- Email: [email protected]
Drift of levitated YBCO superconductor induced by both a variable magnetic field and a vibration
PhysicaC 195 (1992) North-Holland
PHYSICA Ii
41-46
Drift of levitated YBCO superconductor variable magnetic field and a vibration
induced by both a
A.N. Terentiev and A.A. Kuznetsov Institute Received
ofChemicalPhysics, 22 January
Russian Academy
of.Sciences,
II 7977 Moscow, Russia
1992
It is shown that both a variable magnetic field, applied to a levitated superconductor, and a vibration of a permanent magnet induce vertical drift of a magnetically levitated YBCO superconductor. The drift is observed only when a field amplitude exceeds the threshold value. Depinning of flux lines by a variable magnetic field is a probable origin of the superconductor drift. Possible causes of the origin of a variable magnetic field in a superconducting bearing are discussed.
1. Introduction The discovery of high-l”, superconductivity has stimulated interest in the potential application of superconductor levitation to bearings [ l-31. In connection with this application it is very important to study the stability of the main bearing parameters: load capacity, stiffness, gap between a superconductor and a permanent magnet. When a superconductor is levitated above a magnet, and vice versa, the magnetic field of the permanent magnet penetrates the superconductor, creating a vortex system. Owing to the pinning, the vortex system can exist in a nonequilibrium state. Thermal fluctuations make vortices jump from one pinning centre to another, resulting in the relaxation phenomena in superconductors. One of the examples of such phenomena is the time-dependent decay of a magnetic moment at a fixed external magnetic field [4]. Thereby, one can assume that relaxation phenomena occur in superconducting bearings. This problem has been studied in ref. [ 5 1. However, the authors did not observe a change in the levitation height of a YBCO superconductor. The authors concluded that a change in levitation height does not occur in a static field. In ref. [ 6 ] it was shown that the behaviour of a levitated superconductor changes considerably in a variable magnetic field. A variable field with amplitude exceeding HP, where HP is the field value re0921-4534/92/$05.00
0 1992 Elsevier Science Publishers
sulting in the penetration of magnetic field to the centre of a superconductor, gets a levitated superconductor to relax to the levitation height corresponding to the reversible magnetic moment of the superconductor. In ref. [ 71 it was observed that a vibration of a magnet levitated above a YBCO superconductor induces a change in levitation height. So, the time stability of levitation elements of superconducting bearings, the effect of a variable magnetic field component, and vibration on it, have to be studied. The aim of the present work was to study the vertical drift of a YBCO superconductor levitated above a magnet and the influence on it of both a variable magnetic field component and a vibration of the magnet.
2. Experimental In order to perform the experiment with a superconductor levitation, the device shown in fig. 1 has been designed. The glass tube passed through the Dewar filled with liquid nitrogen. The superconducting specimen was placed inside the tube. Both ends of the tube were closed with optically transparent windows. Before the experiment, the tube was attached to the vacuum main. The specific platform contained a ring-shaped permanent magnet rigidly
B.V. All rights reserved.
42
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO MlcROSCOPE
VACUUM S”PERCONo”CTOR
I
I MAGNET
Fig. 1. Schematic experiment.
moqnetfi 700
diagram
ofthe apparatus
used for the levitation
fleld.Oe,
600
500
400
> 300
200
100
0 0
1
distance
2
from
the
magnet,
tor. That is why we made the superconductor levitate by a standard procedure to maintain equivalent conditions in all the experiments. At the beginning, the superconductor lay on the internal surface of the tube and the magnet was far down from the tube. Then, the magnet was raised in order to provide the same definite levitation height in all the experiments. After that, an observation of the drift was performed. The vertical coordinate of the levitated superconductor was determined by the light microscope having a long working distance. An AC generator connected to a power amplifier was used to supply the current through the coil. The alternating field amplitude and the distribution of magnetic field near the magnet were determined by a Hall probe. A vertical vibration of the magnet waas induced by the electromechanical vibrator attached to the magnet with the help of a rigid rod. The magnetization curve of the sample was determined by the Faraday balance method with the help of the Bruker system. The YBa2CuJ07_-x powder was produced by a freeze drying technique from nitrate solutions. Salt powders were annealed at 850°C (0.5 h) in air. YBaZCu307_-x powder was carefully mixed in an agate mortar in acetone, pressed in pellets and sintered in oxygen at 9 15°C (5 h) and then cooled. The grain size ranged from 10 to 30 urn. Transition temperature was 92 K. Transport critical current density was 100 A/cm=. The sample was of cube shape with side dimension 1.2 mm.
mm
Fig. 2. Distribution of the vertical component of the field of the permanent magnet along the vertical axis. Dashed lines show initial positions of the top and the bottom of the levitated superconductor.
connected to the air-core electric coil. The permanent magnet ( SmCos) magnetized along its axis had the dimensions of 34 mm outer diameter, 17 mm inner diameter and 10 mm thickness. Distribution of the field along the magnet axis is shown in fig. 2. The axis of the coil coincided with the axis of the magnet. At room temperature the magnet was placed below the tube. After the Dewar had been filled with liquid nitrogen the platform was moved up so that the superconductor rose from the glass and began to levitate within the tube. Levitation height is known to depend on th magnetic history of the superconduc-
3. Results In the case of superconductor levitation in a static magnetic field, a change in levitation height is not observed within the accuracy of 20 urn for 1 h. This means that the velocity of the vertical motion of the superconductor does not exceed 5x lo-’ urn/s at most. When an alternating current is applied to the coil the superconductor starts to move vertically downwards. We called this motion the drift of a levitated superconductor. The velocity of the drift depends strongly on the amplitude of the alternating magnetic field and on the frequency. In fig. 3, time dependences of the levitation height at different amplitudes are presented. One can see that the higher the alternating field amplitude the faster is the drift
43
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO
levitation
height,
initial
mm
velocity,
pm’9
10
2.5,
I
*
OL 0
1
I
500
1000
1500
2000
I
2500
I 3000
0 0
2
4
of the superconductor. In order to characterize the alternating field dependence of the drift, we determined the average velocity values at the initial part of the trajectory of the drifting superconductor 2.282.09 mm (see fig. 3). Field amplitude dependences of superconductor drift at 50 Hz and at 100 Hz are presented in fig. 4. The dependences presented are characterized by the existence of a threshold value of field amplitude H*. An alternating field exceeding H* induces the superconductor drift. When the field amplitude is less than P the drift is not observed. The value of IP depends on the field frequency; it equals 6.5 Oe at 50 Hz and 10 Oe at 100 Hz. Since the permanent magnet generates an inhomogeneous magnetic field, one can assume that a vertical vibrational of the magnet leads to the generation of an alternating field component and as a consequence it drives the superconductor to drift. Indeed, it is observed that, when a vertical vibration of the magnet with amplitude -60 u and frequency 50 Hz is induced, the superconductor starts to lower. This result is presented in fig. 5. Thus, both an external alternating field and a vibration of the magnet lead to the drift of the levitated superconductor.
6
8
alternating
time3
Fig. 3. Time dependences of levitation height at different amplitudes of alternating magnetic field (50 Hz): x -7.24 Oe, U-8.17 Oe, *-8.7 Oe, +-9.7 Oe. Levitation height is determined as the distance between the surface of the magnet and the bottom of the superconductor.
0
,**, field.
n
I
10
12
14
Oe
Fig. 4. Field amplitude dependences of the superconductor drift velocity at 50 Hz-*, and at 100 Hz-O.
2,5ratton
height,
mm
Is 2.
A
a a
1.5 t
1
0.5 I
OL 0
50
I
I
100
150
time,
I
200
250
s
Fig. 5. Drift of the levitated superconductor induced by a vertical vibration of the magnet. Levitation height is determined as the distance between the surface of the magnet and the bottom of the superconductor.
4. Discussion In using
new superconductors
in bearings,
the
44
A.N. Terentiev, A.A. Kuznetsov / Dri$ of levitated YBCO
magnetic field of a permanent magnet penetrates into a superconductor in the form of Abrikosov’s vortices. The magnetic moment of a superconductor in the mixed state can be subdivided into two components: a reversible component M,,, and an irreversible one Mi,,,. The value of irreversible magnetic moment depends on the magnetic history of a specimen, grain size and the value of the critical current as well [ 8 1. The irreversible magnetic moment vanishes when vortices reach homogeneous distribution in a superconductor. However, the inhomogeneous distribution of vortices provided by the pinning force leads to the passing of macroscopic current and, as a consequence, the irreversible magnetic moment appears. Inhomogeneous distribution of vortices is metastable and thermal fluctuations make vortices jump from one pinning centre to another. This process causes the distribution of vortices to be more homogeneous and the irreversible magnetic moment to decrease. This effect is well observed when the hysteresis loop of a superconductor is determined. When an external field sweep is stopped, a relaxation of magnetization to a reversible value is observed [4]. It is obvious that, if a levitated superconductor had an irreversible magnetic moment, a vertical drift of the superconductor could be induced by thermal fluctuations. In our experiments the permanent magnet approached the superconductor to raise it from the surface. Therefore, taking into consideration the field distribution near the magnet (fig. 2), one can conclude that the magnetization of the superconductor evolves in an increasing external field regime until the superconductor starts to levitate. This regime is similar to a zero field cooling regime. It leads to the arising of an irreversible magnetic moment of the levitated superconductor so that the net magnetic moment exceeds the reversible one. This conclusion is supported by the magnetization measurements of the superconductor. An average external magnetic field for a levitated superconductor is about 150 Oe (see fig. 2). Reverssuperconductor magnetization of the ible (M++M-)/2, where M+ and M- are different branches of the major hysteresis loop, is about 2 times smaller than the zero field cooling magnetization in the field of 150 Oe (see fig. 6). Consequently, the state of the superconductor levitated above the magnet is thermodynamically unstable and a time-de-
i -0
6
-0.4
-0
2
magnetic
02
0
field,
04
0.6
kOe
Fig. 6. Hysterisis loop of the superconductor
used in levitation experiments. *-reversible magnetization of the superconductor determined as (M+ +M-)/2, where M+ and M- are different branches of the major hysteresis loop.
pendent decrease of levitation height is possible under such experimental conditions. Experimental results presented show that the superconductor levitated in a static field does not change its levitation height. Strictly speaking, this means that the drift velocity is less than the experimental accuracy of 5 x 10e3 pm/s. This result is in agreement with the one obtained in ref. [ 5 1, where motion of a levitated superconductor was not observed within the accuracy - 10 v-4 pm/s. Therefore, thermal fluctuations are too weak to induce the drift of a levitated superconductor in a static magnetic field. However, drift of the levitated superconductor is found to appear as a result of applying an alternating field component or inducing a vertical vibration of the magnet. The dependence of the drift velocity on the amplitude of alternating field shows the existence of a threshold value of the field amplitude H*. Superconductor drift appears when the amplitude exceeds this threshold value and the velocity of the drift increases with field amplitude increase. Since the superconductor is levitated in the rather high field of 150 Oe, which is well above H,,, weak links between the grains are destroyed and the superconductor may be considered as a collection of sepa-
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO
rately magnetized grains [ 9 1. The existence of the threshold amplitude makes us propose that the drift of a superconductor results from the depinning of vortices inside the grains by an alternating magnetic field. At low AC amplitude there exists the regime where flux motion is reversible in the pinning well. Depinning occurs only when AC amplitude exceeds a certain value H*. According to ref. [ lo], the condition for the onset of vortex motion is that the discontinuity in the component of the magnetic field parallel to the surface reaches a critical values JJ, where J, is the critical current density inside the grains and ;I is the penetration depth. Under the present experimental conditions, the amplitude of the alternating field has to exceed JJ. in order to cause the vortex motion inside the grains. The threshold value P was found to depend on frequency: P = 6.5 Oe at 50 Hz and H* = 10 Oe at 10 Hz. It is not clear if it is an intrinsic property of pinned vortices or only the consequence of the existence of resonance frequencies in the permanent magnet-levitated superconductor system. Therefore, an alternating magnetic field makes the permanent magnet-levitated superconductor system relax to its thermodynamic equilibrium, inducing the drift of the levitated superconductor. The detailed explanation of the drift may be as follows. When an AC field is applied to a levitated superconductor the decreasing field regime will appear. In the decreasing field branch, the attractive component will appear in magnetization which will decrease the repulsive force of the superconductor, thus decreasing the levitation height. As a result, the magnetic field which the superconductor experiences will be increased, and magnetization decreases by this process causing a further decrease in levitation height. The same process will follow as long as an AC field is applied. However, this consideration is not complete because mass inertia effects are not taken into account. The analysis of inertia effects is in progress now. In developing a superconducting bearing it is important to take into consideration at least two possible origins of an alternating field applied to a superconductor. 1) A permanent magnet is the cause of an inhomogeneous magnetic field. Because of that, a vibration of the magnet relative to a superconductor produces an alternating field component. 2) Rotation of a levitated magnet, even around its sym-
45
metry axis, leads to the generation of an alternating field owing to the inhomogeneity of magnetization of real magnets. This effect is the origin of a frictional torque in a superconducting bearing [ 2,111. Thus, both the vibration of a levitated magnet or a superconductor and the rotation of a magnet or a superconductor generate an alternating field which can cause a vortex motion inside the superconductor and, as a consequence, produce a vertical drift of the levitated element of a superconducting bearing. It is important to note that the progress in load capacity of superconducting bearings is now provided by using melt-quenched ceramic [ 12 1. In such a system the load capacity increases owing to the increase of the irreversible magnetization of the superconductor. Therefore, the state of a magnet levitated above a superconductor is thermodynamically unstable and vertical drift due to vibration or rotation of the magnet is a probable phenomenon in such a system.
5. Conclusions We have designed the system for microscopic observation of a vertical motion of magnetically levitated YBa2Cu307_-x superconductor. It is found that an alternating magnetic field applied to a superconductor makes it drift vertically down. The drift is induced when the amplitude of the alternating field exceeds the threshold value. Unpinning of flux lines by the alternating field is the probable cause of the drift observed. The possibility of a drift of levitated elements in superconducting bearings is discussed.
Acknowledgement The authors would like to thank G.N. Filatov his excellent technical assistance.
for
References [ 1] B.R. Weinberger,
L. Lynds and J.R. Hull, Supercond. Sci. Technol. 3 ( 1990) 38 I. (21 F.C. Moon and P.-Z. Chang, Appl. Phys. Lett. 56 (1990) 397.
46
A.N. Terentiev, A.A. Kuznetsov /Drift oflevitated YBCO
[31 W.K. Chu, C.K. McMichael, K.B. Ma, M.A. Lamb, L. Chow, R.L. Meng and P.H. Hor, Int. Symp. on Magnetic Suspension Technology, NASA Langley Research Center, August 199 1, to be published. [4] C. Keller, H. Kupfer, R. Meier-Hirmer, U. Wiech, V. Selvamanickam and K. Salama, Cryogenics 30 ( 1990) 4 10. [ 51 N.N. Krasnyuk and M.P. Mitrofanov, Superconductivity: physics, chemistry, technique 3 ( 1990) 3 18 (in Russian). [6] A.N. Terentiev, Physica C 166 (1990) 71.
[ 71 V.V. Nemoshkalenko, E.H. Brand& A.A. Kordyuk and B.G. Nikitin, Physica C 170 ( 1990) 48 1. [8] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [9] V.R. Karasik, O.E. Omelianovsky and T.G. Togonidze, Supercond. Sci. Technol. 1 ( 1989) 329. [lo] E.H. Brandt, Appl. Phys. Lett. 53 (1988) 1554. [ 111 B.R. Weinberger, L. Lynds, J.R. Hull and U. Balachandran, Appl. Phys. Lett. 59 ( 1991) 1132. [ 121 F.C. Moon, P.-Z. Chang, H. Hojaji, A. Barkatt and A.N. Thorpe, Jpn. J. Appl. Phys. 29 (1990) 1257.
PHYSICA Ii
41-46
Drift of levitated YBCO superconductor variable magnetic field and a vibration
induced by both a
A.N. Terentiev and A.A. Kuznetsov Institute Received
ofChemicalPhysics, 22 January
Russian Academy
of.Sciences,
II 7977 Moscow, Russia
1992
It is shown that both a variable magnetic field, applied to a levitated superconductor, and a vibration of a permanent magnet induce vertical drift of a magnetically levitated YBCO superconductor. The drift is observed only when a field amplitude exceeds the threshold value. Depinning of flux lines by a variable magnetic field is a probable origin of the superconductor drift. Possible causes of the origin of a variable magnetic field in a superconducting bearing are discussed.
1. Introduction The discovery of high-l”, superconductivity has stimulated interest in the potential application of superconductor levitation to bearings [ l-31. In connection with this application it is very important to study the stability of the main bearing parameters: load capacity, stiffness, gap between a superconductor and a permanent magnet. When a superconductor is levitated above a magnet, and vice versa, the magnetic field of the permanent magnet penetrates the superconductor, creating a vortex system. Owing to the pinning, the vortex system can exist in a nonequilibrium state. Thermal fluctuations make vortices jump from one pinning centre to another, resulting in the relaxation phenomena in superconductors. One of the examples of such phenomena is the time-dependent decay of a magnetic moment at a fixed external magnetic field [4]. Thereby, one can assume that relaxation phenomena occur in superconducting bearings. This problem has been studied in ref. [ 5 1. However, the authors did not observe a change in the levitation height of a YBCO superconductor. The authors concluded that a change in levitation height does not occur in a static field. In ref. [ 6 ] it was shown that the behaviour of a levitated superconductor changes considerably in a variable magnetic field. A variable field with amplitude exceeding HP, where HP is the field value re0921-4534/92/$05.00
0 1992 Elsevier Science Publishers
sulting in the penetration of magnetic field to the centre of a superconductor, gets a levitated superconductor to relax to the levitation height corresponding to the reversible magnetic moment of the superconductor. In ref. [ 71 it was observed that a vibration of a magnet levitated above a YBCO superconductor induces a change in levitation height. So, the time stability of levitation elements of superconducting bearings, the effect of a variable magnetic field component, and vibration on it, have to be studied. The aim of the present work was to study the vertical drift of a YBCO superconductor levitated above a magnet and the influence on it of both a variable magnetic field component and a vibration of the magnet.
2. Experimental In order to perform the experiment with a superconductor levitation, the device shown in fig. 1 has been designed. The glass tube passed through the Dewar filled with liquid nitrogen. The superconducting specimen was placed inside the tube. Both ends of the tube were closed with optically transparent windows. Before the experiment, the tube was attached to the vacuum main. The specific platform contained a ring-shaped permanent magnet rigidly
B.V. All rights reserved.
42
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO MlcROSCOPE
VACUUM S”PERCONo”CTOR
I
I MAGNET
Fig. 1. Schematic experiment.
moqnetfi 700
diagram
ofthe apparatus
used for the levitation
fleld.Oe,
600
500
400
> 300
200
100
0 0
1
distance
2
from
the
magnet,
tor. That is why we made the superconductor levitate by a standard procedure to maintain equivalent conditions in all the experiments. At the beginning, the superconductor lay on the internal surface of the tube and the magnet was far down from the tube. Then, the magnet was raised in order to provide the same definite levitation height in all the experiments. After that, an observation of the drift was performed. The vertical coordinate of the levitated superconductor was determined by the light microscope having a long working distance. An AC generator connected to a power amplifier was used to supply the current through the coil. The alternating field amplitude and the distribution of magnetic field near the magnet were determined by a Hall probe. A vertical vibration of the magnet waas induced by the electromechanical vibrator attached to the magnet with the help of a rigid rod. The magnetization curve of the sample was determined by the Faraday balance method with the help of the Bruker system. The YBa2CuJ07_-x powder was produced by a freeze drying technique from nitrate solutions. Salt powders were annealed at 850°C (0.5 h) in air. YBaZCu307_-x powder was carefully mixed in an agate mortar in acetone, pressed in pellets and sintered in oxygen at 9 15°C (5 h) and then cooled. The grain size ranged from 10 to 30 urn. Transition temperature was 92 K. Transport critical current density was 100 A/cm=. The sample was of cube shape with side dimension 1.2 mm.
mm
Fig. 2. Distribution of the vertical component of the field of the permanent magnet along the vertical axis. Dashed lines show initial positions of the top and the bottom of the levitated superconductor.
connected to the air-core electric coil. The permanent magnet ( SmCos) magnetized along its axis had the dimensions of 34 mm outer diameter, 17 mm inner diameter and 10 mm thickness. Distribution of the field along the magnet axis is shown in fig. 2. The axis of the coil coincided with the axis of the magnet. At room temperature the magnet was placed below the tube. After the Dewar had been filled with liquid nitrogen the platform was moved up so that the superconductor rose from the glass and began to levitate within the tube. Levitation height is known to depend on th magnetic history of the superconduc-
3. Results In the case of superconductor levitation in a static magnetic field, a change in levitation height is not observed within the accuracy of 20 urn for 1 h. This means that the velocity of the vertical motion of the superconductor does not exceed 5x lo-’ urn/s at most. When an alternating current is applied to the coil the superconductor starts to move vertically downwards. We called this motion the drift of a levitated superconductor. The velocity of the drift depends strongly on the amplitude of the alternating magnetic field and on the frequency. In fig. 3, time dependences of the levitation height at different amplitudes are presented. One can see that the higher the alternating field amplitude the faster is the drift
43
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO
levitation
height,
initial
mm
velocity,
pm’9
10
2.5,
I
*
OL 0
1
I
500
1000
1500
2000
I
2500
I 3000
0 0
2
4
of the superconductor. In order to characterize the alternating field dependence of the drift, we determined the average velocity values at the initial part of the trajectory of the drifting superconductor 2.282.09 mm (see fig. 3). Field amplitude dependences of superconductor drift at 50 Hz and at 100 Hz are presented in fig. 4. The dependences presented are characterized by the existence of a threshold value of field amplitude H*. An alternating field exceeding H* induces the superconductor drift. When the field amplitude is less than P the drift is not observed. The value of IP depends on the field frequency; it equals 6.5 Oe at 50 Hz and 10 Oe at 100 Hz. Since the permanent magnet generates an inhomogeneous magnetic field, one can assume that a vertical vibrational of the magnet leads to the generation of an alternating field component and as a consequence it drives the superconductor to drift. Indeed, it is observed that, when a vertical vibration of the magnet with amplitude -60 u and frequency 50 Hz is induced, the superconductor starts to lower. This result is presented in fig. 5. Thus, both an external alternating field and a vibration of the magnet lead to the drift of the levitated superconductor.
6
8
alternating
time3
Fig. 3. Time dependences of levitation height at different amplitudes of alternating magnetic field (50 Hz): x -7.24 Oe, U-8.17 Oe, *-8.7 Oe, +-9.7 Oe. Levitation height is determined as the distance between the surface of the magnet and the bottom of the superconductor.
0
,**, field.
n
I
10
12
14
Oe
Fig. 4. Field amplitude dependences of the superconductor drift velocity at 50 Hz-*, and at 100 Hz-O.
2,5ratton
height,
mm
Is 2.
A
a a
1.5 t
1
0.5 I
OL 0
50
I
I
100
150
time,
I
200
250
s
Fig. 5. Drift of the levitated superconductor induced by a vertical vibration of the magnet. Levitation height is determined as the distance between the surface of the magnet and the bottom of the superconductor.
4. Discussion In using
new superconductors
in bearings,
the
44
A.N. Terentiev, A.A. Kuznetsov / Dri$ of levitated YBCO
magnetic field of a permanent magnet penetrates into a superconductor in the form of Abrikosov’s vortices. The magnetic moment of a superconductor in the mixed state can be subdivided into two components: a reversible component M,,, and an irreversible one Mi,,,. The value of irreversible magnetic moment depends on the magnetic history of a specimen, grain size and the value of the critical current as well [ 8 1. The irreversible magnetic moment vanishes when vortices reach homogeneous distribution in a superconductor. However, the inhomogeneous distribution of vortices provided by the pinning force leads to the passing of macroscopic current and, as a consequence, the irreversible magnetic moment appears. Inhomogeneous distribution of vortices is metastable and thermal fluctuations make vortices jump from one pinning centre to another. This process causes the distribution of vortices to be more homogeneous and the irreversible magnetic moment to decrease. This effect is well observed when the hysteresis loop of a superconductor is determined. When an external field sweep is stopped, a relaxation of magnetization to a reversible value is observed [4]. It is obvious that, if a levitated superconductor had an irreversible magnetic moment, a vertical drift of the superconductor could be induced by thermal fluctuations. In our experiments the permanent magnet approached the superconductor to raise it from the surface. Therefore, taking into consideration the field distribution near the magnet (fig. 2), one can conclude that the magnetization of the superconductor evolves in an increasing external field regime until the superconductor starts to levitate. This regime is similar to a zero field cooling regime. It leads to the arising of an irreversible magnetic moment of the levitated superconductor so that the net magnetic moment exceeds the reversible one. This conclusion is supported by the magnetization measurements of the superconductor. An average external magnetic field for a levitated superconductor is about 150 Oe (see fig. 2). Reverssuperconductor magnetization of the ible (M++M-)/2, where M+ and M- are different branches of the major hysteresis loop, is about 2 times smaller than the zero field cooling magnetization in the field of 150 Oe (see fig. 6). Consequently, the state of the superconductor levitated above the magnet is thermodynamically unstable and a time-de-
i -0
6
-0.4
-0
2
magnetic
02
0
field,
04
0.6
kOe
Fig. 6. Hysterisis loop of the superconductor
used in levitation experiments. *-reversible magnetization of the superconductor determined as (M+ +M-)/2, where M+ and M- are different branches of the major hysteresis loop.
pendent decrease of levitation height is possible under such experimental conditions. Experimental results presented show that the superconductor levitated in a static field does not change its levitation height. Strictly speaking, this means that the drift velocity is less than the experimental accuracy of 5 x 10e3 pm/s. This result is in agreement with the one obtained in ref. [ 5 1, where motion of a levitated superconductor was not observed within the accuracy - 10 v-4 pm/s. Therefore, thermal fluctuations are too weak to induce the drift of a levitated superconductor in a static magnetic field. However, drift of the levitated superconductor is found to appear as a result of applying an alternating field component or inducing a vertical vibration of the magnet. The dependence of the drift velocity on the amplitude of alternating field shows the existence of a threshold value of the field amplitude H*. Superconductor drift appears when the amplitude exceeds this threshold value and the velocity of the drift increases with field amplitude increase. Since the superconductor is levitated in the rather high field of 150 Oe, which is well above H,,, weak links between the grains are destroyed and the superconductor may be considered as a collection of sepa-
A.N. Terentiev, A.A. Kuznetsov /Drift of levitated YBCO
rately magnetized grains [ 9 1. The existence of the threshold amplitude makes us propose that the drift of a superconductor results from the depinning of vortices inside the grains by an alternating magnetic field. At low AC amplitude there exists the regime where flux motion is reversible in the pinning well. Depinning occurs only when AC amplitude exceeds a certain value H*. According to ref. [ lo], the condition for the onset of vortex motion is that the discontinuity in the component of the magnetic field parallel to the surface reaches a critical values JJ, where J, is the critical current density inside the grains and ;I is the penetration depth. Under the present experimental conditions, the amplitude of the alternating field has to exceed JJ. in order to cause the vortex motion inside the grains. The threshold value P was found to depend on frequency: P = 6.5 Oe at 50 Hz and H* = 10 Oe at 10 Hz. It is not clear if it is an intrinsic property of pinned vortices or only the consequence of the existence of resonance frequencies in the permanent magnet-levitated superconductor system. Therefore, an alternating magnetic field makes the permanent magnet-levitated superconductor system relax to its thermodynamic equilibrium, inducing the drift of the levitated superconductor. The detailed explanation of the drift may be as follows. When an AC field is applied to a levitated superconductor the decreasing field regime will appear. In the decreasing field branch, the attractive component will appear in magnetization which will decrease the repulsive force of the superconductor, thus decreasing the levitation height. As a result, the magnetic field which the superconductor experiences will be increased, and magnetization decreases by this process causing a further decrease in levitation height. The same process will follow as long as an AC field is applied. However, this consideration is not complete because mass inertia effects are not taken into account. The analysis of inertia effects is in progress now. In developing a superconducting bearing it is important to take into consideration at least two possible origins of an alternating field applied to a superconductor. 1) A permanent magnet is the cause of an inhomogeneous magnetic field. Because of that, a vibration of the magnet relative to a superconductor produces an alternating field component. 2) Rotation of a levitated magnet, even around its sym-
45
metry axis, leads to the generation of an alternating field owing to the inhomogeneity of magnetization of real magnets. This effect is the origin of a frictional torque in a superconducting bearing [ 2,111. Thus, both the vibration of a levitated magnet or a superconductor and the rotation of a magnet or a superconductor generate an alternating field which can cause a vortex motion inside the superconductor and, as a consequence, produce a vertical drift of the levitated element of a superconducting bearing. It is important to note that the progress in load capacity of superconducting bearings is now provided by using melt-quenched ceramic [ 12 1. In such a system the load capacity increases owing to the increase of the irreversible magnetization of the superconductor. Therefore, the state of a magnet levitated above a superconductor is thermodynamically unstable and vertical drift due to vibration or rotation of the magnet is a probable phenomenon in such a system.
5. Conclusions We have designed the system for microscopic observation of a vertical motion of magnetically levitated YBa2Cu307_-x superconductor. It is found that an alternating magnetic field applied to a superconductor makes it drift vertically down. The drift is induced when the amplitude of the alternating field exceeds the threshold value. Unpinning of flux lines by the alternating field is the probable cause of the drift observed. The possibility of a drift of levitated elements in superconducting bearings is discussed.
Acknowledgement The authors would like to thank G.N. Filatov his excellent technical assistance.
for
References [ 1] B.R. Weinberger,
L. Lynds and J.R. Hull, Supercond. Sci. Technol. 3 ( 1990) 38 I. (21 F.C. Moon and P.-Z. Chang, Appl. Phys. Lett. 56 (1990) 397.
46
A.N. Terentiev, A.A. Kuznetsov /Drift oflevitated YBCO
[31 W.K. Chu, C.K. McMichael, K.B. Ma, M.A. Lamb, L. Chow, R.L. Meng and P.H. Hor, Int. Symp. on Magnetic Suspension Technology, NASA Langley Research Center, August 199 1, to be published. [4] C. Keller, H. Kupfer, R. Meier-Hirmer, U. Wiech, V. Selvamanickam and K. Salama, Cryogenics 30 ( 1990) 4 10. [ 51 N.N. Krasnyuk and M.P. Mitrofanov, Superconductivity: physics, chemistry, technique 3 ( 1990) 3 18 (in Russian). [6] A.N. Terentiev, Physica C 166 (1990) 71.
[ 71 V.V. Nemoshkalenko, E.H. Brand& A.A. Kordyuk and B.G. Nikitin, Physica C 170 ( 1990) 48 1. [8] C.P. Bean, Phys. Rev. Lett. 8 (1962) 250. [9] V.R. Karasik, O.E. Omelianovsky and T.G. Togonidze, Supercond. Sci. Technol. 1 ( 1989) 329. [lo] E.H. Brandt, Appl. Phys. Lett. 53 (1988) 1554. [ 111 B.R. Weinberger, L. Lynds, J.R. Hull and U. Balachandran, Appl. Phys. Lett. 59 ( 1991) 1132. [ 121 F.C. Moon, P.-Z. Chang, H. Hojaji, A. Barkatt and A.N. Thorpe, Jpn. J. Appl. Phys. 29 (1990) 1257.