- Email: [email protected]
A thermally actuated superconducting flux pump
Available online at www.sciencedirect.com
Physica C 468 (2008) 153–159 www.elsevier.com/locate/physc
A thermally actuated superconducting flux pump Timothy Coombs *, Zhiyong Hong, Xiaomin Zhu Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, United Kingdom Received 6 June 2007; received in revised form 5 October 2007; accepted 5 November 2007 Available online 21 November 2007
Abstract The concept of a superconducting flux pump is relatively straightforward. A small magnetic field repeatedly applied will lead to a much larger field being trapped within the superconductor. This field is limited by the volume of the superconductor and by its critical current but not by the excitation field. Here we will describe a new technique which facilitates the creation of high magnetic fields and where the magnitude of the trapped field is limited by the superconductor not the magnetising field. The technique is demonstrated using measurements taken using samples of bulk YBCO as YBCO has a very high irreversibility field and has the potential to trap high magnetic fields. The technique could be applied to other superconductors such as BSCCO or MgB2 and in other forms such as thin or thick films. Ó 2007 Elsevier B.V. All rights reserved. PACS: 94.20.Ws Keywords: Trapped fields; Flux pumps; Magnetism
1. Introduction High temperature superconductors have been under development for 20 years now and come in a variety of different forms of a large number of different materials. Of particular note are the YBCO bulks which using a melt seeded technique have been developed to the extent where 14.4 T can be trapped in the gap between a pair of 27 mm zinc doped samples at 22.5 K [1]. Mini-magnets of such strength have clear potential uses but these have been limited by the fact that a field of equal (when field cooled) or greater (when pulse magnetised) magnitude is required to magnetise them. This paper describes a practical method for achieving a flux pump and thereby obviating the need for a large magnetising field. Arrangements for flux pumps have been proposed before van Klundert et al. give an excellent review [2] in which they make clear that either you need *
Corresponding author. Tel.: +44 1223 748315. E-mail address: [email protected] (T. Coombs).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.11.003
mechanical or thermal superconducting switches, or a moving normal region which is smaller than the material in which it sits so that currents are shorted round it instead of going into the magnet circuit. Example systems based on these principles are described in [3,4]. The method described herein has two unique features. The first is that at no point is the superconductor driven normal we are simply making modifications to the critical state. The second is that the critical state is not modified by a moving magnet or an array of solenoids but by a thermal pulse which modifies the magnetisation of a magnetic material thus sweeping vortices into the material. The method described in this paper comprises automatically controlling a magnetic material to generate a pulse of magnetic flux travelling over a surface of said superconductor. Since the pulse can be repeatedly applied each pass stores incrementally more magnetic flux in the superconductor. The system may be employed for either magnetising or de-magnetising a superconductor, or for dynamically changing the magnetisation of a superconductor, depending
154
T. Coombs et al. / Physica C 468 (2008) 153–159
t=0.1s
t=0.2s
t=0.3s
t=0.4s
t=0.5s
t=0.6s
t=0.7s
t=0.8s
t=1.0s
t=1.1s
t=0.9s
reduced (or equivalently increased) permeability in the ordered material. The method relies on flux remaining trapped in the superconductor so that the fields applied are always below the irreversibility line. Figs. 1 and 2 are calculated analytically to illustrate the progression of the magnetic pulse. Fig. 3 depicts the test rig which was built, Figs. 4 and 5 are included to show the
t=1.2s
Fig. 1. Magnetic ordering of the switchable material at different time steps. In the figure a thermal pulse is shown travelling in from the right hand edge of a circularly symmetric puck of the switchable magnetic material. The figure shows the right hand half of the puck and the progression of the pulse with time, t.
upon whether the pulse of magnetic flux is applied to build up or decrease the magnetisation of the superconductor. When magnetising a superconductor the field is controlled so that after each sweep of magnetic flux over the surface of a superconductor flux is trapped within the superconductor, and in this way a very large field can be built up in a superconductor using multiple sweeps of a relatively small field. The field is controlled by changes in magnetisation or permeability. Soft magnetic materials such as analogues of Prussian Blue undergo a change in permeability and hard ones such as NdFeB undergo changes in magnetisation in response to changes in their temperatures. A thermal pulse can induce a thermal wave which travels through the body of the material and consequently a magnetic pulse which travels with the wave. The material which is being heated need not itself generate a substantial magnetic field and we will describe an implementation of the technique which relies upon concentration of an external or separately applied magnetic field locally in the superconductor by creating a region of
Fig. 3. Experimental rig. This rig is designed to replicate the conditions represented by Figs. 1 and 2. The rig is circularly symmetric and the right hand half is depicted. Thermal pulses as shown in Fig. 1 travel along the paths A and B which in turn drag magnetic flux across the superconductor as shown in Fig. 2. The rig may be operated with any or all of the superconductor, prussian blue and magnet in place and is adjustable vertically as represented by the double headed arrow.
Fig. 2. Distribution of current and flux density at different time steps in one cycle. This figure shows the same puck as in Fig. 1 above a superconducting puck. In this figure the effect of the thermal pulse depicted in Fig. 1 is shown as the movement of magnetic flux from right to left as represented by the flux lines. The time steps are the same as those for Fig. 1 and the effect on the superconductor is to induce currents in the shaded regions, the induced currents are flowing perpendicular to the surface shown.
T. Coombs et al. / Physica C 468 (2008) 153–159
155
Table 1 Specifications and results of trapped field measurements on YBCO samples in liquid nitrogen at 77 K
Fig. 4. Magnetisation versus temperature for NdFeB. NdFeB undergoes a reversible change in magnetisation with temperature as is shown here. The trace was measured using the experimental arrangement shown in Fig. 3 and with the superconductor and the Prussian blue removed.
temperature dependence of both the Prussian Blue analogue used and NdFeB. Table 1 is included to show the flux trapping ability of the superconducting samples used in the experiments and Figs. 6 and 7 show the results obtained using the rig depicted in Fig. 3. 2. Method If a heat pulse is applied to the edge of a body then that heat is transmitted through the body in the form of a ther-
Superconductor sample
Round
Hexagonal
Diameter (mm) Thickness (mm) Central field (mT) (0.5 T field cooling)
13 3.5 54
23 4 326
mal wave. That thermal wave may be used to control magnetisation in a hard magnetic material such as NdFeB, whose magnetisation decreases continuously below about 120 K, or permeability in a soft magnetic material such as one of the Prussian Blue analogues. There are a range of Prussian Blue analogues which become ferromagnetic at cryogenic temperatures and which are therefore ideal for being paired with superconductors. The passage of the thermal wave induces a magnetic pulse and after the passage of the thermal wave the body reverts to its original temperature and thus the NdFeB or Prussian blue return to their original state. Using this technique it is therefore possible to generate a series of unidirectional magnetic pulses which, according to Faraday’s law, will induce circulating currents in the superconductor which build up with each application and therefore magnetise the superconductor. Figs. 1 and 2 illustrate the process and were generated using the equation scheme given in the Analysis section below. Fig. 1 shows the progression of a thermal pulse across a circular puck of magnetisable material, there are many candidates for this material but results are presented III here for NiII 1:5 ½Cr ðCNÞ6 which is an analogue of Prussian
Squid measurements of Ni II [Cr III (CN ) ] 1.5 6 8.00E+04
20K
6.00E+04
40K 60K 4.00E+04
70K
M (A/m)
2.00E+04
100K -2.00E+06
-1.50E+06
-1.00E+06
0.00E+00 -5.00E+05 0.00E+00
5.00E+05
1.00E+06
1.50E+06
2.00E+06
-2.00E+04
-4.00E+04
-6.00E+04
-8.00E+04
H (A/m)
III Fig. 5. Squid measurement of ferromagnetic transition of NiII 1:5 ½Cr ðCNÞ6 . Five MH loops at various temperatures are plotted. These show the transition occurring between 100 K and 70 K and the magnetisation increasing with reducing temperature.
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Fig. 6. Results from 13 mm round sample. The arrows represent the order in which the sample was first cooled and then warmed and then cooled and then warmed and finally cooled again. With each cycle there is a further magnetisation of the superconductor.
equations to be solved to calculate the induced currents are: 1 rðAz þ MÞ ¼ J z ð1aÞ r l0 lr oAz ð1bÞ Ez ¼ ot Ez =qSc Superconductor subdomain Jz ¼ ð1cÞ Ez =qair Air subdomain where qair is a constant value and the nonlinear resistivity of the superconductor is defined using an EJ law as follows: 1=n
Fig. 7. Results from 13 mm round and 23 mm hexagonal samples using NdFeB as switching material. In this figure the Prussian blue has been removed and the magnet is adjacent to the superconductor. Removal of the Prussian blue has reduced the reluctance of the magnetic path leading to higher applied magnetic fields and greater net magnetisation per cycle of the superconductor.
Blue. The puck is a ring and the figure shows the right hand half in cross-section. In Fig. 2 the material depicted in Fig. 1 is shown above a superconducting disc. The figure clearly shows flux being drawn across the surface of the superconductor and the currents which are induced in the superconductor as a result. 3. Analysis A mathematical model can be constructed in order to analyse the arrangement described in Figs. 1 and 2. The
qSc ¼
E0 ðn1Þ=n jEz j þ q0 Jc
ð2Þ
This equation would lead to a singularity if the total resistivity was zero and therefore to avoid this occurring a small offset q0 (1e12 X) has been added. In the example given the problem is axially symmetric so if we examine the Laplacian in cyclindrical coordinates we obtain 1 o oAu o 2 Au 2 r r Au ¼ ð3Þ þ 2 r or or oz Substitute (3) into (1a) and noting that M in the superconductor is zero gives 1 1 o oAu o 2 Au r ð4Þ þ 2 ¼ Ju l0 lr r or or oz
T. Coombs et al. / Physica C 468 (2008) 153–159
157
In the problem there are three distinct regions, superconductor, air and magnet. All internal boundaries satisfy the Neumann boundary condition that is that Au is continuous across the boundary. The external boundary of the problem is defined by the Dirichlet boundary condition
plied by Arepoc limited and this Hall probe is calibrated for measurements over the entire thermal range presented.
Au ¼ 0
Fig. 4 shows how the magnetisation of the NdFeB magnet used in the rig varies with temperature. From these curves it can be seen that the change in field of the NdFeB is entirely reversible, as it was found that there was no net reduction in magnetisation when the magnet was returned to room temperature. This curve is in good experimental agreement with published data [5]. There is a small amount of hysteresis, so that the cooling and warming traces are slightly offset, this is evident from the increased thickness of the line at around 100 K. Thus thermal cycling of NdFeB can achieve the desired change in magnetic field which will magnetise the superconductor as it can be clearly seen from Fig. 4 that NdFeB’s magnetisation is rapidly changing, with temperature below the critical temperature of the YBCO and therefore thermal cycling of NdFeB can be used to pump flux into the superconductor. The manufacturing process for Prussian Blue analogues is an extremely simple precipitation reaction, Prussian Blue itself has a Curie point at around 5.6 K, but analogues have been created with a range of Curie points. They precipitate out from solution in powder form and tend to have poor thermal conductivity. One practical method of forming bulk structures is to use a metallic binder such as silver Dag , which also increases the thermal and electrical conductivity while not adversely affecting the packing factor and therefore the overall magnetic moment. Pucks formed using a silver Dag binder and a press were used in the experimental rig. Fig. 5 shows M–H loops for a Prussian Blue analogue, III NiII 1:5 ½Cr ðCNÞ6 at different temperatures, the measurements were taken using powder samples and the results have been corrected for the sample shape and size and therefore M is equivalent to magnetisation. When the applied field (horizontal axis) is constant reducing the temperature has the effect of increasing the total field. The analogue has an effective relative permeability of only three and a saturation magnetisation of about 60 mT at 40 K. At an applied field of 2.5 105 A/m (0.3 T) changing the temperature between 45 K and 70 K produces a change in magnetisation of approximately 3 104 A/m (38 mT). The greater this change the greater the amplitude of the magnetic pulse and the more effective the pump. For the experiment the Prussian Blue analogue was formed into a puck a picture of which is included in Fig. 5.
ð5Þ
The magnet itself is magnetised in the z direction and has 0 no transport current hence we use M ¼ and Mz Jz = 0, and therefore Eq. (1a) in the magnet subdomain is written as M z 1 r r Az þ ¼0 ð6Þ l0 lr 0 Finally the initial condition is to assume that Au is zero everywhere, then, based on the above coupled equations, the variable Au can be solved and from the solution obtain the flux density B as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7Þ B ¼ B2r þ B2z where Br ¼
oAu , oz
Bz ¼
Au r
þ
oAu . or
4. Experimental apparatus Fig. 3 shows a vertical cross-section through one half of a rotationally symmetric experimental test rig (the axis of symmetry is the left hand edge) which was designed so that the behaviour of each item could be tested both in isolation and in combination. The assembly is modular and enables measurements to be taken with and without the Prussian Blue, with and without the superconductor and with the Hall probes either adjacent to the superconductor or adjacent to the magnet. Note that the arrangement of Fig. 3 is not to scale. In the figure the arrows labelled A and B indicate the thermal path for the magnet and the Prussian Blue analogue. There is a small thermal leakage path between the superconductor and the Prussian Blue analogue which is provided by a fibre washer. The washer is used as a spacer to protect the Hall probe. The rig is in a vacuum chamber and there are gaps above and below the Prussian Blue and the magnet. The Prussian Blue analogue on which the bulk of the experimental work was performed was III NiII 1:5 ½Cr ðCNÞ6 . Results generated using this rig are shown in Figs. 4, 6 and 7. Fig. 4 shows the results with just the magnet present. Fig. 6 shows the results obtained with magnet, Prussian Blue analogue and superconductor present and Fig. 7 shows results with magnet and superconductor present. In each case the experimental technique used was to cycle the temperature using the cold head. The geometry of the rig may be varied by moving the top section, which is supported on Brass rods up and down as indicated by the double-headed arrow but the geometry was fixed throughout the course of each experiment. The Hall probe was a HHP-NP high sensitivity Hall probe sup-
5. Magnetic materials
TM
6. Experimental results Measurements were taken on two samples of YBCO. The first supplied by Dr. Hari Babu of the IRC in Superconductivity was a 13 mm circular sample and the second supplied by Superconducting Components Inc
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was a 23 mm hexagonal sample. Both samples were cut and polished prior to experimentation and a flux map was taken for each sample. Table 1 summarises the properties of each sample. Two samples were used to illustrate the point that the overall trapped field is a function of the superconductor rather than the applied field. Both samples were pumped identically, but the hexagonal sample having a higher saturation field produced a greater moment. Fig. 6 shows data taken using the 13 mm round superIII conducting section and with NiII 1:5 ½Cr ðCNÞ6 coupled with NdFeB. The results were measured using the apparatus described in Fig. 3. The results are plotted using the temperature of the top of the rig as a reference and the superconducting transition can be clearly seen in the top right of the figure showing that the superconductor was in the superconducting state throughout the experiment. Measurements were taken using two Hall probes one close to the centre line of the rig and the other offset from the centre-line. The arrows show the progression of the measurement which involves cooling then warming followed by cooling then warming. In Fig. 6 as the system is cooled the superconductor is being magnetised in the same sense as the applied field. As the system is cooled vortices are swept from the edge of the superconductor to the centre of the superconductor. The superconductor is being magnetised in the same sense as the applied magnetic field so this acts to reinforce the field and results in a reduction in the gradient which would have occurred had the superconductor not been present. As the system is warmed the direction of the pumping is reversed and the change in magnetisation of the superconductor is now in the opposite sense to the applied magnetic field. This results in a negative gradient and an overall reduction in the net magnetic field, despite the fact that at this point the overall applied magnetic field (due to warming of the magnet) is increasing. It is this change in sign of the gradient which provides firm evidence of pumping. In the absence of pumping the superconductor would change its magnetisation as the applied field changed but the overall effect would be a reduction in the rate of change of the total magnetic field and the total magnetic field would trend upwards not down. The temperature in Fig. 6 is not the temperature of the superconductor. The temperature represents the temperature of the Prussian Blue analogue and this is deliberately only weakly coupled thermally to the superconductor hence there is a large temperature difference between the measurement and the temperature of the superconductor. This is evident in the clear discontinuity in measured field which occurs at the point at which the superconductor reaches its critical temperature. On the trace this appears at about 180 K, however it shows that the superconductor was superconducting throughout the pumping sequence. Further measurements were taken having removed the Prussian Blue and therefore using NdFeB on its own to
generate the magnetic pulse. The experimental rig used is the same as that shown in Fig. 3 but the removal of the Prussian Blue analogue has allowed the magnet to be moved down, so that it is adjacent to the superconductor. The results are shown in Fig. 7. Fig. 7 is shown to illustrate that the total trapped field obtained is dependent on the superconductor rather than the magnetisation method. Three traces are shown. One for the 13 mm superconducting sample one for the 23 mm hexagonal superconducting sample and the final one shows the magnet behaviour on its own (i.e. with no superconductor present). In this figure the magnetisation of both samples as the rig is cooled can be clearly seen as a reduction in gradient. At the coldest point both of the superconductors have trapped large amounts of field. The small superconductor of the order of 120 mT and the large of the order of 200 mT. When the sample is warmed the direction of pumping reverses and as in Fig. 6 the gradient again changes sign as the superconductor is now being magnetised in the opposite sense by the pumping.
7. Conclusions This paper both describes and demonstrates a practical method of magnetising superconducting samples. A simple analytical model has been created demonstrating the physical basis for the flux pumping method which is to create regions of moving magnetic field using thermal excitation. This moving magnetic field sweeps vortices into the superconductor leaving the superconductor with a net magnetisation. A simple rig has been constructed and measurements taken which demonstrate the technique using an analogue of Prussian Blue and NdFeB. The measurements were taken using two different superconducting samples to demonstrate that the total trapped field is a function of the flux trapping abilities of the superconductor and is not limited by the magnetisation method. The measurements taken used samples of bulk YBCO but the method is generic and could be applied to a range of superconducting materials [6] e.g. BSCCO, MgB2 in a range of forms (e.g. thin and thick films). In addition because the method is applied to the surface of a superconductor multiple magnetisation fixtures may be used each of which can apply different numbers of pumps to different parts of the superconductor. This means that the magnetic field above the superconductor can be patterned and shaped.
References [1] Stefan Gruss, Giinter Fuchs, Gernot Krabbes, Peter Verges, Peter Schatzle, Karl-Hartmut Muller, Jorg Fink, Ludwig Schultz, IEEE Trans. Appl. Superconduct. 11 (I) (2001) 3720. [2] L.J.M. van de Klundert, H.H.J. ten Kate, Cryogenics 21 (1981) 195.
T. Coombs et al. / Physica C 468 (2008) 153–159 [3] Yong-Soo Yoon, Sang-Jin Lee, Ho-Min Kim, Tae Kuk Ko, IEEE Trans. Appl. Superconduct. 9 (4) (1999) 4708, 4714. [4] YoonDo Chung, Tsutomu Hoshino, Taketsune Nakamura, Current pumping performance of linear-type magnetic flux pump with use of feedback control circuit system, IEEE Trans. Appl. Superconduct. 16 (2) (2006) 1638–1641.
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[5] Toru Hara, Takashi Tanaka, Hideo Kitamura, Teruhiko Bizen, Xavier Mare´chal, Takamitsu Seike, Tsutomu Kohda, Yutaka Matsuura, Phys. Rev. ST Accel. Beam 7 (2004) 050702. [6] Timothy Arthur Coombs, superconducting systems, patent application number WO2007045929, 2007.
Physica C 468 (2008) 153–159 www.elsevier.com/locate/physc
A thermally actuated superconducting flux pump Timothy Coombs *, Zhiyong Hong, Xiaomin Zhu Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, United Kingdom Received 6 June 2007; received in revised form 5 October 2007; accepted 5 November 2007 Available online 21 November 2007
Abstract The concept of a superconducting flux pump is relatively straightforward. A small magnetic field repeatedly applied will lead to a much larger field being trapped within the superconductor. This field is limited by the volume of the superconductor and by its critical current but not by the excitation field. Here we will describe a new technique which facilitates the creation of high magnetic fields and where the magnitude of the trapped field is limited by the superconductor not the magnetising field. The technique is demonstrated using measurements taken using samples of bulk YBCO as YBCO has a very high irreversibility field and has the potential to trap high magnetic fields. The technique could be applied to other superconductors such as BSCCO or MgB2 and in other forms such as thin or thick films. Ó 2007 Elsevier B.V. All rights reserved. PACS: 94.20.Ws Keywords: Trapped fields; Flux pumps; Magnetism
1. Introduction High temperature superconductors have been under development for 20 years now and come in a variety of different forms of a large number of different materials. Of particular note are the YBCO bulks which using a melt seeded technique have been developed to the extent where 14.4 T can be trapped in the gap between a pair of 27 mm zinc doped samples at 22.5 K [1]. Mini-magnets of such strength have clear potential uses but these have been limited by the fact that a field of equal (when field cooled) or greater (when pulse magnetised) magnitude is required to magnetise them. This paper describes a practical method for achieving a flux pump and thereby obviating the need for a large magnetising field. Arrangements for flux pumps have been proposed before van Klundert et al. give an excellent review [2] in which they make clear that either you need *
Corresponding author. Tel.: +44 1223 748315. E-mail address: [email protected] (T. Coombs).
0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.11.003
mechanical or thermal superconducting switches, or a moving normal region which is smaller than the material in which it sits so that currents are shorted round it instead of going into the magnet circuit. Example systems based on these principles are described in [3,4]. The method described herein has two unique features. The first is that at no point is the superconductor driven normal we are simply making modifications to the critical state. The second is that the critical state is not modified by a moving magnet or an array of solenoids but by a thermal pulse which modifies the magnetisation of a magnetic material thus sweeping vortices into the material. The method described in this paper comprises automatically controlling a magnetic material to generate a pulse of magnetic flux travelling over a surface of said superconductor. Since the pulse can be repeatedly applied each pass stores incrementally more magnetic flux in the superconductor. The system may be employed for either magnetising or de-magnetising a superconductor, or for dynamically changing the magnetisation of a superconductor, depending
154
T. Coombs et al. / Physica C 468 (2008) 153–159
t=0.1s
t=0.2s
t=0.3s
t=0.4s
t=0.5s
t=0.6s
t=0.7s
t=0.8s
t=1.0s
t=1.1s
t=0.9s
reduced (or equivalently increased) permeability in the ordered material. The method relies on flux remaining trapped in the superconductor so that the fields applied are always below the irreversibility line. Figs. 1 and 2 are calculated analytically to illustrate the progression of the magnetic pulse. Fig. 3 depicts the test rig which was built, Figs. 4 and 5 are included to show the
t=1.2s
Fig. 1. Magnetic ordering of the switchable material at different time steps. In the figure a thermal pulse is shown travelling in from the right hand edge of a circularly symmetric puck of the switchable magnetic material. The figure shows the right hand half of the puck and the progression of the pulse with time, t.
upon whether the pulse of magnetic flux is applied to build up or decrease the magnetisation of the superconductor. When magnetising a superconductor the field is controlled so that after each sweep of magnetic flux over the surface of a superconductor flux is trapped within the superconductor, and in this way a very large field can be built up in a superconductor using multiple sweeps of a relatively small field. The field is controlled by changes in magnetisation or permeability. Soft magnetic materials such as analogues of Prussian Blue undergo a change in permeability and hard ones such as NdFeB undergo changes in magnetisation in response to changes in their temperatures. A thermal pulse can induce a thermal wave which travels through the body of the material and consequently a magnetic pulse which travels with the wave. The material which is being heated need not itself generate a substantial magnetic field and we will describe an implementation of the technique which relies upon concentration of an external or separately applied magnetic field locally in the superconductor by creating a region of
Fig. 3. Experimental rig. This rig is designed to replicate the conditions represented by Figs. 1 and 2. The rig is circularly symmetric and the right hand half is depicted. Thermal pulses as shown in Fig. 1 travel along the paths A and B which in turn drag magnetic flux across the superconductor as shown in Fig. 2. The rig may be operated with any or all of the superconductor, prussian blue and magnet in place and is adjustable vertically as represented by the double headed arrow.
Fig. 2. Distribution of current and flux density at different time steps in one cycle. This figure shows the same puck as in Fig. 1 above a superconducting puck. In this figure the effect of the thermal pulse depicted in Fig. 1 is shown as the movement of magnetic flux from right to left as represented by the flux lines. The time steps are the same as those for Fig. 1 and the effect on the superconductor is to induce currents in the shaded regions, the induced currents are flowing perpendicular to the surface shown.
T. Coombs et al. / Physica C 468 (2008) 153–159
155
Table 1 Specifications and results of trapped field measurements on YBCO samples in liquid nitrogen at 77 K
Fig. 4. Magnetisation versus temperature for NdFeB. NdFeB undergoes a reversible change in magnetisation with temperature as is shown here. The trace was measured using the experimental arrangement shown in Fig. 3 and with the superconductor and the Prussian blue removed.
temperature dependence of both the Prussian Blue analogue used and NdFeB. Table 1 is included to show the flux trapping ability of the superconducting samples used in the experiments and Figs. 6 and 7 show the results obtained using the rig depicted in Fig. 3. 2. Method If a heat pulse is applied to the edge of a body then that heat is transmitted through the body in the form of a ther-
Superconductor sample
Round
Hexagonal
Diameter (mm) Thickness (mm) Central field (mT) (0.5 T field cooling)
13 3.5 54
23 4 326
mal wave. That thermal wave may be used to control magnetisation in a hard magnetic material such as NdFeB, whose magnetisation decreases continuously below about 120 K, or permeability in a soft magnetic material such as one of the Prussian Blue analogues. There are a range of Prussian Blue analogues which become ferromagnetic at cryogenic temperatures and which are therefore ideal for being paired with superconductors. The passage of the thermal wave induces a magnetic pulse and after the passage of the thermal wave the body reverts to its original temperature and thus the NdFeB or Prussian blue return to their original state. Using this technique it is therefore possible to generate a series of unidirectional magnetic pulses which, according to Faraday’s law, will induce circulating currents in the superconductor which build up with each application and therefore magnetise the superconductor. Figs. 1 and 2 illustrate the process and were generated using the equation scheme given in the Analysis section below. Fig. 1 shows the progression of a thermal pulse across a circular puck of magnetisable material, there are many candidates for this material but results are presented III here for NiII 1:5 ½Cr ðCNÞ6 which is an analogue of Prussian
Squid measurements of Ni II [Cr III (CN ) ] 1.5 6 8.00E+04
20K
6.00E+04
40K 60K 4.00E+04
70K
M (A/m)
2.00E+04
100K -2.00E+06
-1.50E+06
-1.00E+06
0.00E+00 -5.00E+05 0.00E+00
5.00E+05
1.00E+06
1.50E+06
2.00E+06
-2.00E+04
-4.00E+04
-6.00E+04
-8.00E+04
H (A/m)
III Fig. 5. Squid measurement of ferromagnetic transition of NiII 1:5 ½Cr ðCNÞ6 . Five MH loops at various temperatures are plotted. These show the transition occurring between 100 K and 70 K and the magnetisation increasing with reducing temperature.
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T. Coombs et al. / Physica C 468 (2008) 153–159
Fig. 6. Results from 13 mm round sample. The arrows represent the order in which the sample was first cooled and then warmed and then cooled and then warmed and finally cooled again. With each cycle there is a further magnetisation of the superconductor.
equations to be solved to calculate the induced currents are: 1 rðAz þ MÞ ¼ J z ð1aÞ r l0 lr oAz ð1bÞ Ez ¼ ot Ez =qSc Superconductor subdomain Jz ¼ ð1cÞ Ez =qair Air subdomain where qair is a constant value and the nonlinear resistivity of the superconductor is defined using an EJ law as follows: 1=n
Fig. 7. Results from 13 mm round and 23 mm hexagonal samples using NdFeB as switching material. In this figure the Prussian blue has been removed and the magnet is adjacent to the superconductor. Removal of the Prussian blue has reduced the reluctance of the magnetic path leading to higher applied magnetic fields and greater net magnetisation per cycle of the superconductor.
Blue. The puck is a ring and the figure shows the right hand half in cross-section. In Fig. 2 the material depicted in Fig. 1 is shown above a superconducting disc. The figure clearly shows flux being drawn across the surface of the superconductor and the currents which are induced in the superconductor as a result. 3. Analysis A mathematical model can be constructed in order to analyse the arrangement described in Figs. 1 and 2. The
qSc ¼
E0 ðn1Þ=n jEz j þ q0 Jc
ð2Þ
This equation would lead to a singularity if the total resistivity was zero and therefore to avoid this occurring a small offset q0 (1e12 X) has been added. In the example given the problem is axially symmetric so if we examine the Laplacian in cyclindrical coordinates we obtain 1 o oAu o 2 Au 2 r r Au ¼ ð3Þ þ 2 r or or oz Substitute (3) into (1a) and noting that M in the superconductor is zero gives 1 1 o oAu o 2 Au r ð4Þ þ 2 ¼ Ju l0 lr r or or oz
T. Coombs et al. / Physica C 468 (2008) 153–159
157
In the problem there are three distinct regions, superconductor, air and magnet. All internal boundaries satisfy the Neumann boundary condition that is that Au is continuous across the boundary. The external boundary of the problem is defined by the Dirichlet boundary condition
plied by Arepoc limited and this Hall probe is calibrated for measurements over the entire thermal range presented.
Au ¼ 0
Fig. 4 shows how the magnetisation of the NdFeB magnet used in the rig varies with temperature. From these curves it can be seen that the change in field of the NdFeB is entirely reversible, as it was found that there was no net reduction in magnetisation when the magnet was returned to room temperature. This curve is in good experimental agreement with published data [5]. There is a small amount of hysteresis, so that the cooling and warming traces are slightly offset, this is evident from the increased thickness of the line at around 100 K. Thus thermal cycling of NdFeB can achieve the desired change in magnetic field which will magnetise the superconductor as it can be clearly seen from Fig. 4 that NdFeB’s magnetisation is rapidly changing, with temperature below the critical temperature of the YBCO and therefore thermal cycling of NdFeB can be used to pump flux into the superconductor. The manufacturing process for Prussian Blue analogues is an extremely simple precipitation reaction, Prussian Blue itself has a Curie point at around 5.6 K, but analogues have been created with a range of Curie points. They precipitate out from solution in powder form and tend to have poor thermal conductivity. One practical method of forming bulk structures is to use a metallic binder such as silver Dag , which also increases the thermal and electrical conductivity while not adversely affecting the packing factor and therefore the overall magnetic moment. Pucks formed using a silver Dag binder and a press were used in the experimental rig. Fig. 5 shows M–H loops for a Prussian Blue analogue, III NiII 1:5 ½Cr ðCNÞ6 at different temperatures, the measurements were taken using powder samples and the results have been corrected for the sample shape and size and therefore M is equivalent to magnetisation. When the applied field (horizontal axis) is constant reducing the temperature has the effect of increasing the total field. The analogue has an effective relative permeability of only three and a saturation magnetisation of about 60 mT at 40 K. At an applied field of 2.5 105 A/m (0.3 T) changing the temperature between 45 K and 70 K produces a change in magnetisation of approximately 3 104 A/m (38 mT). The greater this change the greater the amplitude of the magnetic pulse and the more effective the pump. For the experiment the Prussian Blue analogue was formed into a puck a picture of which is included in Fig. 5.
ð5Þ
The magnet itself is magnetised in the z direction and has 0 no transport current hence we use M ¼ and Mz Jz = 0, and therefore Eq. (1a) in the magnet subdomain is written as M z 1 r r Az þ ¼0 ð6Þ l0 lr 0 Finally the initial condition is to assume that Au is zero everywhere, then, based on the above coupled equations, the variable Au can be solved and from the solution obtain the flux density B as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7Þ B ¼ B2r þ B2z where Br ¼
oAu , oz
Bz ¼
Au r
þ
oAu . or
4. Experimental apparatus Fig. 3 shows a vertical cross-section through one half of a rotationally symmetric experimental test rig (the axis of symmetry is the left hand edge) which was designed so that the behaviour of each item could be tested both in isolation and in combination. The assembly is modular and enables measurements to be taken with and without the Prussian Blue, with and without the superconductor and with the Hall probes either adjacent to the superconductor or adjacent to the magnet. Note that the arrangement of Fig. 3 is not to scale. In the figure the arrows labelled A and B indicate the thermal path for the magnet and the Prussian Blue analogue. There is a small thermal leakage path between the superconductor and the Prussian Blue analogue which is provided by a fibre washer. The washer is used as a spacer to protect the Hall probe. The rig is in a vacuum chamber and there are gaps above and below the Prussian Blue and the magnet. The Prussian Blue analogue on which the bulk of the experimental work was performed was III NiII 1:5 ½Cr ðCNÞ6 . Results generated using this rig are shown in Figs. 4, 6 and 7. Fig. 4 shows the results with just the magnet present. Fig. 6 shows the results obtained with magnet, Prussian Blue analogue and superconductor present and Fig. 7 shows results with magnet and superconductor present. In each case the experimental technique used was to cycle the temperature using the cold head. The geometry of the rig may be varied by moving the top section, which is supported on Brass rods up and down as indicated by the double-headed arrow but the geometry was fixed throughout the course of each experiment. The Hall probe was a HHP-NP high sensitivity Hall probe sup-
5. Magnetic materials
TM
6. Experimental results Measurements were taken on two samples of YBCO. The first supplied by Dr. Hari Babu of the IRC in Superconductivity was a 13 mm circular sample and the second supplied by Superconducting Components Inc
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was a 23 mm hexagonal sample. Both samples were cut and polished prior to experimentation and a flux map was taken for each sample. Table 1 summarises the properties of each sample. Two samples were used to illustrate the point that the overall trapped field is a function of the superconductor rather than the applied field. Both samples were pumped identically, but the hexagonal sample having a higher saturation field produced a greater moment. Fig. 6 shows data taken using the 13 mm round superIII conducting section and with NiII 1:5 ½Cr ðCNÞ6 coupled with NdFeB. The results were measured using the apparatus described in Fig. 3. The results are plotted using the temperature of the top of the rig as a reference and the superconducting transition can be clearly seen in the top right of the figure showing that the superconductor was in the superconducting state throughout the experiment. Measurements were taken using two Hall probes one close to the centre line of the rig and the other offset from the centre-line. The arrows show the progression of the measurement which involves cooling then warming followed by cooling then warming. In Fig. 6 as the system is cooled the superconductor is being magnetised in the same sense as the applied field. As the system is cooled vortices are swept from the edge of the superconductor to the centre of the superconductor. The superconductor is being magnetised in the same sense as the applied magnetic field so this acts to reinforce the field and results in a reduction in the gradient which would have occurred had the superconductor not been present. As the system is warmed the direction of the pumping is reversed and the change in magnetisation of the superconductor is now in the opposite sense to the applied magnetic field. This results in a negative gradient and an overall reduction in the net magnetic field, despite the fact that at this point the overall applied magnetic field (due to warming of the magnet) is increasing. It is this change in sign of the gradient which provides firm evidence of pumping. In the absence of pumping the superconductor would change its magnetisation as the applied field changed but the overall effect would be a reduction in the rate of change of the total magnetic field and the total magnetic field would trend upwards not down. The temperature in Fig. 6 is not the temperature of the superconductor. The temperature represents the temperature of the Prussian Blue analogue and this is deliberately only weakly coupled thermally to the superconductor hence there is a large temperature difference between the measurement and the temperature of the superconductor. This is evident in the clear discontinuity in measured field which occurs at the point at which the superconductor reaches its critical temperature. On the trace this appears at about 180 K, however it shows that the superconductor was superconducting throughout the pumping sequence. Further measurements were taken having removed the Prussian Blue and therefore using NdFeB on its own to
generate the magnetic pulse. The experimental rig used is the same as that shown in Fig. 3 but the removal of the Prussian Blue analogue has allowed the magnet to be moved down, so that it is adjacent to the superconductor. The results are shown in Fig. 7. Fig. 7 is shown to illustrate that the total trapped field obtained is dependent on the superconductor rather than the magnetisation method. Three traces are shown. One for the 13 mm superconducting sample one for the 23 mm hexagonal superconducting sample and the final one shows the magnet behaviour on its own (i.e. with no superconductor present). In this figure the magnetisation of both samples as the rig is cooled can be clearly seen as a reduction in gradient. At the coldest point both of the superconductors have trapped large amounts of field. The small superconductor of the order of 120 mT and the large of the order of 200 mT. When the sample is warmed the direction of pumping reverses and as in Fig. 6 the gradient again changes sign as the superconductor is now being magnetised in the opposite sense by the pumping.
7. Conclusions This paper both describes and demonstrates a practical method of magnetising superconducting samples. A simple analytical model has been created demonstrating the physical basis for the flux pumping method which is to create regions of moving magnetic field using thermal excitation. This moving magnetic field sweeps vortices into the superconductor leaving the superconductor with a net magnetisation. A simple rig has been constructed and measurements taken which demonstrate the technique using an analogue of Prussian Blue and NdFeB. The measurements were taken using two different superconducting samples to demonstrate that the total trapped field is a function of the flux trapping abilities of the superconductor and is not limited by the magnetisation method. The measurements taken used samples of bulk YBCO but the method is generic and could be applied to a range of superconducting materials [6] e.g. BSCCO, MgB2 in a range of forms (e.g. thin and thick films). In addition because the method is applied to the surface of a superconductor multiple magnetisation fixtures may be used each of which can apply different numbers of pumps to different parts of the superconductor. This means that the magnetic field above the superconductor can be patterned and shaped.
References [1] Stefan Gruss, Giinter Fuchs, Gernot Krabbes, Peter Verges, Peter Schatzle, Karl-Hartmut Muller, Jorg Fink, Ludwig Schultz, IEEE Trans. Appl. Superconduct. 11 (I) (2001) 3720. [2] L.J.M. van de Klundert, H.H.J. ten Kate, Cryogenics 21 (1981) 195.
T. Coombs et al. / Physica C 468 (2008) 153–159 [3] Yong-Soo Yoon, Sang-Jin Lee, Ho-Min Kim, Tae Kuk Ko, IEEE Trans. Appl. Superconduct. 9 (4) (1999) 4708, 4714. [4] YoonDo Chung, Tsutomu Hoshino, Taketsune Nakamura, Current pumping performance of linear-type magnetic flux pump with use of feedback control circuit system, IEEE Trans. Appl. Superconduct. 16 (2) (2006) 1638–1641.
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[5] Toru Hara, Takashi Tanaka, Hideo Kitamura, Teruhiko Bizen, Xavier Mare´chal, Takamitsu Seike, Tsutomu Kohda, Yutaka Matsuura, Phys. Rev. ST Accel. Beam 7 (2004) 050702. [6] Timothy Arthur Coombs, superconducting systems, patent application number WO2007045929, 2007.