a.c. TRANSPORT CURRENT LOSSES IN TRANSVERSE AND LONGITUDINAL d.c. FIELDS

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a.c. TRANSPORT CURRENT LOSSES IN

TRANSVERSE AND LONGITUDINAL d.c. FIELDS

J. de Reuver, G. Mulder, L.J.M. van de Klundert

To cite this version:

J. de Reuver, G. Mulder, L.J.M. van de Klundert. a.c. TRANSPORT CURRENT LOSSES IN

TRANSVERSE AND LONGITUDINAL d.c. FIELDS. Journal de Physique Colloques, 1984, 45 (C1),

pp.C1-479-C1-482. �10.1051/jphyscol:1984198�. �jpa-00223754�

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Colloque C l , suppl6ment au no 1, Tome 45, janvier 1984 page Cl-479

a , c , TRANSPORT CURRENT LOSSES I N TRANSVERSE AND LONGITUDINAL decn

F I

ELDS

J . L . de Reuver, G . B . J . Mulder and L.J.M. van de Klundert

m e n t e U n i v e r s i t y o f Technology, Department o f Applied Physics, P. 0. B. 217, 7500 AE Enschede, The Netherlands

RBsume

-

Les c a r a c t g r i s t i q u e s de l a dependance s u r l e s p e r t e s en c o u r a n t a l - t e r n a t i f de l ' h i s t o i r e e t de l a d i r e c t i o n du champ magnetique c o n t i n u s o n t r a p p o r t d e s .

A b s t r a c t - C h a r a c t e r i s t i c s on a . c . t r a n s p o r t c u r r e n t l o s s e s of t h e i n f l u e n c e of d i r e c t i o n and h i s t o r y of t h e d . c . f i e l d a r e r e p o r t e d .

Experiments i n t h i s f i e l d of r e s e a r c h have been performed i n an e a r l i e r p e r i o d u s i n g an o t h e r measurement technique / I / . R e s u l t s with t h e o p p o s i t e experiment, c o n s i s t i n g of a d . c . t r a n s p o r t c u r r e n t and an a . c . magnetic f i e l d h a s been achieved by Ogasawara / 2 / . A next s t e p i n our r e s e a r c h program w i l l be t h e exposure o f t h e wire t o an a.c.

c u r r e n t a s w e l l a s an a . c . f i e l d . I n advance, e x c l u s i v e information on t h e c r i t i c a l c u r r e n t d e n s i t y dependence on t h e l o c a l magnetic f i e l d has t o be o b t a i n e d e s p e c i a l l y i n t h e low f i e l d range. The used measurement technique h a s been d e s c r i b e d b e f o r e /6/.

The t e s t l e n g t h , i n t h i s c a s e , is 60 mm.

THEORY

1. Transverse d.c. f i e l d .

During a.c. t r a n s p o r t c u r r e n t o p e r a t i o n without a n a p p l i e d a . c . f i e l d t h e s e l f f i e l d e f f e c t o c c u r s i n m u l t i f i l a m e n t a r y w i r e s . T h i s f e a t u r e e n a b l e s us t o c a l c u l a t e t h e c u r r e n t d i s t r i b u t i o n i n t h e same way a s i n t h e c a s e of s i n g l e c o r e w i r e s .

The c r i t i c a l c u r r e n t d e n s i t y ( j c ) can be o b t a i n e d by an averaging procedure. The j c dependence on B i s u s u a l l y d e s c r i b e d by t h e K i m model.

jc(B) = j O / ( l

+ I B I / B ~ )

(1)

Assuming t h e C r i t i c a l S t a t e Model t h e magnetic and e l e c t r i c f i e l d s can be determined by t h e reduced Maxwell e q u a t i o n s :

+

+ + -t t

V x B = p j ( B ) a n d V x E = - B .

0 c ^{( 2 )}

I n g e n e r a l an a p p l i c a t i o n of a d.c. f i e l d w i l l cause a d e c r e a s e of j,. E s p e c i a l l y i n the high f i e l d range t h e i n f l u e n c e of t h e magnetic f i e l d due t o t h e t r a n s p o r t c u r r e n t w i l l be n e g l i g i b l e . I t i s j u s t i f i e d t o f i x jc a t t h e v a l u e t h a t belongs t o Bdc. The l o s s p e r c y c l e may be w r i t t e n a s :

f o r low c u r r e n t amplitudes compared with t h e c r i t i c a l c u r r e n t . S u b s t i t u t i o n of jc (Bdc) g i v e s :

BdC + BO - " ^" )

A p r o p e r t y of t h e t w i s t e d m u l t i f i l a m e n t a r y wire i s t h a t t h e c u r r e n t d i s t r i b u t i o n remains r a d i a l symmetric. The c u r r e n t p e r f i l a m e n t w i l l be determined by t h e s p o t were t h e f i l a m e n t g e t s s a t u r a t e d . A t t h i s s p o t t h e f i e l d h a s a maximum and t h e r e f o r e t h e c r i t i c a l c u r r e n t a minimum. A s t h e f i l a m e n t i s n o t s a t u r a t e d everywhere, magneti- s a t i o n c u r r e n t s due t o t h e magnetic d . c . f i e l d occur a s w e l l . m t i c i p a t i n g on t h e r e s u l t s and d i s c u s s i o n here t h e importance of t h e h i s t o r y of t h e d.c. f i e l d i s mentioned. When t h e f i e l d i s swept from a high t o a low l e v e l t h e f i e l d i n s i d e t h e Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984198

CI-480 JOURNAL DE

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m a g n e t i s a t i o n a r e a of t h e f i l a m e n t i s h i g h e r t h e n t h e e x t e r n a l f i e l d . Sweeping i n t h e o t h e r d i r e c t i o n t h e i n t e r n a l f i e l d i s lower t h a n t h e e x t e r n a l f i e l d . To avoid t h i s , t h e superconductor can be brought i n t o t h e normal s t a t e by i n c r e a s i n g i t s temperature above Tc u s i n g a h e a t e r . Doing t h i s a t a c e r t a i n d . c . f i e l d l e v e l , f l u x g r a d i e n t s d i s a p p e a r . A f t e r a r e t u r n i n t o t h e superconductive s t a t e no magnetisation c u r r e n t s appear, due t o t h e f a c t t h a t Type I1 superconductors do n o t show r e v e r s i b i l i t y . The i n t r o d u c t i o n of h i g h l y conductive m a t r i x m a t e r i a l g e n e r a l l y i n c r e a s e s t h e l o s s e s with i n c r e a s i n g frequency. This l o s s c o n t r i b u t i o n w i l l be a d d i t i v e f o r p r a c t i c a l c a s e s .

2. Longitudinal d.c. f i e l d .

The i n f l u e n c e on t h e a . c . t r a n s p o r t c u r r e n t l o s s e s , applying t h i s f i e l d t y p e , has been i n v e s t i g a t e d b e f o r e /3/. The t h e o r e t i c a l background i s based on t h e i s s u e of t h e l o n g i t u d i n a l f i e l d e f f e c t /4/. I n terms of t h e c r i t i c a l c u r r e n t d e n s i t y , a dependence on t h e l o n g i t u d i n a l f i e l d i s an a p p r o p r i a t e emperical approach /5/ t o d e s c r i b e t h e l o s s behaviour. I n t h e framework of t h e C r i t i c a l S t a t e Model a j u s t i f i c a t i o n can be o b t a i n e d by comparing t h e r e s u l t s of t h e V - I c h a r a c t e r i s t i c method and t h e magneti- s a t i o n method. The l o s s measurement belongs t o t h e l a t t e r c a t e g o r y .

Table 1 - T e s t w i r e s .

f l l $ f i l C ~ m l Cu:S.C. m a t e r i a l t w i s t p i t c h NO manufactorer

+

^{wire [mml n}

^.

... Cml

I MCA .35 114 21.6 1.35 ~ b ~ i / C u N i 12

2 MCA .30 574 8.6 1.10 NbTi/CuNi 12

3 MCA .12 1 80 2.00 NbT i/CuN i -

4 Airco - 2 0 10285 1 . 0 2.70 N ~ T ~ / C U / C U N ~ * 1.1

*

CuNi b a r r i e r s of .18 pm

RESULTS AND DISCUSSION 1. Transverse d.c. f i e l d .

I n F i g . 1 t h e a - c . t r a n s p o r t c u r r e n t l o s s v o l t a g e s a g a i n s t t h e a p p l i e d d.c. f i e l d a r e given. From t h e s e p l o t s t h e a r a m e t e r s of t h e K i m model have been deduced a s des- c r i b e d b e f o r e ( J o = 1.43 l o i g */m2 and Bo = 0.44 T ) . These f i g u r e s can be used i n numerical c a l c u l a t i o n s . A r e c o n s t r u c t i o n of t h e l o s s c u r v e s with a accuracy of 5%

can be achieved f o r t h e high f i e l d range. T h i s r e c o n s t r o c t i o n i s based on t h e assumption t h a t a v e c t o r summation of t h e e x t e r n a l f i e l d and t h e f i e l d due t o t h e c u r r e n t determines t h e a c t u a l l o c a l f i e l d and t h e f a c t t h a t t h e c u r r e n t d i s t r i b u t i o n i s determined by t h e s p o t where t h e f i e l d magnitude r e a c h e s i t s h i g h e s t magnitude.

The summation, however, does n o t f i t f o r t h e low f i e l d behaviour. To i n v e s t i g a t e t h e magnetisation i n f l u e n c e , experiments with a d.c. f i e l d sweep through z e r o have been performed ( s e e Fig. 2 ) . Going from a high f i e l d amplitude t o a iow one we p a s s -

- _> 8

- \

>

!

^G

,.

2

m.

L

-02 -0: 0

>.

" _- H,,ITI

-- ''

Fig. 2

-

Loss v o l t a g e ( v ) a g a i n s t Fig. 1 - Loss v o l t a g e ( v ) a g a i n s t t r a n s - t r a n s v e r s e d - c . f i e l d ( B ~ , ) f o r 1 0 0 ~ v e r s e d . c . f i e l d (B+) f o r v a r i o u s dur- and 40 H z . wire no. 1

r e n t s . Wire no. 2; frequency: 40 H z .

+:

without magnetisation c u r r e n t s .

two minima. A rough i n d i c a t i o n of t h e magnetic f i e l d i n s i d e t h e f i l a m e n t s i s t h a t it i s higher t h a n t h e e x t e r n a l f i e l d . T h e r e f o r e t h e lowest f i e l d s i n s i d e t h e f i l a m e n t s occur a t a f i e l d v a l u e a f t e r having passed zero. C a l c u l a t i o n s , u s i n g t h i s model, indeed show a minimum a f t e r having passed zero. The f i r s t minimum h a s a lower v a l u e . T h i s depends s t r o n g l y on t h e assumptions made on t h e i n t e r n a l f i e l d dependence on t h e e x t e r n a l f i e l d . To a v o i d m a g n e t i s a t i o n e f f e c t s t h e wire was quenched a t a s t a t i o n a r y d.c. f i e l d , recovered and s u p p l i e d with t h e a . c . t r a n s p o r t c u r r e n t . The o b t a i n e d r e s u l t s show two minima with symmetry according t o t h e z e r o f i e l d a x i s . S i m i l a r experiments on a s i n g l e c o r e w i r e have been performed. See F i g . 3 . The l o s s behaviour due t o t h e d.c. f i e l d now does n o t only depend s t r o n g l y on t h e sweep d i r e c t i o n of t h e f i e l d b u t a l s o on t h e p o i n t of r e t u r n . Obviously t h e high magnitude of t h e m a g n e t i s a t i o n c u r r e n t s , p o s s i b l y of t h e same o r d e r of magnitude a s t h e t r a n s p o r t c u r r e n t s , determines t h e behaviour r i g o r o u s l y .

Fig. 3

-

Loss v o l t a g e ( v ) a g a i n s t t r a n s v e r s e d.c. f i e l d (Bdc) f o r 40 A , 40 Hz f o r wire no. 3 with sweep sequence.

Fig. 4 - Loss v o l t a g e (v) a g a i n s t t r a n s v e r s e d.c. f i e l d (Bdc) f o r v a r i o u s c u r r e n t s a t 40 Hz. Wire no. 4.

An i n t e r e s t i n g , and perhaps an important, f e a t u r e i s t h e l o c a t i o n of t h e minima. In t h e c a s e of t h e s i n g l e c o r e wire t h i s l o c a t i o n depends on t h e c u r r e n t amplitude a s h a s been seen b e f o r e u s i n g s l a b s and a.c. f i e l d s superposed on a d.c. f i e l d /7/. I n t h e c a s e of m u l t i f i l a m e n t w i r e s , however, t h e l o c a t i o n seems independent of t h e a p p l i e d c u r r e n t amplitude. T e s t i n g a n o t h e r wire with t h i c k e r f i l a m e n t s t h e v a l u e of t h e f i e l d where t h e minimum o c c u r s s h i f t s t o h i g h e r f i e l d s .

A t y p i c a l f e a t u r e of t h i s measurement technique i s t h a t an u n s t a b l e behaviour w i t h r e s p e c t t o t h e e x t e r n a l f i e l d and t h e p o s s i b i l i t y t h a t t h e t r a n s p o r t c u r r e n t remains e x i s t i n g can be observed a c c i d e n t l y . Experiments a t high c u r r e n t l e v e l s show t h a t t h e l o s s v o l t a g e spontaneously drops t o t h e v a l u e , t h a t can be o b t a i n e d by quenching t h e w i r e and i n s e r t i n g t h e c u r r e n t a f t e r w a r d s a s d e s c r i b e d b e f o r e /8/. The wire t e s t e d f o r i t s c u r r e n t c a r r y i n g p r o p e r t i e s h a s been i n v e s t i g a t e d b e f o r e f o r i t s a . c . f i e l d behaviour by Ogasawara /9/. The r e s u l t s on t h e t r a n s p o r t c u r r e n t l o s s e s a r e shown ,in Fig. 4. No minimum o c c u r s .

2. Longitudinal d - c . f i e l d .

I n Fig. 5 the l o s s v o l t a g e s a g a i n s t f i e l d magnitude a r e given f o r a s i n g l e c o r e wire.

The l o s s e s d e c r e a s e c o n s i d e r a b l y with i n c r e a s i n g f i e l d . Obviously t h e l o n g i t u d i n a l f i e l d e f f e c t o c c u r s . A r e l a t e d o b s e r v a t i o n / l o / i s t h a t t h e e q u i l i b r i u m s t a t e i s o b t a i n e d a f t e r some c y c l e s , i n our c a s e s t h r e e . A f t e r quenching t h e wire it t a k e s a g a i n t h r e e c y c l e s of t h e e x t e r n a l f i e l d t o reach a f i n a l l e v e l .

The behaviour of t h e m u l t i f i l a m e n t a r y w i r e s i s n e a r l y i d e n t i c a l t o t h a t of s i n g l e c o r e wire ( F i g . 6 ) . U n t i l now no s i g n i f i c a n t d e t e r m i n a t i o n on t h e i n f l u e n c e of f i l a m e n t s i z e and t w i s t p i t c h can be made.

I n Fig. 7 t h e l o s s v o l t a g e a g a i n s t f i e l d of a wire w i t h h i g h l y conductive m a t r i x m a t e r i a l i s shown. A dependence of t h e sweep d i r e c t i o n and of t h e sweep v e l o c i t y has been observed. T h i s e f f e c t depends on t h e s h i e l d i n g c u r r e n t s i n t h e o u t e r f i l a m e n t s which a r e coupled by t h e m a t r i x /11/. These s h i e l d i n g c u r r e n t s decay i n approximately 60 s e c . The behaviour of t h e l o s s e s d i f f e r s s t r o n g l y from t h e o b s e r v a t i o n made of t h e

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-02 -3' 0 018,.,,ITI

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F i g . 5 - Loss v o l t a g e ( v ) a g a l n s f l o n g i t u d i n a l d.c. f i e l d (Bdc) a t 40 A, 40 Hz f o r w i r e no. 3 w i t h sweep sequence.

-

F i g . 6

-

Loss v o l t a g e ( v ) a g a i n s t l o n g i t u d i n a l d.c. f i e l d (Bdc) f o r v a r i o u s c u r r e n t s a t 4 0 Hz f o r w i r e no. 2 .

o t h e r w i r e s . A f t e r a d e c r e a s e , a minimum o c c u r s f o l l o w e d by a s t e a d y i n c r e a s e . T h i s w i r e , however, h a s an extremelysmalltwistpitch. T h e r e f o r e t h e f i l a m e n t s have a n a n g l e w i t h t h e f i e l d o f a = 300. F o r c e f r e e c u r r e n t e f f e c t s a r e n o t 1 i k e l y . n o w .

CONCWSION

By measuring a . c . t r a n s p o r t c u r r e n t l o s s v o l t a g e s a b e t t e r u n d e r s t a n d i n g o f c u r r e n t d i s t r i b u t i o n s can b e o b t a i n e d i n t h e c a s e s t h a t e x t e r n a l f i e l d s a r e a p p l i e d . The c r i - t i c a l c u r r e n t d e n s i t y dependence on t h e m a g n e t i c i n d u c t i o n c a n b e d e t e r m i n e d i n t h i s way.

The o c c u r e n c e o f a minimum i n t h e l o s s e s a t a c e r t a i n l e v e l of t h e t r a n s v e r s e d.c.

1 3 1 f i e l d c a n b e i n v e s t i g a t e d i n a p r o p e r way

s o t h a t more comprehensive s u g g e s t i o n s on

<o. t h e a c t u a l b e h a v i o u r can b e g i v e n .

A c o n t i n u o u s d e c r e a s e up t o 2T o f t h e l o s s e s i n a l o n g i t u d i n a l d.c. f i e l d i n

l5 8, I T ) 20 t h e c a s e o f most w i r e s g i v e s u p p o r t t o

t h e i d e a t h a t t h e c r i t i c a l c u r r e n t i n - Fig. 7 - Loss v o l t a g e ( v ) a g a i n s t c r e a s e s w i t h i n c r e a s i n g l o n g i t u d i n a l f i e l d . l o n g i t u d i n a l d.c. f i e l d (Bdc) f o r

v a r i o u s c u r r e n t s a t 40 H z . Wire no. 4.

REFERENCES

1. A s d e n t e , M . , ICMC (1982)167.

2. Ogasawara, T., C r y o g e n i c s (1980)216.

3. Nakayama, Y . , ICEC 5 (1974)129.

4. ,Yamafuji, K., ICEC 5 (1974)132.

5. F e v r i e r , A., C r y o g e n i c s (1983) 185.

6. De Reuver, J . L . , ICEC 9 (!982)719.

7. G i j s b e r t s e , E.A., P h y s i c a (1981159.

8. Wilson, M.N., J. Phys. D. Appl. Phys.

3

(197011547.

9. Ogasawara, T . , MAG

19

(1983)248.

10. F u n a k i , K . , Jap. J. o f Appl. Ph.

2

(19821299.

11. M r c k , B . , Rev. d e Ph. Appl.

11

(19761369.