THEORETICAL AND EXPERIMENTAL STUDIES OF THE STABILITY IN CVD Nb3Sn SUPERCONDUCTING COMPOSITE TAPES

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THEORETICAL AND EXPERIMENTAL STUDIES OF THE STABILITY IN CVD Nb3Sn

SUPERCONDUCTING COMPOSITE TAPES

Zhang Qirui, Song Shengnian, Jiao Zhengkuan

To cite this version:

Zhang Qirui, Song Shengnian, Jiao Zhengkuan. THEORETICAL AND EXPERIMENTAL STUDIES

OF THE STABILITY IN CVD Nb3Sn SUPERCONDUCTING COMPOSITE TAPES. Journal de

Physique Colloques, 1984, 45 (C1), pp.C1-535-C1-539. �10.1051/jphyscol:19841109�. �jpa-00223577�

JOURNAL DE PHYSIQUE

Colloque C1, supplkment au n o 1, Tome 45, janvier 1984 page Cl-535

THEORETICAL AND EXPERIMENTAL STUDIES OF T H E STABILITY IN CVD Nb3Sn SUPERCONDUCTING COMPOSITE TAPES

Zhang ~ i r u i + , Song s h e n g n i a n i and J i a o 2hengkuanir

I n s t i t u t fiir MetaZZphysik der Universitat Giittingen, 0-3400 Giittingen, F.R. G.

' ~ e ~ a r t r n e n t of Physics, University of Science and Technology of China, Hefei, China

ii I n s t i t u t e of Plasma Physics, Academia Sinica, Hefei, China

Resume

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s u l t a t s theoriques sont en bon accord avec l e s experiences f a i t e s avec des bobines maquettes e t avec l e s r e s u l t a t s p u b l i e s . En se basant s u r l a s t a b i l i t e dynamique, l ' u n i f i c a t i o n des c r i t e r e s de s t a b i l i t e c r y o s t a t i q u e , dynamique e t adiabatique e s t d i s c u t e .

Abstract

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The t h e o r e t i c a l r e s u l t s are i n good agreement w i t h our experiments w i t h s i m u l a t i o n c o i l s o r w i t h the r e p o r t e d r e s u l t s . Based on the t h e o r y o f t h e dynamic s t a b i l i t y , t h e u n i f i c a t i o n o f the c r y o s t a t i c , dynamic and a d i a b a t i c s t a b i l i t y has been d i s - cussed.

I

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I t i s we1 1 known t h a t f o r h i g h f i e l d ( 1 0 Tesla o r more) superconducting magnets t h e s t a b i l i t y o f t h e Nb,Sn o r V,Ga composite tapes i n t h e perpendicular f i e l d and/or under h i g h s t r e s s i s v e r y important. This s u b j e c t has been discussed e x t e n s i v e l y [1,21. I n t h i s paper we r e p o r t some r e s u l t s o f t h e o r e t i c a l and experimental inves- t i g a t i o n s on t h e s t a b i l i t y o f composite tapes.

The s t a b i l i t y c r i t e r i a are given. Based on these c r i t e r i a one can show t h a t f o r given conductor geometry and heat t r a n s f e r t o t h e surroundings, an optimum Cu/sc r a t i o e x i s t s a t which t h e s t a b i l i z e d conductor possesses the h i g h e s t o v e r a l l cur- r e n t d e n s i t y . I t i s suggested t h a t the c r y o s t a t i c and a d i a b a t i c s t a b i l i t y are two l i m i t s o f t h e dynamic s t a b i l i t y and the a p p l i c a t i o n ranges o f t h e d i f f e r e n t s t a b i - l i t y c r i t e r i a are given.

I 1

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L e t 0 , 6 E , 6E be the f l u c t u a t i o n o f the temperature, e l e c t r i c f i e l d and magnetic i n d u c t i o n , r e s p e c t i v e l y , around t h e i r i n i t i a l e q u i l i b r i u m values. Then t h e dynamics o f t h e process w i t h i n a composite conductor i s determined by Maxwell's equations and the heat d i f f u s i o n equation f o r the f l u c t u a t i o n s

a

O X ( & [ ) =

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*on l e a v e from t h e U n i v e r s i t y of S c i e n c e and Technology of China

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841109

JOURNAL DE PHYSIQUE

where c, K, p , o , c a r e t h e e f f e c t i v e s p e c i f i c h e a t , h e a t c o n d u c t i v i t y , r e s i s t i v i t y , s t r e s s , and s t r a i n o f t h e composite [31, r e s p e c t i v e l y . i i s t h e r a t e o f t h e p l a s t i c d e f o r m a t i o n , 17 = 1 / ( 1 + X ) i s t h e volume f r a c t i o n o f t h e superconductor, and x i s t h e Cu/sc r a t i o .

-.

dE C

If we make a l i n e a r a p p r o x i m a t i o n , 6d = , 6JS = TO , eqs. ( 2 ) , ( 3 ) can be r e - w r i t t e n as

F o r t h e c r i t i c a l v a l u e o f t h e t r a n s p o r t c u r r e n t , by means o f Bean's c r i t i c a l s t a t e model we get from eqs. ( I ) , ( 4 ) , ( 5 ) an e q u a t i o n o f t h e t i m e dependence o f t h e tem- p e r a t u r e f l u c t u a t i o n

where Do =,K/c i s t h e e f f e c t i v e h e a t d i f f u s i b i l i t y , and 4, = p/u, t h e e f f e c t i v e magnetic d i f f u s i b i l i t y , T o = - J ( a J / a T ) - ' i s t h e characteristic t e m p e r a t u r e o f t h e superconductor i n a g i v e n a p 6 l i e 6 f i e l d . The s t a b i l i t y i s o n l y o b t a i n e d f o r

ao/at 5 0.

Fig 1 Two

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C o n s i d e r i n g a s i m p l i f i e d two-dimensional p l a t e model ( s e e F i g . I ) , we d e f i n e t h e h e a t t r a n s f e r parameter o f t h e composite t a p e t o t h e s u r r o u n d i n g s as J,I = h 1 b / h d S , which c h a r a c t e r i z e s t h e s i z e o f t h e s u p e r c o n d u c t i n g t a p e and t h e c o o l i n g c o n d i t i o n , h and h ' a r e t h e r e s p e c t i v e h e a t t r a n s f e r c o e f f i c i e n t s f r o m t h e edges and t h e s u r - faces o f t h e composite t a p e t o t h e s u r r o u n d i n g s . b and ds a r e shown i n F i g . 1. From eq. ( 6 ) t h e dynamic s t a b i l i t y c r i t e r i o n can t h e n be w r i t t e n as

T h i s f o r m u l a determines t h e upper l i m i t o f t h e c r i t i c a l t r a n s p o r t c u r r e n t d e n s i t y , i n t h e case where t h e s t r e s s e f f e c t i s considered. I f t h e s t r e s s e f f e c t i s n e g l e c t e d t h e s t a b i l i t y c r i t e r i o n (eq. ( 7 ) ) reduces t o

111. EXPERIMENTAL RESULTS AND DISCUSSION

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F o r t h e experiments CVD Nb3Sn tapes, developed by t h e Changsha Research I n s t i t u t e o f M i n i n g and M e t a l l u r g y , were used which c o n s i s t s o f a Ni-Ro s t a i n l e s s s t e e l t a p e w i t h a w i d t h o f 2.5 mm and two Nb3Sn l a y e r s w i t h a t h i c k n e s s o f 10 pm on each s i d e . The samples had a l e n g t h o f 8

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The dependence o f Ic on dcU i s shown i n F i g . 2. The parameters used i n t h e c a l c u - l a t i o n r e f e r t o t h e l i t e r a t u r e [2,31. There e x i s t s a good agreement between t h e e x p e r i m e n t a l v a l u e s and t h e t h e o r e t i c a l p r e d i c t i o n .

2. The Optimum Copper-clad Thickness

L e t t h e t h i c k n e s s o f t h e m a t r i x tape be 2 d o , and d e f i n e 5 ⁼ do/ds, t h e n t h e o v e r - a l l c u r r e n t d e n s i t y o f t h e composite t a p e i s

s u b s t i t u t i n g t h e upper l i m i t o f t h e c r i t i c a l t r a n s p o r t c u r r e n t d e n s i t y g i v e n by c r i t e r i o n ( 8 ) t o eq. ( 9 ) . We o b t a i n J a as a f u n c t i o n o f t h e volume f r a c t i o n X. I t can e a s i l y be shown t h a t Ja has i t s maximum v a l u e when o > 5, 1 .e., h ' / h > do/b.

The c o r r e s p o n d i n q c o n d i t i o n f o r t h e s u p e r c o n d u c t i n g volume f r a c t i o n i s

The Ja - X p l o t i s shown i n F i g . 3. Knowing t h a t qop i s an i n c r e a s i n g f u n c t i o n o f oj, i t p h y s i c a l l y means t h a t one s h o u l d i n c r e a s e t h e amount o f c o p p e r - c l a d d i n g f o r en- s u r i n g s t a b i l i t y o f composite t a p e i n a p e r p e n d i c u l a r f i e l d i f t h e s u r f a c e c o o l i n g i s p o o r . O f course, t h e b e s t way i s i m p r o v i n g t h e c o o l i n g c o n d i t i o n t o b r i n g t h e p o t e n t i a l o f c o p p e r - c l a d d i n g s t a b i l i z a t i o n i n t o f u l l p l a y .

3. S t r e s s E f f e c t

Comparing c r i t e r i o n ( 7 ) and ( 8 ) , i t i s obvious t h a t t h e s t r e s s a and t h e mechanical p r o p e r t i e s o f t h e m a t e r i a l ( a t / a T ) p l a y a n i m p a r t a n t r o l e i n t h e s t a b i l i z a t i o n o f t h e composite tapes.

I n g e n e r a l , f o r t y p i c a l v a l u e s o f aC/aT

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^lo-'

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J O U R N A L DE PHYSIQUE

LOO

d,(pm)

F g 2 D e p e r d e ~ e of I, on dc, I30 KG1

101 experimental curve Ibl theoretical curve

Fig 3 Dependence of J. on x (a) theorettol curve 130KGl Ibl experimental curve l30KGI Ic) theoretical curve (LOKG I Id) experimental curve ILOKG]

Expression ( 7 ) can a l s o e x p l a i n t h e t r a i n i n g e f f e c t which i s caused by s t r a i n hard- ening, i . e . , by decrease o f at/aT owing t o quench.

4. U n i f i c a t i o n o f Dynamic, C r y o s t a t i c , and A d i a b a t i c S t a b i l i t y

Deducing the dynamic s t a b i l i t y c r i t e r i o n t h e processes o f magnetic d i f f u s i o n , heat d i f f u s i o n and t h e p l a s t i c deformation o f the superconducting m a t e r i a l were con- cidered. Therefore, this_ s t a b i l i t y c r i t e r i o n i s a general expression. For

v = DO/Dm G: 1, hv < < I ( h = hb/K) i t was a l r e a d y shown t h a t t h i s general expression reduces t o the a d i a b a t i c s t a b i l i t y c r i t e r i o n [21.

I n t h e case o f a 2D p l a t e geometry, when ^T- << 1 ( v > > l ) hv>> 1, equation ( 8 ) can be s i m p l i f i e d t o t h a t given by Wilson I11

I n f a c t , expression ( 8 ) can be w r i t t e n as

where a i s t h e S t e k l y s t a b i l i t y parameter f o r t h e 2D model shown i n Fig. 1,

i.e., t h e c r y o s t a t i c s t a b i l i t y c r i t e r i o n can a l s o be deduced from t h e general

expression (7), (8) which i s i n agreement w i t h our experimental r e s u l t s . I n Fig. 4 t h e dependence o f IC on dCu i s shown i n a l o g - l o g p l o t f o r d i f f e r e n t f i e l d s . When dcu exceeds a c e r t a i n value, t h e slope o f t h e curves approaches t h e c h a r a c t e r i s t i c value o f the c r y o s t a t i c s t a b i l i t y (112).

Accordingly, we reach t h e f o l l o w i n g conclusion. The c r y o s t a t i c , t h e dynamic and t h e a d i a b a t i c s t a b i l i t y can be t a c k l e d based on an u n i f i e d theory, i.e., t h e dyna- m i c s t a b i l i t y i s e s s e n t i a l , t h e c r y o s t a t i c and a d i a b a t i c s t a b i l i t y c r i t e r i o n s are two l i m i t s o f t h e dynamic s t a b i l i t y . For v 1 and hv > 1 t h e c r y o s t a t i c s t a b i l i t y and f o r v *: 1 , hv << 1 t h e a d i a b a t i c s t a b i l i t y c r i t e r i o n can be used. The dynamic s t a b i l i t y c r i t e r i o n i s t h e general expression which i s , however, b e l i e v e d t o be t h e o n l y s u i t a b l e one f o r the design o f s t a b i l i z e d composite conductors used i n t h e medi urn s i z e superconducting magnets.

Fig L I, vs d,, Curves for diferent fields la1 LOKG; Ibl30KG

We wish t o thank Prof. Dr. H.C. Freyhardt and Dr. H.A. Wagner f o r t h e i r support d u r i n g the p r e p a r a t i o n o f the manuscript

.

References

[I1 M.N. Wilson, IEEE Trans. Magn., MAG-13 (1977) 440 I21 J.J. Duchateau, B. Turck, J. A p p m s . , 46 (1975) 4989

I31 Zhang Q i r u i , Song Shengnian, Acta phys. Te*. Humilis Sin.,

5

[51 C.C. Koch, D.S. Easton, F y o g e n i c s ,

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