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Physica C 468 (2008) 153–159

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 2007Available online 21 November 2007

Abstract

The concept of a superconducting flux pump is relatively straightforward. A small magnetic field repeatedly applied will lead to amuch larger field being trapped within the superconductor. This field is limited by the volume of the superconductor and by its criticalcurrent 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 trappedfield is limited by the superconductor not the magnetising field. The technique is demonstrated using measurements taken using samplesof bulk YBCO as YBCO has a very high irreversibility field and has the potential to trap high magnetic fields. The technique could beapplied to other superconductors such as BSCCO or MgB2 and in other forms such as thin or thick films.� 2007 Elsevier B.V. All rights reserved.

PACS: 94.20.Ws

Keywords: Trapped fields; Flux pumps; Magnetism

1. Introduction

High temperature superconductors have been underdevelopment for 20 years now and come in a variety of dif-ferent forms of a large number of different materials. Ofparticular note are the YBCO bulks which using a meltseeded technique have been developed to the extent where14.4 T can be trapped in the gap between a pair of 27 mmzinc doped samples at 22.5 K [1].

Mini-magnets of such strength have clear potential usesbut 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 aflux pump and thereby obviating the need for a largemagnetising field. Arrangements for flux pumps have beenproposed before van Klundert et al. give an excellentreview [2] in which they make clear that either you need

0921-4534/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.physc.2007.11.003

* Corresponding author. Tel.: +44 1223 748315.E-mail address: tac1000@cam.ac.uk (T. Coombs).

mechanical or thermal superconducting switches, or a mov-ing normal region which is smaller than the material inwhich it sits so that currents are shorted round it insteadof going into the magnet circuit. Example systems basedon 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 drivennormal we are simply making modifications to the criticalstate. The second is that the critical state is not modifiedby a moving magnet or an array of solenoids but by a ther-mal pulse which modifies the magnetisation of a magneticmaterial thus sweeping vortices into the material.

The method described in this paper comprises automat-ically controlling a magnetic material to generate a pulse ofmagnetic flux travelling over a surface of said superconduc-tor. Since the pulse can be repeatedly applied each passstores incrementally more magnetic flux in thesuperconductor.

The system may be employed for either magnetising orde-magnetising a superconductor, or for dynamicallychanging the magnetisation of a superconductor, depending

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=0.9s

t=1.0s t=1.1s t=1.2s

Fig. 1. Magnetic ordering of the switchable material at different timesteps. In the figure a thermal pulse is shown travelling in from the righthand edge of a circularly symmetric puck of the switchable magneticmaterial. The figure shows the right hand half of the puck and theprogression of the pulse with time, t.

Fig. 3. Experimental rig. This rig is designed to replicate the conditionsrepresented by Figs. 1 and 2. The rig is circularly symmetric and the righthand half is depicted. Thermal pulses as shown in Fig. 1 travel along thepaths A and B which in turn drag magnetic flux across the superconductoras shown in Fig. 2. The rig may be operated with any or all of thesuperconductor, prussian blue and magnet in place and is adjustablevertically as represented by the double headed arrow.

154 T. Coombs et al. / Physica C 468 (2008) 153–159

upon whether the pulse of magnetic flux is applied to buildup or decrease the magnetisation of the superconductor.When magnetising a superconductor the field is controlledso that after each sweep of magnetic flux over the surface ofa superconductor flux is trapped within the superconduc-tor, and in this way a very large field can be built up in asuperconductor using multiple sweeps of a relatively smallfield.

The field is controlled by changes in magnetisation orpermeability. Soft magnetic materials such as analoguesof Prussian Blue undergo a change in permeability andhard ones such as NdFeB undergo changes in magnetisa-tion in response to changes in their temperatures. A ther-mal pulse can induce a thermal wave which travelsthrough the body of the material and consequently a mag-netic pulse which travels with the wave.

The material which is being heated need not itself gener-ate a substantial magnetic field and we will describe animplementation of the technique which relies upon concen-tration of an external or separately applied magnetic fieldlocally in the superconductor by creating a region of

Fig. 2. Distribution of current and flux density at different time steps in one cypuck. In this figure the effect of the thermal pulse depicted in Fig. 1 is shown aslines. The time steps are the same as those for Fig. 1 and the effect on the superare flowing perpendicular to the surface shown.

reduced (or equivalently increased) permeability in theordered material.

The method relies on flux remaining trapped in thesuperconductor so that the fields applied are always belowthe irreversibility line.

Figs. 1 and 2 are calculated analytically to illustrate theprogression of the magnetic pulse. Fig. 3 depicts the test rigwhich was built, Figs. 4 and 5 are included to show the

cle. This figure shows the same puck as in Fig. 1 above a superconductingthe movement of magnetic flux from right to left as represented by the fluxconductor is to induce currents in the shaded regions, the induced currents

Fig. 4. Magnetisation versus temperature for NdFeB. NdFeB undergoes areversible change in magnetisation with temperature as is shown here. Thetrace was measured using the experimental arrangement shown in Fig. 3and with the superconductor and the Prussian blue removed.

Table 1Specifications and results of trapped field measurements on YBCOsamples in liquid nitrogen at 77 K

Superconductor sample Round Hexagonal

Diameter (mm) 13 23Thickness (mm) 3.5 4Central field (mT) (0.5 T field cooling) 54 326

T. Coombs et al. / Physica C 468 (2008) 153–159 155

temperature dependence of both the Prussian Blue ana-logue used and NdFeB. Table 1 is included to show the fluxtrapping ability of the superconducting samples used in theexperiments and Figs. 6 and 7 show the results obtainedusing the rig depicted in Fig. 3.

2. Method

If a heat pulse is applied to the edge of a body then thatheat is transmitted through the body in the form of a ther-

Squid measurements of

-8.00E+04

-6.00E+04

-4.00E+04

-2.00E+04

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

-2.00E+06 -1.50E+06 -1.00E+06 -5.00E+05 0.00E+0

H (A/m

M (A

/m)

Fig. 5. Squid measurement of ferromagnetic transition of NiII1:5½CrIIIðCNÞ6�. Fiv

occurring between 100 K and 70 K and the magnetisation increasing with red

mal wave. That thermal wave may be used to control mag-netisation in a hard magnetic material such as NdFeB,whose magnetisation decreases continuously below about120 K, or permeability in a soft magnetic material suchas one of the Prussian Blue analogues. There are a rangeof Prussian Blue analogues which become ferromagneticat cryogenic temperatures and which are therefore idealfor being paired with superconductors. The passage ofthe thermal wave induces a magnetic pulse and after thepassage of the thermal wave the body reverts to its originaltemperature and thus the NdFeB or Prussian blue return totheir original state. Using this technique it is therefore pos-sible to generate a series of unidirectional magnetic pulseswhich, according to Faraday’s law, will induce circulatingcurrents in the superconductor which build up with eachapplication and therefore magnetise the superconductor.Figs. 1 and 2 illustrate the process and were generatedusing the equation scheme given in the Analysis sectionbelow. Fig. 1 shows the progression of a thermal pulseacross a circular puck of magnetisable material, there aremany candidates for this material but results are presentedhere for NiII

1:5½CrIIIðCNÞ6� which is an analogue of Prussian

0 5.00E+05 1.00E+06 1.50E+06 2.00E+06

)

100K

70K

20K

40K

60K

1.5 6[ ( ) ]II IIINi Cr CN

e MH loops at various temperatures are plotted. These show the transitionucing temperature.

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 thenwarmed and finally cooled again. With each cycle there is a further magnetisation of the superconductor.

Fig. 7. Results from 13 mm round and 23 mm hexagonal samples usingNdFeB as switching material. In this figure the Prussian blue has beenremoved and the magnet is adjacent to the superconductor. Removal ofthe Prussian blue has reduced the reluctance of the magnetic path leadingto higher applied magnetic fields and greater net magnetisation per cycleof the superconductor.

156 T. Coombs et al. / Physica C 468 (2008) 153–159

Blue. The puck is a ring and the figure shows the right handhalf in cross-section. In Fig. 2 the material depicted inFig. 1 is shown above a superconducting disc. The figureclearly shows flux being drawn across the surface of thesuperconductor and the currents which are induced in thesuperconductor as a result.

3. Analysis

A mathematical model can be constructed in order toanalyse the arrangement described in Figs. 1 and 2. The

equations to be solved to calculate the induced currentsare:

r � � 1

l0lrrðAz þMÞ

� �¼ J z ð1aÞ

Ez ¼ �oAz

otð1bÞ

J z ¼Ez=qSc Superconductor� subdomain

Ez=qair Air subdomain

�ð1cÞ

where qair is a constant value and the nonlinear resistivityof the superconductor is defined using an E�J law asfollows:

qSc ¼E1=n

0

JcjEzjðn�1Þ=n þ q0 ð2Þ

This equation would lead to a singularity if the total resis-tivity was zero and therefore to avoid this occurring a smalloffset q0 (1e�12 X) has been added. In the example giventhe problem is axially symmetric so if we examine theLaplacian in cyclindrical coordinates we obtain

r2Au ¼1

ro

orroAu

or

� �þ o2Au

o2zð3Þ

Substitute (3) into (1a) and noting that M in the supercon-ductor is zero gives

� 1

l0lr

1

ro

orroAu

or

� �þ o2Au

o2z

� �¼ Ju ð4Þ

T. Coombs et al. / Physica C 468 (2008) 153–159 157

In the problem there are three distinct regions, super-conductor, air and magnet. All internal boundaries satisfythe Neumann boundary condition that is that Au is contin-uous across the boundary. The external boundary of theproblem is defined by the Dirichlet boundary condition

Au ¼ 0 ð5Þ

The magnet itself is magnetised in the z direction and has

no transport current hence we use M ¼ 0Mz

� �and

Jz = 0, and therefore Eq. (1a) in the magnet subdomainis written as

r � � 1

l0lr

r Az þ�Mz

0

� �� �� �¼ 0 ð6Þ

Finally the initial condition is to assume that Au is zeroeverywhere, then, based on the above coupled equations,the variable Au can be solved and from the solution obtainthe flux density B as

B ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2

r þ B2z

qð7Þ

where Br ¼ � oAu

oz , Bz ¼ Au

r þoAu

or .

4. Experimental apparatus

Fig. 3 shows a vertical cross-section through one half ofa rotationally symmetric experimental test rig (the axis ofsymmetry is the left hand edge) which was designed so thatthe behaviour of each item could be tested both in isolationand in combination. The assembly is modular and enablesmeasurements to be taken with and without the PrussianBlue, with and without the superconductor and with theHall probes either adjacent to the superconductor or adja-cent to the magnet. Note that the arrangement of Fig. 3 isnot to scale.

In the figure the arrows labelled A and B indicate thethermal path for the magnet and the Prussian Blue ana-logue. There is a small thermal leakage path between thesuperconductor and the Prussian Blue analogue which isprovided by a fibre washer. The washer is used as a spacerto protect the Hall probe. The rig is in a vacuum chamberand there are gaps above and below the Prussian Blueand the magnet. The Prussian Blue analogue on whichthe bulk of the experimental work was performed wasNiII

1:5½CrIIIðCNÞ6�. Results generated using this rig areshown in Figs. 4, 6 and 7. Fig. 4 shows the results with justthe magnet present. Fig. 6 shows the results obtained withmagnet, Prussian Blue analogue and superconductor pres-ent and Fig. 7 shows results with magnet and superconduc-tor present. In each case the experimental technique usedwas to cycle the temperature using the cold head. Thegeometry of the rig may be varied by moving the top sec-tion, which is supported on Brass rods up and down asindicated by the double-headed arrow but the geometrywas fixed throughout the course of each experiment. TheHall probe was a HHP-NP high sensitivity Hall probe sup-

plied by Arepoc limited and this Hall probe is calibratedfor measurements over the entire thermal range presented.

5. Magnetic materials

Fig. 4 shows how the magnetisation of the NdFeB mag-net used in the rig varies with temperature. From thesecurves it can be seen that the change in field of the NdFeBis entirely reversible, as it was found that there was no netreduction in magnetisation when the magnet was returnedto room temperature. This curve is in good experimentalagreement with published data [5]. There is a small amountof hysteresis, so that the cooling and warming traces areslightly offset, this is evident from the increased thicknessof the line at around 100 K. Thus thermal cycling ofNdFeB can achieve the desired change in magnetic fieldwhich will magnetise the superconductor as it can beclearly seen from Fig. 4 that NdFeB’s magnetisation israpidly changing, with temperature below the criticaltemperature of the YBCO and therefore thermal cyclingof NdFeB can be used to pump flux into the super-conductor.

The manufacturing process for Prussian Blue analoguesis an extremely simple precipitation reaction, Prussian Blueitself has a Curie point at around 5.6 K, but analogues havebeen created with a range of Curie points. They precipitateout from solution in powder form and tend to have poorthermal conductivity. One practical method of formingbulk structures is to use a metallic binder such as silverDagTM, which also increases the thermal and electrical con-ductivity while not adversely affecting the packing factorand therefore the overall magnetic moment. Pucks formedusing a silver Dag binder and a press were used in theexperimental rig.

Fig. 5 shows M–H loops for a Prussian Blue analogue,NiII

1:5½CrIIIðCNÞ6� at different temperatures, the measure-ments were taken using powder samples and the resultshave been corrected for the sample shape and size andtherefore M is equivalent to magnetisation. When theapplied field (horizontal axis) is constant reducing the tem-perature has the effect of increasing the total field. The ana-logue has an effective relative permeability of only threeand a saturation magnetisation of about 60 mT at 40 K.At an applied field of 2.5 � 105 A/m (0.3 T) changing thetemperature between 45 K and 70 K produces a changein magnetisation of approximately 3 � 104 A/m (38 mT).The greater this change the greater the amplitude of themagnetic pulse and the more effective the pump.

For the experiment the Prussian Blue analogue wasformed into a puck a picture of which is included in Fig. 5.

6. Experimental results

Measurements were taken on two samples of YBCO.The first supplied by Dr. Hari Babu of the IRC inSuperconductivity was a 13 mm circular sample and thesecond supplied by Superconducting Components Inc

158 T. Coombs et al. / Physica C 468 (2008) 153–159

was a 23 mm hexagonal sample. Both samples were cutand polished prior to experimentation and a flux mapwas taken for each sample. Table 1 summarises the prop-erties of each sample. Two samples were used to illustratethe point that the overall trapped field is a function of thesuperconductor rather than the applied field. Both sam-ples were pumped identically, but the hexagonal samplehaving a higher saturation field produced a greatermoment.

Fig. 6 shows data taken using the 13 mm round super-conducting section and with NiII

1:5½CrIIIðCNÞ6� coupled withNdFeB. The results were measured using the apparatusdescribed in Fig. 3. The results are plotted using the tem-perature of the top of the rig as a reference and the super-conducting transition can be clearly seen in the top right ofthe figure showing that the superconductor was in thesuperconducting state throughout the experiment.

Measurements were taken using two Hall probes oneclose to the centre line of the rig and the other offset fromthe centre-line. The arrows show the progression of themeasurement which involves cooling then warming fol-lowed by cooling then warming.

In Fig. 6 as the system is cooled the superconductor isbeing magnetised in the same sense as the applied field.As the system is cooled vortices are swept from the edgeof the superconductor to the centre of the superconductor.The superconductor is being magnetised in the same senseas the applied magnetic field so this acts to reinforce thefield and results in a reduction in the gradient which wouldhave occurred had the superconductor not been present. Asthe system is warmed the direction of the pumping isreversed and the change in magnetisation of the supercon-ductor is now in the opposite sense to the applied magneticfield. This results in a negative gradient and an overallreduction in the net magnetic field, despite the fact thatat this point the overall applied magnetic field (due towarming of the magnet) is increasing. It is this change insign of the gradient which provides firm evidence of pump-ing. In the absence of pumping the superconductor wouldchange its magnetisation as the applied field changed butthe overall effect would be a reduction in the rate of changeof the total magnetic field and the total magnetic fieldwould trend upwards not down.

The temperature in Fig. 6 is not the temperature of thesuperconductor. The temperature represents the tempera-ture of the Prussian Blue analogue and this is deliberatelyonly weakly coupled thermally to the superconductorhence there is a large temperature difference between themeasurement and the temperature of the superconductor.This is evident in the clear discontinuity in measured fieldwhich occurs at the point at which the superconductorreaches its critical temperature. On the trace this appearsat about 180 K, however it shows that the superconductorwas superconducting throughout the pumping sequence.

Further measurements were taken having removed thePrussian Blue and therefore using NdFeB on its own to

generate the magnetic pulse. The experimental rig used isthe same as that shown in Fig. 3 but the removal of thePrussian Blue analogue has allowed the magnet to bemoved down, so that it is adjacent to the superconductor.The results are shown in Fig. 7. Fig. 7 is shown to illustratethat the total trapped field obtained is dependent on thesuperconductor rather than the magnetisation method.Three traces are shown. One for the 13 mm superconduc-ting sample one for the 23 mm hexagonal superconductingsample and the final one shows the magnet behaviour on itsown (i.e. with no superconductor present). In this figure themagnetisation of both samples as the rig is cooled can beclearly seen as a reduction in gradient. At the coldest pointboth of the superconductors have trapped large amounts offield. The small superconductor of the order of 120 mT andthe large of the order of 200 mT. When the sample iswarmed the direction of pumping reverses and as inFig. 6 the gradient again changes sign as the superconduc-tor is now being magnetised in the opposite sense by thepumping.

7. Conclusions

This paper both describes and demonstrates a practicalmethod of magnetising superconducting samples. A simpleanalytical model has been created demonstrating the phys-ical basis for the flux pumping method which is to createregions of moving magnetic field using thermal excitation.This moving magnetic field sweeps vortices into the super-conductor leaving the superconductor with a net magneti-sation. A simple rig has been constructed andmeasurements taken which demonstrate the techniqueusing an analogue of Prussian Blue and NdFeB. The mea-surements were taken using two different superconductingsamples to demonstrate that the total trapped field is afunction of the flux trapping abilities of the superconductorand is not limited by the magnetisation method. The mea-surements taken used samples of bulk YBCO but themethod is generic and could be applied to a range of super-conducting materials [6] e.g. BSCCO, MgB2 in a range offorms (e.g. thin and thick films).

In addition because the method is applied to the surfaceof a superconductor multiple magnetisation fixtures maybe used each of which can apply different numbers ofpumps to different parts of the superconductor. This meansthat the magnetic field above the superconductor can bepatterned and shaped.

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