dBz/dz of the SM between the distance range from -150mm to -395mm, when the exciting current is 50A. We can find that the values of the Bz and dBz/dz at the position of -300mm are both larger than that at -260mm. From the above experimental results and our former research results [16] we can conclude that the Bz and especially the dBz/dz are bigger, the attenuation of the forces are larger. 9
Simultaneously, it can be found that the force reduction of the bulk cooled by ZFC method is faster than that cooled by FC method, in another words, the FC method is beneficial to improve the relaxation performance of the HTS. 1.0 0.9 0.8
point A point B point C point D
0.6 80
0.5 0.4 0.3 0.2
B
70
Levitation Force ( N )
F/Fmax
0.7
A
60 50
C ZFC -300mm
Force
40 30
D
20
field increase
10 0 -5
0
5
10
15
20
25
30
35
Time ( min )
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ln ( t+1 )
Fig.6 The influence of the magnetic field intensity on the relaxation performances
From the insert of Fig.6, we can find that the point B and D are the moments that the maximum and minimum values of the levitation force are obtained, during the whole field increase process. The point A and C are just the moments that the levitation forces attain an identical value. From the measured Bz values of the SM, the Bz at point A, B, C and D are 1.39T, 2.17T, 2.81T and 4.47T, separately. Fig. 6 shows that the force attenuation at point A is the smallest, and that at point D is the largest. Moreover, we can see that although the force obtained at point A and C are identical, the force attenuation at point C is larger than that at point A. Combined with the magnetic field of the four different points, it can be conclude that the external magnetic field is stronger, the force attenuation of the bulk is larger. The factor to impact the relaxation properties of the HTS bulk is mainly determined by the magnetic field intensity, but not the force acted on the bulk.
4 Conclusion In the gradient varying low magnetic field, the forces exerted on the bulk all increased with increasing the external magnetic fields and vice versa. With the increasing of the Ie, the hysteresis loss of the bulk also became more and more obvious. Moreover, the influence of the moving times on the levitation force could be neglected, in the case that the HTS's moving times increased. In the intensity varying magnetic field, the levitation forces measured in the field increase and decrease process exhibited an approximate anti-symmetrical character, due to the direction of the induced Is in the HTS changed. Moreover, because of the full penetration of the external magnetic field in the bulk, the variation tendency of the force clearly displayed two different segments, no matter in the field increase or decrease process. The Bz and especially the dBz/dz of the SM were bigger, the attenuation of the forces were larger. Because of the rapid transformation or jumping behavior of the interior magnetic flux of the HTS bulk, 10
a large force attenuation was found in the high magnetic field. Moreover, the FC method was verified to be helpful to improve the relaxation performance of the HTS. The factor to impact the relaxation properties of the HTS bulk is mainly determined by the magnetic field intensity, but not the force acted on the bulk.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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