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Self Field Effect Compensation in an HTS TubeBruno Douine, Kévin Berger, Jean Lévêque, Denis Netter, Olivia Arbey,

Nancy Barthelet

To cite this version:Bruno Douine, Kévin Berger, Jean Lévêque, Denis Netter, Olivia Arbey, et al.. Self Field Effect Com-pensation in an HTS Tube. IEEE Transactions on Applied Superconductivity, Institute of Electricaland Electronics Engineers, 2008, 18 (3), pp. 1698-1703. <10.1109/TASC.2008.2000903>. <hal-00348415>

1698 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Self Field Effect Compensation in an HTS TubeBruno Douine, Kévin Berger, Jean Lévêque, Denis Netter, Olivia Arbey, and Nancy Barthelet

Abstract—It is well known that the critical current density ofa superconducting material depends on the magnetic flux density

. There exists an electric method to measure the ( ) deducedfrom the ( ) measurements. The problem with this method isthe self field effect because the magnetic flux density is always thesum of the applied magnetic flux density and the self magnetic fluxdensity. This paper presents a special experimental arrangement,compensating fully or partially the self magnetic flux density in anHTS tube. It allows characterizing the true zero magnetic flux den-sity behaviour of the superconducting material. The experimentalresults of the compensation are discussed. A theoretical analysisbased on Bean’s model is presented and gives results close to theexperimental ones. The proposed compensation is not perfect butthe experiments and the theoretical analysis allow validation of thecompensation principle.

Index Terms—Critical current density, self field effect, supercon-ductor.

I. INTRODUCTION

I T IS well known that the critical current density in a su-perconducting material depends on the magnetic flux den-

sity . The characteristic is very important to calculateAC losses in superconducting wires. Indeed, the evaluation ofthese losses is necessary for the design of the cooling system forany superconducting device. The superconducting power cablegeometry is similar to that of a tube [1], [2]. Despite the inho-mogeneous nature of power cables, the loss is often compared tothe monoblock model using average current densities and mag-netic flux density. For this reason it is important to know wellthe dependence of a tube.

Measurements of can be achieved by electrical trans-port (direct) [3] or magnetic (indirect) [4] methods. In this paper,the electrical method used to define the of a supercon-ducting tube is studied. Electrical transport measurements areachieved by the standard four-probe technique, which involvesinjecting a dc current in the superconducting tube and mea-suring the voltage drop [3]. Throughout this paper, the ex-tremity effects are neglected because the voltage taps are suf-ficiently distant from the tube extremities. The critical current

Manuscript received October 5, 2007; revised January 14, 2008, March 5,2008, and March 8, 2008. First published June 27, 2008; current version pub-lished September 4, 2008. This paper was recommended by Associate EditorJ. Willis.

B. Douine, J. Lévêque, D. Netter, O. Arbey, and N. Barthelet are with the Uni-versity of Nancy, Groupe de Recherche en Electrotechnique et Electronique deNancy, 54506 Vandoeuvre, France (e-mail: bruno.douine@green.uhp-nancy.fr;jean.leveque@green.uhp-nancy.fr; denis.netter@green.uhp-nancy.fr).

K. Berger is with the Grenoble Electrical Engineering Laboratory, 38042Grenoble, France (e-mail: Kevin.Berger@g2elab.inpg.fr).

Color versions of one or more of the figures in this paper are available athttp://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASC.2008.2000903

Fig. 1. Measured J (B ) for a BiSCCO tube at 77 K.

density can be deduced from the measurements thanksto the following hypotheses:

1) the distribution of the current density is uniform in the su-perconducting material section and so ;

2) the electric field has only one component along the tubeaxis and so ( is the distance between the voltagetaps).

In this case, one can deduce from . The value of thecritical current density depends on the measurementcriterion. This criterion corresponds to the critical electric field

that is often chosen as 1 V/cm. To theoretically calculate,for example, ac losses or magnetization, we can use Bean’s crit-ical state model that defines the relation between electric field

and current density as or .To obtain the experimental curve of , the tube was fed

with direct current and submitted to an external magnetic fluxdensity parallel to the axis [3]. The sample voltagedrop versus is measured for different external magnetic fluxdensities . From the measured critical currentcorresponding to the voltage drop equal to 1 V/cm L, we candeduce supposing complete currentpenetration. Fig. 1 shows the curve related to this function for aBiSCCO tube at 77 K.

and are different because:1) is a microscopic quantity and is a macro-

scopic quantity;2) is not equal to because of the self magnetic flux

density

and

When the value of is sufficiently large, becomesnegligible and the values of are very close to .When the value of is close to , can be verydifferent from .

1051-8223/$25.00 © 2008 IEEE

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DOUINE et al.: SELF FIELD EFFECT COMPENSATION IN AN HTS TUBE 1699

Fig. 2. Self magnetic field compensation setup and principle.

In this paper, a method of self field compensation in the elec-trical measurement method of for a superconductingtube is presented. This compensation allows one to make a linkbetween and . The principle of compensationis valid as long as the material is isotropic.

Some authors have already studied the self field effect in su-perconducting tapes and its compensation [5] but not in su-perconducting tubes. First, the principle of our compensationmethod and measurements are presented. Then, a theoreticalanalysis is proposed.

II. PRINCIPLE OF SELF MAGNETIC FIELD COMPENSATION

AND MEASUREMENTS

A. Self Magnetic Field Compensation Principle

Knowing that the self magnetic flux density in the tube is az-imuthal, one has to create another azimuthal magnetic flux den-

sity opposed to (Fig. 2). In this paper, we propose

to generate using another superconducting tube inside theone studied (Fig. 2). We choose a superconducting tube to min-imize the losses that would be generated by a copper tube. Theinternal tube is noted tube no. 1 and the studied one is noted tubeno. 2 (Fig. 2). The currents passing through tube no. 1 and tubeno. 2 are noted, respectively, and . To compensate the selffield effect, and have to be opposed (Fig. 2). Without anexternal magnetic field, the magnetic flux density in tube no. 2

is equal to . So if . It isa priori impossible to cancel everywhere in the tube sectionbut one can reduce the average

The reduction reduces the self field effect and increasesthe critical current for several magnetic fields as can be seen inthe next sections. One question remains: what is the value ofthat minimizes the self field effect in tube no. 2?

Fig. 3. Compensation experimental bench.

B. Experimental Setup

To perform the self field compensation, a special experi-mental setup (Fig. 3) was made.

The studied tube no. 2 consists of a hollow cylin-drical current lead. It is a compacted composite ofBi Pb Sr Ca Cu O with a critical temperature

of 108 K (CAN Superconductors). The section of thesuperconductor is about 30 mm ( 10%). The internaland external diameters of tube no. 2 are 8 and 10.1 mm. Theminimal critical current of tube no. 2, guaranteed by themanufacturer, is 80 A (at 77 K with the 1- V criterion). So theminimal critical current density is about 2.7 A/mm . Thecritical current of tube no. 1 is higher than because wewant to vary between 0 and above .

There are two independent current supplies, one for andanother for . A nanovoltmeter is used to measure the voltage

between the two taps of tube no. 2 (the external one) (Fig. 3).

C. Measurement Results and Discussions

To answer to the question at the end of Section II-A, six mea-surements are presented:

1) without external magnetic flux densityand without compensation (Fig. 4);

2) for several with to determine the currentthat minimizes (Fig. 5);

3) with and with compensation(Fig. 4);

4) with and without compensation(Fig. 6);

5) for several with to determine the currentthat minimizes (Figs. 7 and 8);

6) with and compensation(Fig. 9).

From the first curve (Fig. 4), the critical current withoutexternal magnetic field of tube no. 2 is deduced:

A. In a second step, several high values of (80, 82,85, and 87 A) are chosen around to have sufficient volt-ages for measurement. Then, for each value, a curveis determined (Fig. 5). One observes that the minimum of

is when is about . The determination of the exact

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1700 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Fig. 4. Measured U(I ) curve of tube no. 2 with and without compensation.

Fig. 5. Measured U(I ) curves for several I values.

Fig. 6. Measure of sample voltage drop versus direct current for different ex-ternal magnetic flux densities.

value of is difficult because the curve is flat aroundso we decided to perform the self field compensation

with . From the curve with

Fig. 7. Measured U(I ) curves for high different values of B and one valueof I each.

Fig. 8. Measured U(I ) curves for low different values of B and one valueof I each.

Fig. 9. Measured U(I ) curves of tube no. 2 with and without compensationfor B = 1:75 mT.

(Fig. 4), the compensated critical current without external mag-netic field of tube no. 2 is deduced: A.

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DOUINE et al.: SELF FIELD EFFECT COMPENSATION IN AN HTS TUBE 1701

Fig. 10. Measured J with and without self field compensation versus B .

Thanks to this partial self field effect compensation, the crit-ical current was increased by almost 5%. In a fourth step, thesample voltage drop is measured without compensation

for different external magnetic flux densities(Fig. 6) from a higher value than self field (70 mT) to a lowervalue (1.75 mT; the maximal self magnetic flux density of tubeno. 2 is about 4 mT for A). The curvewithout compensation is deduced (Fig. 1). For each value of

, we choose only one value of for one curveto have significant voltage (15 V V). Thereare two kinds of curves. If is significantly higherthan the self magnetic flux density (7 to 70 mT, Fig. 7), thecurve is flat and the compensation is not valid. For example,for mT and A, the self magnetic flux den-sity is about 1.4 mT and . If

is close to the self magnetic flux density (3.5 and 1.75 mT,Fig. 8), one still observes that the minimum of appearswhen is about . For example, for mT and

A, the self magnetic flux density is about 2.4 mT and. In the sixth step, the curve

(Fig. 9) with and for mT is presented.The compensated critical current with the external magneticfield of tube no. 2 is deduced: mT A.For mT, mT A. Finally,

curves with and without compensation are plotted(Fig. 10). In the low field regime, the superposition of externalmagnetic field with the self magnetic field has an influence on

, and the compensation permit to increase . Improve-ments made to are weak but this experiment validates thecompensation principle. In the high magnetic field regime, theself magnetic field has no influence on , and one can say that

.

III. THEORETICAL ANALYSIS

In this section, a theoretical analysis of the self field compen-sation is presented. We want to find the value of that max-imizes the critical current and so the critical current density

for . We choose because it is the bestcompensation case and it is the simplest calculation case. In-deed in this case, the current density is along the tube axis. On

Fig. 11. Reference frame and dimensions of the superconducting tube.

the other hand, if , the current density adopts a helicalpath around the tube.

The case of a superconducting tube fed by a dc current andexposed to an internal magnetic flux density is studied. Thedimensions of the tube (Fig. 11) are internal radius , externalradius , section , and length . The -axis is along the axisof the tube. The relation between the magnetic flux density andthe current density is governed by the Maxwell equation

(1)

By symmetry, the current density is oriented along theaxis. In addition , , and the current density in tubeno. 2 have only one component

The magnetic flux density in the superconducting material isthe sum of the different magnetic flux densities

The analytical calculation of the magnetic flux density andcurrent density distributions in the superconducting material isdifficult [3] because (1) with has to be solved.One can simplify calculation of these distributions with threehypotheses.

1) To calculate , is taken as a constant (Bean’smodel) and so

(2)

2) To calculate , a linear relation is chosen. and are con-

stants and depend on the superconducting material.3) The critical current and the full penetra-

tion current [3] are equal.With these hypotheses one can calculate as follows:

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1702 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Fig. 12. Critical current I of the studied superconducting tube versus I .

with and.

So maximizing is equivalent to minimizing .Equation (2) and allows one to calculate

The internal tube that creates is viewed as an infinite longwire and so

The relation is represented in Fig. 12 and we caneasily obtain from

We can apply this formula to our superconducting tube. Thecritical current without external magnetic field is Aand A/mm . One thus finds

A. This value is close to as it was shownin the experimental part. Despite the strong hypothesizes, the

calculation validates the experimental results.

IV. CONCLUSION

This paper presented the self field effect compensation in a su-perconducting tube for the measurements of the curve. Aspecial experimental arrangement allows results in an increase

in the measured critical current when the external magnetic fieldis close to the self field. It consists of placing another supercon-ducting tube inside the studied one. This second tube creates amagnetic field opposed to the self field to reduce the self fieldeffect. Several presented experiments show that the compensa-tion is real and allow determining the curve with com-pensation. This curve is slightly higher than the curve withoutcompensation. A theoretical analysis based on the Bean modeland some strong hypotheses are presented. For compensatingthe self field effects, experimental and theoretical results showthat the internal tube current must be equal to one half of thestudied tube current. The proposed compensation is not perfect,but the experiments and the theoretical analysis allow validatingthe compensation principle. Finally, this work opens the door toa further work: what new arrangement would allow for a bettercompensation of the self field inside the superconducting tube?This is an inverse problem that consists of finding the externalmagnetic field configuration which creates an azimuthal mag-netic field perfectly opposed to the self field of the studied tube.

REFERENCES

[1] F. Gomory and L. Gherardi, “Transport AC losses in round supercon-ducting wire consisting of two concentric shells with different criticalcurrent density,” Physica C, vol. 280, pp. 151–157, 1997.

[2] M. Daumling, “AC loss in two ac carrying superconducting concentrictubes—The duo block model,” Physica C, vol. 403, pp. 57–59, 2004.

[3] B. Douine, K. Berger, J. Leveque, D. Netter, and A. Rezzoug, “Influ-ence of Jc(B) on the full penetration current of superconducting tube,”Physica C, vol. 443, pp. 23–28, 2006.

[4] P. Vanderbemden, “Determination of Critical Current in Bulk HighTemperature Superconductors by Magnetic Flux Profile MeasuringMethods,” Ph. D. Thesis, Univ. of Liège, Liège, Belgium, 1999.

[5] S. Spreafico, L. Gherardi, S. Fleshler, D. Tatelbaum, J. Leone, D. Yu,and G. Snitchler, “The effect of self field on current capacity in Bi-2223composite strands,” IEEE Trans. Appl. Supercond., vol. 9, no. 2, pp.2159–2162, Jun. 1999.

Bruno Douine was born in Montereau, France, in1966. He received the Ph. D. degree in electrical en-gineering from the University of Nancy, France, in2001.

He is currently a Lecturer at the University ofNancy. As a member of the Groupe de Rechercheen Electrotechnique et Electronique de Nancy, hismain subjects of research concern characterizationand modelization of superconducting material.

Kévin Berger was born in Montbéliard, France,on January, 16, 1980. He received the Ph.D. degreein electrical engineering from Université HenriPoincaré, Nancy, France, in 2006.

He then joined the Grenoble Electrical Engi-neering Laboratory (G2Elab) and the Néel Institut,Grenoble in 2006 as a post-doctoral researcher inorder to work on superconductor modeling usingFLUX software and a conduction cooled SMES. Hisresearch interests deal with the design and modelingof superconducting devices like cryomagnets while

taking into account coupled magneto-thermal behavior. His research topicsalso include electrical characterization of superconducting material and ACloss measurements.

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DOUINE et al.: SELF FIELD EFFECT COMPENSATION IN AN HTS TUBE 1703

Jean Lévêque was born in Angers, France, in 1963.He received the Ph. D. degree in electrical engi-neering from the University of Grenoble, France, in1993.

He is currently Professor at the University ofNancy, France. As a member of the Groupe deRecherche en Electrotechnique et Electronique deNancy, his main subjects of research concern char-acterization and modelization of superconductingmaterial and applications.

Denis Netter was born in Auchel, France, in 1969.He received the Ph. D. degree in electrical engi-neering from the University of Nancy, France, in1997.

He is currently a Lecturer at the University ofNancy. As a member of the Groupe de Recherche enElectrotechnique et Electronique de Nancy, his mainsubjects of research concern superconducting appli-cations and stochastic methods to calculate nonlineardiffusion of the magnetic field in superconductingmaterial.

Olivia Arbey was born in France, in 1984. Shereceived the M.S. and Engineering degrees fromENSEM Institut National Polytechnique de Lorraine(INPL) in 2007. She is currently working towardthe Ph. D. degree at FEMTO Institute at Besançon,France.

Nancy Barthelet was born in France, in 1982. Shereceived the M.S. and Engineering degrees fromENSEM Institut National Polytechnique de Lorraine(INPL) in 2007.

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