AC losses in multifilamentary Nb3Sn conductors

September 30, 2017 | Autor: Paul Sikora | Categoría: Engineering, Physical sciences
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IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-15, NO. 1, JANUARY 1979

260

AC LOSSES iN MULTIFILAMENTARY Nb3Sn COhIXJCTORS J.P.

Charlesworth"and

ABSTRACT We h a v e s t u d i e d l o s s e s a t 4.2K i n a number of multifilamentary Nb and NrgSn w i r e s f a b r i c a t e d by t h e bronzeroute.Lossesdue t oa l t e r n a t i n gc u r r e n t and t o t r a n s v e r s e a l t e r n a t i n g f i e l d showed a f o u r t h power depencianceon c u r r e n t o r f i e l d w'lich i s incompatible withthecriticalstate model,even when theobserved f i e l d dependenceof t h e b u l k c r i t i c a l - c u r r e n t d e n s i t y i s t a k e ni n t oa c c o u n t . Inordertorevealthesourceofthe low l o s s e s i n o u r m a t e r i a l s more c l e a r l y , we have s t u d i e d l o s s e s w i t h t h ef i e l dp a r a l l e lt ot h ef i l a m e n ts u r f a c e . As e x p e c t e d ,t h er e s u l t s show t h a t l o s s e s i n Nb f i l a m e n t s a r e low because of the presence of the Meissner state. However, s u p e r f i c i a l l y s i m i l a r r e s u l t s f o r Nb3Sn f i l a m e n t sc a n n o tb ei n t e r p r e t e da se v i d e n c ef o ra n anomalous l o w e rc r i t i c a lf i e l d ; a more l i k e l y explanation i s the presence of a surfacecurrent. Although a s i m p l e s u r f a c e c u r r e n t model cannotaccount indetailforthetransversefieldlosses, one i n c o r p o r a t i n g l o s s e s due t o s u r f a c e r o u g h n e s s , f i e l d o r i e n t a t i o n e f f e c t s and t h e f i e l d dependence of t h e surface current can probably provide an adequate description.

P.T.

Sikora+

t h e method Of Salmon and Catteral17, modified by t h e useof a lock-inamplifier,insteadof a multiplier, takingthephasereference from a l i q u i d n i t r o g e n c o o l e dm u t u a li n d u c t o ri nt h es a m p l ec u r r e n tc i r c u i t . The sampleswere b i f i l a r c o i l s , 25mm d i a . by 5Om long. Alternatingfieldlosses Losses iri a l t e r n a t i n j f i e l d weremeasured by t h e method of G r i f f i t h s e t a1 F o rt r a n s v e r s ef i e l d measurements, t h e samplesweresingle-layer,closewol:rd, o p e n - c i r c u i t c o i l s , 4mm d i a . by 20mm long,while forlongitudinalfield measurements 34 p i e c e s 25mm long wereused.

.

B i a sf i e l d s

A superconducting solenoid wound from mf NbTi wire couldbeusedtoSupply a steady bias field in both the abovetypesofmeasurement. The l a r g eb o r e of t h i s s o l e n o i d e n s u r e d t h a t it was onlyweaklycoupled to the sample c i r c u i t ; a d i r e c t comparisonof r e s u l t sf o r zerobiasfieldwithandwithoutthesolenoid showed t h a t e r r o r s a r i s i n g from t h i s c o u p l i n g were d e t e c t a b l e only a t t h e l o w e s t loss l e v e l s , i n s i g n i f i c a n t f o r t h e arguments present here.

INTRODUCTION

Therehavebeenseveralreports'' *' t h a ta c l o s s e s i n NbsSn f a l l , a t low f i e l d s , below those e x p e c t e df r o mt h ec r i t i c a ls t a t e model. Most o ft h e s e r e p o r t s haveconcerned c y l i n d r i c a l samples o r t a p e materialandthe low l o s s e s have u s u a l l y b e e n a t t r i b u t e dt ot h ep r e s e n c eo f a surfacecurrent,orsurface p i n n i n gr e g i o n ,s c r e e n i n gt h ei n t e r i o r from f l u x penetration" a l t h o u g h i n one casenon-uniform flux p e n e t r a t i o n was proposed'.Therehas a l s o been a suggestionthatthelowercriticalfield HC1 o f NbsSn couldbehigherthanthegenerallyacceptedvalue5. We h a v e p r e v i o u s l y r e p o r t e d r e s u l t s on multifilamentary (mf) Nb3Sn6 without coming t o a c l e a r c o n c l u s i o na st ot h ec a u s eo ft h ed e p a r t u r e from c r i t i c a l s t a t e model behaviour. One o t h e rs t u d yo f mf Nb3Sn4 gave a dependenceof l o s s on c u r r e n t s i m i l a r t o oursbutcoveredonly a smallrangeofcurrent.These authorsalsoproposed a s u r f a c e c u r r e n t on t h e b a s i s ofthetemperaturedependenceofthelosses. We have now extendedour work by t h e a d d i t i o n o f l o s s measurem e n t sw i t ht h ef i e l dp a r a l l e lt ot h ef i l a m e n ta x i s , a c o n f i g u r a t i o n which should more c l e a r l y r e v e a l s u r f a c e effects or the influence oftheXeissnerstate. Forconvenience, we have g e n e r a l l y r e p o r t e d m a g n e t i cf i e l dv a l u e si nu n i t so f poH ( T e s l a )r a t h e r than H (amp m- )

',

.

Magnetisationmeasurements Swept-field magnetisation loops were obtained on t h e same s m a l l c o i l samplesused fortransversefield l o s s e s ,u s i n gt h ee l e c t r o n i ci n t e g r a t i o nt e c h n i q u e g , the results being analysed by t h e method of F i e t z and Webb" The samplesreported on here showed no r a t e dependence.

.

Descriptionofsamples The samples were made from w i r e , f a b r i c a t e d by t h e bronzeroute a t AERE Harwell,containing1369,3145,or 6031 filaments,occupying 20-25% ofthe volume i n a Cu-7.7at.%Snmatrix. On completionofmechanical f a b r i c a t i o n( u n r e a c t e dw i r e )t h ef i l a m e n t s were Nb, and weresubsequentlyconverted t o NbsSnby h e a t t r e a t m e n t a t 6OO0C t o 75OoC ( r e a c t e d w i r e ) . For some samples,degreeofreaction was measured by f i n d i n g t h e volume ofsuperconductorexcludingflux a t t h el o w e s tp r a c t i c a b l ef i e l da m p l i t u d e . Comparison withanunreactedsamplegavetheexpansion due t o r e a c t i o n , from which t h e d e q r e e o f r e a c t i o n c o u l d be estimated,assuming 38% e x p a n s i o nf o rf u l lr e a c t i o n . Longitudinalfieldsamples were 0.495mm d i a . and were n o tt w i s t e d ; a l l othersamples were t w i s t e d a t a p i t c h o f 6.5mm, beingreduced t o 0.43mm d i a . i n t h e process.

EXPERIMENTAL METHODS RESULTS A l l loss measurementswere

c a r r i e d o u t a t 4.2K. Most of the data reproduced herewere obtained at a frequencyof 10Hz buthigherfrequencymeasurements were a l s o made t o e s t a b l i s h t h a t t h e l o s s e s o b s e r v e d were h y s t e r e t i c . Alternating current

losses

Losses due t o a l t e r n a t i n g c u r r e n t ManuscriptreceivedSeptember28,

* AERE, +

Alternatingcurrent losses

Harwell,Didcot,

weremeasured

1978.

Oxon., OX11 ORA, UK.

UniversityCollege,Cork,Ireland.

by

and t r a n s v e r s e a l t e r n a t i n g f i e l d

H y s t e r e t i c l o s s e s i n t h e s e m a t e r i a l s , due t o a l t e r n a t i n g c u r r e n t I , a r e w e l l described by a power-law c u r r e n t dependenceof t h e form I n , where theexponent n l i e si nt h er a n g e 3.8 t o4 . 3 ;t h e good f i t extendsover a widerangeofcurrentforboth Nb and Nb3Sn ( F i g . 1 ) . Losses i n t r a n s v e r s e a l t e r n a t i n g f i e l d a l s o show a correspondingdependenceoftheform hnon peak a l t e r n a t i n g f i e l d h;with a similarrangeof n ( F i g . 2 ) , again common t o b o t h N b and NbsSn. This roughly fourth power dependencecouldbe accountedforin Nb3Sn by t h e c r i t i c a l s t a t e model with

001S-9464/79/0100-9260S00.75 0 1979 IEEE

261

0

v d

Rmted 1369 f i l 3145

fll

6031 f t I Unreacled 1369 f l l

9

I

1

6031 fllamcnt 1369 filament

dI

A

A A A

64

I (TI

AppliedField Fig. 3.

."

104

3

1

10

Surface Current (r.rn.s.arnp.rn-l)-

-

IO

Dependence of J on H derived from magnetisation.

Longitudinal fieldlosses

Figure 4 compares the behaviourof reacted and unreacted samples in the longitudinal field conthe inclusion of a bulk critical-current density Jc figuration. There is a sharp rise inloss starting at with a dependence on applied field of the H form about 114mT in Nb and a similar steep increase in the JC(H)=C1/H. However, as we have argued in more detail range 70-90mT in NbsSn. In both cases results from elsewhere6, this formof Jc (H) is incompatible with 1369 and 6031 filament material agree well, when other data. In particular, the form Jc(H)=C1/JH fits normalised to the same filament surface area. magnetisation data down to 300mT (Fig. 3); there no is We have also studied partially reacted samples reason to expect a more rapid dependence at lower (Fig. 5 ) . Even 3% reacted material shows a rise fields. corresponding to that in fully reacted material before The critical state model cannot be applied Nb to crossing to the unreacted curve, while 30% reacted without taking into account the large influence of the material crosses at a higher level. Thus, the rise in Meissner state, in which losses arise from penetration the range 70-90mT is characteristic of Nb3Sn and is into surfaceasperities'' but no bulk penetration not substantially affected by the degree of reaction. occurs untilHC1 is exceeded. Fig. 1.

Alternating current losses.

n 6031 fil.

hreacted

1369 fil A 6031 f i l .

1 .4

L

0

I

no:*I

2 B

+

h

6031 f i l data d i v i d e d by 2.1 tocompen~att

for a d d i t m a l filament surface.

a'&

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s

1no I

IO0

I

IO

Psok f i e l d (mT)-

Fig. 2.

Transverse alternating field losses.

Fig. 4.

Longitudinal field losses.

262

lo-? CF173, 1369 f l l . 0,495 mm d ia. unreacted reacted 3%

-.. - 30% - -81%

I

i

. .

Fig. 7 .

I; *I

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Fig. 5.

E f f e c to fp a r t i a lr e a c t i o n l o n g i t u d i n a lf i e l dl o s s e s .

on

When a s m a l l b i a s f i e l d i s a p p l i e d t o t h e Nb f i l a ments(Fig. 6 ) , t h es t a r to ft h es h a r pr i s er e m a i n s i d e n t i f i a b l e and i s s h i f t e d i n such a way t h a t t h e sum of b i a s f i e l d andpeak a l t e r n a t i n g f i e l d r e m a i n s c o n s t a n t ;t h i s i s thebehaviourexpected i ft h er i s e were caused by exceeding H C 1 . For Nb3Sn f i l a m e n t ss u c h a s h i f tc a n n o tb ei d e n t i f i e d( F i g . 7 ) ; i n s t e a d ,a st h e biasfieldincreases,the loss c u r v eg r a d u a l l y approachesanalmostuniform power law which, i n a b i a s f i e l d o f 218mT, has an exponentofabout 3.2. Fluxmotion(d@/dt) waveforms a r e shown i n Fig. 8 . The waveform f o r u n r e a c t e d m a t e r i a l shows c l e a r l y t h a t , i n Nb f i l a m e n t s , b u l k p e n e t r a t i o n d o e s n o t t a k e p l a c e after field reversal until some c h a r a c t e r i s t i c f i e l d i s

E f f e c to fb i a sf i e l d on l o n g i t u d i n a lf i e l d l o s s e si n Nb3Sn f i l a m e n t s . Curves a r e displace2forclarity. exceeded.€or NbsSn f i l a m e n t s a t 71mT t h e waveform c l o s e l yr e s e m b l e st h ep r e d i c t i o no fM e l v i l l e ' 'f o r surfaceroughnesspenetration i n theMeissnerstate. However, a t h i g h e r f i e l d s , b u l k p e n e t r a t i o n a p p e a r s t o betakingplacealmostimmediatelyafterfield r e v e r s a l .F l u xm o t i o na st h ef i e l dd e c l i n e s from t h e peak b u i l d s up much more s l o w l y w i t h i n c r e a s e d f i e l d amplitudethandoesthepenetration on t h e r i s i n g f i e l d afterreversal. DISCUSSION Longitudinalfieldresults The main c h r a c t e r i s t i c i n l o n g i t u d i n a l f i e l d , f o r both Nb and NbsSn f i l a m e n t s , i s a f l u x e x c l u s i o n f i e l d ( f e f ) , belowwhich no s i g n i f i c a n t p e n e t r a t i o n o f f l u x i n t ot h ei n t e r i o r ofthefilamentstakesplace.For Nb filamentsthefef is surelytobeidentifiedwith HC1. I t s v a l u e ,a ta b o u t 114mT, i s r e a s o n a b l ef o rh e a v i l y cold-worked Nb i n comparison, f o r i n s t a n c e , w i t h a value of 127mT f o rs i n g l ec r y s t a l Nb8. The fefremains i d e n t i f i a b l e andconstantundertheinfluenceofsmall b i a s f i e l d s and i t s i n f l u e n c e on t h e d @ / d t waveform i s c l e a r l y v i s i b l e , even when s i g n i f i c a n t b u l k p e n e t r a t i o n is present. Turning now t o NbsSn f i l a m e n t s , one could regard as s u p p o r t f o r t h e viewof Shaw e t a15 the high fef t h a t HC1 i s much g r e a t e r t h a n t h e u s u a l l y a c c e p t e d valueof 20mT. To some e x t e n to u r measurements i n biasfieldsupportthis view, i n t h a t t h e y show t h a t behaviourentirelycompatiblewith a bulk critical-

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3

E f f e c t of b i a sf i e l d on l o n g i t u d i n a l fieldlossesin Nb f i l a m e n t s .

,

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Fiq. 8.

'.,' I

107mT

Unreacted

Fluxmotion(d@/dt) waveforms f o r Nb3Sn and Nb f i l a m e n t s a t v a r i o u s peak f i e l d s .

263 s t a t e i n t e r p r e t a t i o n is r e s t o r e d by a b i a s f i e l d o f only 200mT. However, a more d e t a i l e d comparisonof biasfieldresultswiththosefor Nb f i l a m e n t s , raises severe doubts about identifyi.ng the fef with HC1 i n Nb3Sn. The v a l u eo ft h ef e f is l e s ss h a r p l yd e f i n e d t h a n i n Nb and it i s n o t s h i f t e d i n t h e e x p e c t e d manner by b i a s f i e l d s . The d@/dt waveforms p r o v i d ef u r t h e r e v i d e n c ea g a i n s tt h e high-Hc, hypothesis;they show t h a t , o n c eb u l kp e n e t r a t i o nh a ss t a r t e d , it occurs from f i e l d s w e l l below t h e f e f , c o m p a t i b l e , w i t h i n e x p e r i m e n t a lr e s o l u t i o n ,w i t ha n HC1 of 20mT. Consideration must t h e r e f o r e b e g i v e n t o a n e x p l a n a t i o n b a s e d on s u r f a c e e f f e c t s , i n p a r t i c u l a r a s u r f a c eb a r r i e rt of l u xe n t r y ,B u s s i ' e r e ' s measurements on an Nb3Sn samplewith an e s p e c i a l l y smooth s u r f a c e I 2l e a v el i t t l ed o u b tt h a tt h es u r f a c eb a r r i e r e x i s t s i n Nb3Sn and can be large enough t o produce t h ee f f e c t s we haveobserved.Bussi&-e'sresults i n d i c a t e a f e f o f ".100mT i n z e r o b i a s f i e l d , i n excellent agreement with the r e s u l t of Griffiths et a l a on a s i m i l a r s a m p l e a n d , g i v e n t h e d i f f e r e n c e s i n f a b r i c a t i o na n ds a m p l ec o n f i g u r a t i o n ,i nr e a s o n a b l e agreementwithourresult on Nb3Sn f i l a m e n t s . However, Bussizre observes a b a r r i e r which,whiledecreasing rapidlywithfield, is still'l.50mTin 200mT b i a s f i e l d . We can see no e v i d e n c e o f b a r r i e r e f f e c t s i n o u r r e s u l t s a t 200mT b i a s f i e l d b u t t h i s d i f f e r e n c e c o u l d bedue t o d i f f e r e n c e s i n s u r f a c e c o n f i g u r a t i o n o r accuracyofalignmentwiththefield. Similar effects to those w e haveobservedcouldbe produced by a region of high pinning near the surface. A f u r t h e r p o s s i b i l i t y i s t h e e f f e c t , i n t e r p r e t e d by Campbell as beingdue t o r e v e r s i b l e motion of flux v o r t i c e s a b o u t t h e i r p i n n i n g p o ~ i t i o n s ' ~ , which,while it i s e s s e n t i a l l y a b u l k e f f e c t , c a n g i v e r i s e t o an a p p a r e n ts u r f a c eb a r r i e r L 4 Although n e i t h e ro ft h e s e mechanisms i s c l e a r l y i n c o m p a t i b l e w i t h o u r r e s u l t s , they would b o t h s i m u l a t e a b a r r i e r which opposed f l u x e n t r y and e x i t e q u a l l y , w h e r e a s B u s s i s r e f i n d s t h a t the barrier opposes only flux entry"

behave as a s i n g l e$ u p e r c o n d u c t o r ;t h es u r f a c e currents are therefore effectively distributed through the bulk and, once the first layer of filaments is saturated, should appear simply as anenhancement o f t h eb u l k Jc. However, i f t h e f i e l d dependenceofthe s u r f a c e c u r r e n t i s more r a p i d t h a n t h a t o f t h e t r u e bulk Jc, t h e e f f e c t i v e b u l k Jc may approach the J C ( H ) = a / H behaviour which one might naively deduce from t h e loss c u r v e s , r a t h e r t h a n t h e Jc (H)=c~//Hbehaviour of the true bulk Jc.

Transversefieldresults

CONCLUSIONS The p e c u l i a r i t i e s o f low f i e l d l o s s e s i n mf Nb c o m p o s i t e s a r i s e from t h e p r e s e n c e o f t h e M e i s s n e r s t a t e below 114mT. Although losses in mf Nb3Sn composites closely r e s e m b l e t h o s e i n Nb, t h i s c a n n o t b e i n t e r p r e t e d a s i n Nb3Sn. e v i d e n c ef o r a high H C1 The most probable cause of low l o s s e s a t low f i e l d s i n mf,NbsSn i s a s u r f a c e b a r r i e r to f l u x e n t r y . While a s i m p l e s u r f a c e - c u r r e n t model cannot satisfactorily account for the behaviour of the losses, one i n c o r p o r a t i n g l o s s e s due t o s u r f a c e r o u g h n e s s , surfaceorientationeffectsand, mostimportantly,the f i e l d dependenceofthesurfacecurrent,canprobably provideanadequateexplanation. ACKNOWLEDGEMENTS The a u t h o r sw i s ht o acknowledge t h es u p p o r to f Amphlettand t h e u n f a i l i n g i n t e r e s t and encouragementof D r . J . A . Lee. D r . C.B.

REFERENCES

.

.

I f oneacceptsthesurfacebarrierasproviding t h e most p r o b a b l e e x p l a n a t i o n o f o u r l o n g i t u d i n a l f i e l d r e s u l t s , o n e c a ns e e ,i n a general way, t h a t it could leadtotransversefieldlossesfalling,at low f i e l d s , below t h o s e p r e d i c t e d from t h e c r i t i c a l - s t a t e model and Jc. However, a d e t a i l e de x p l a n a t i o n is l e s s thkbulk readily provided. A model which assumes a c o n s t a n t s u r f a c e c u r r e n t , occupying an infinitesimal layer, beyondwhichuniform bulkpinningprevails,leadsto a dependenceof l o s s on f i e l d o r c u r r e n t which, expressed in power-law terms, h a s a stronglyvaryingexponent',in marked c o n t r a s t t o t h er a t h e rc o n s t a n te x p o n e n t we haveobserved.This was o n e o f t h e f a c t o r s which l e d u s , i n an e a r l i e r paper, to reject an explanation based on s u r f a c e Currents,asdidalso Howard e t a l ' f o r t h e i r r e s u l t s on electron-beamevaporated Nb3Sn. However, it now seems more p r o b a b l e t h a t t h e d i s c r e p a n c y a r i s e s from failingsofthe model, ratherthanabsenceof a surface current. Severaladditionalfactors w i l l modify t h e p r e d i c t i o n so ft h e model. P e n e t r a t i o no ff l u xi n t os u r f a c e p r o t r u s i o n sg i v e sr i s et ol o s s e sa n a l o g o u st ot h o s e below HC1 , w i t h o u tn e c e s s a r i l yl e a d i n gt o a breakdown o ft h es u r f a c eb a r r i e r " . The e f f e c to fs u r f a c e orientation on the strength of the barrier must be a majorfactorinthebehaviourof mf m a t e r i a l s i n t r a n s v e r s ef i e l d .F i n a l l y ,t h ef i e l d dependenceof the barrier needs to be included in the model. Alternating current results

I n an a l t e r n a t i n g c u r r e n t l o s s measurement on a mf c o m p o s i t e ,t h es e l ff i e l df o r c e st h ef i l a m e n t st o

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