PROPAGATION OF NORMAL ZONE IN SUPERCONDUCTING WIRE IN CONDUIT FILLED WITH THE PRESSURIZED He II

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PROPAGATION OF NORMAL ZONE IN

SUPERCONDUCTING WIRE IN CONDUIT FILLED WITH THE PRESSURIZED He II

H. Kobayashi, K. Yasukõchi, Y. Usami

To cite this version:

H. Kobayashi, K. Yasukõchi, Y. Usami. PROPAGATION OF NORMAL ZONE IN SUPERCON-

DUCTING WIRE IN CONDUIT FILLED WITH THE PRESSURIZED He II. Journal de Physique

Colloques, 1984, 45 (C1), pp.C1-515-C1-518. �10.1051/jphyscol:19841105�. �jpa-00223573�

JOURNAL DE PHYSIQUE

Colloque C I , suppl6rnent au n o 1, Tome 45, janvier 1984 page C1-515

PROPAGATION OF NORMAL ZONE I N SUPERCONDUCTING WIRE I N CONDUIT F I L L E D

WITH THE PRESSURIZED He I 1

H. Kobayashi, K. Yasukochi and Y. Usami

Atomic Energy Research I n s t i t u t e , Nihon University, Tokyo, Japan

Resume - Nous avons e t u d i e l e s comportements du f r o n t normal de p r o p a g a t i o n a i n s i que de l a p r o p a g a t i o n de l ' i n t e r f a c e e n t r e He I e t He I 1 q u i s o n t i n - d u i t s p a r l e c h a u f f a g e p a r e f f e t J o u l e dans l e c o n d u i t r e m p l i avec l ' h e l i u m I 1 sous p r e s s i o n . Cet a r t i c l e sugg6re une maniere d ' o p t i m i s a t i o n de l a den- s i t 6 de c o u r a n t @levee dans l e c%ble-en-conduit q u i e s t en c o n f l i t avec l a s t a b i l i s a t i o n permanente due a une q u a n t i t e de l i q u i d e r e f r i g e r a n t .

A b s t r a c t - We have s t u d i e d b e h a v i o r s o f t h e normal f r o n t p r o p a g a t i o n as w e l l ' as t h e p r o p a g a t i o n o f t h e i n t e r f a c e between He I and He I 1 which i s induced by t h e j o u l e h e a t i n g i n t h e c o n d u i t f i l l e d w i t h t h e p r e s s u r i z e d He 11. T h i s paper suggests a way o f t h e o p t i m i z a t i o n f o r t h e h i g h o v e r a l l c u r r e n t d e n s i t y i n t h e c a b l e - i n - c o n d u i t which i s i n c o n f l i c t w i t h t h e s t e a d y s t a b i l i z a t i o n due t o an amount o f c o o l a n t .

F o r s t a b l e superconducting magnets w i t h h i g h o v e r a l l c u r r e n t d e n s i t y and o f easy f a b r i c a t i o n , i t i s v a l u a b l e t o s t u d y whether t h e p r e s s u r i z e d He I 1 cooled c a b l e - i n - c o n d u i t i s f e a s i b l e o r n o t . T h i s p r e l i m i n a r y work has been commenced t o a c q u i r e a general grasp o f t h e knowledge on t h e superconducting c a b l e - i n - c o n d u i t c o o l e d w i t h t h e p r e s s u r i z e d He I 1 a t 1 atmospheric pressure (He IIp f o r s h o r t ) . Since He IIp has e x c e l l e n t thermal p r o p e r t i e s /1,2/, t h e r e i s no need t o f o r c e t h e c o o l a n t t o f l o w i n t h e i n t e r n a l l y c o o l e d superconducting c ~ b l e . The zero n e t mass f l o w makes t h e r e f r i g e r a t i o n system s i m p l e , besides h e l i u m f l o w problems which a r e o f f r e q u e n t occurrence i n t h e f o r c e d f l o w c o o l i n g mode a r e a v o i d a b l e /3/.

I n a l o n g c o o l i n g channel, however, we can h a r d l y e x p e c t "thermal s u p e r c o n d u c t i v i t y "

o f He I 1 a g a i n s t t h e l a r g e t r a n s i e n t g e n e r a t i o n o f h e a t / 4 / . A1 t e r n a t i v e l y , t h e e n t h a l p y o f He I 1 from t h e o p e r a t i n g temperature, say t o 1.8 K, t o t h e h 1 in e becomes predominant f o r t h e a b s o r p t i o n o f t h e h e a t / 5 / . Ample amount o f He 11 i s r e q u i r e d f o r t h e s t a b l e o p e r a t i o n , and i t i s i n c o n s i s t e n t w i t h a c h i e v i n g h i g h o v e r a l l c u r r e n t d e n s i t y . Then, t o f i n d a key o f t h e o p t i m i z a t i o n , t h e s t a b i l i z a t i o n c h a r a c t e r i s t i c s , such as t h e v e l o c i t y o f t h e normal f r o n t vp and o f t h e successive c o l l a p s e /6/ o f s u p e r f l u i d i t y v,~,, minimum p r o p a g a t i n g c u r r e n t Imp, c r i t i c a l energy o f d i s t u r b a n c e f o r quench Ed have been i n v e s t i g a t e d . These c h a r a c t e r i s t i c values have been measured as a f u n c t i o n o f t h e volume r a t i o o f c o o l a n t t o superconducting w i r e i n t h e c o n d u i t .

I - EXPERIMENT

Samples used i n t h i s s t u d y have small c a b l e - i n - c o n d u i t l i k e c o n f i g u r a t i o n s . An u n i n - s u l a t e d superconducting Nb-Ti w i r e w i t h 0.35 mm i n diam. and w i t h t h e superconductor- copper r a t i o o f 1.1 was l a i d i n t h e square c o n d u i t w i t h c r o s s - s e c t i o n a l area o f 2 x 2 mn2 where He IIp i s f i l l e d . The c o n d u i t was formed w i t h a grooved FRP h o l d e r o f 2 cm i n diam. and a b a k e l i t e c o v e r as shown i n F i g . l ( a ) . The hydrodynamical l e n g t h was 36 cm and was shortened by p u t t i n g o f f s m a l l screw p l u g s , w h i l e t h e space f o r t h e c o o l a n t was reduced b y packings. To measure t h e temperature o f t h e l i q u i d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841105

CI-516 JOURNAL DE PHYSIQUE

i n s i d e t h e c o n d u i t , f i v e s m a l l carbon-thermometers w i t h dimensions o f 0.5 mm i n length, and 1 mm i n diam. were s e t a t c e r t a i n i n t e r v a l s . Each thermometer was f i x e d i n s m a l l h o l e s i n s i d e t h e c o n d u i t w i t h o u t t o u c h i n g t h e s u r f a c e o f t h e h o l d e r t o a v o i d t h e i n - f l u e n c e o f t h e l a r g e h e a t c a p a c i t y o f t h e h o l d e r so t h a t thermometers were supported i n t h e mid-spaces o f t h e h o l e s w i t h f o u r - l e a d s s i l v e r - p a i n t e d t o t h e t e r m i n a l s o f t h e thermometers. The c o n d u i t i s s p i r a l l e d a l o n g t h e FRP h o l d e r i t s e l f e x c e p t f o r t h e s t r a i g h t p a r t f o r t h e h e a t e r as shown i n F i g . l ( b ) . The sample was p l a c e d i n t h e b o r e o f a s u p e r c o n d u c t i n g magnet which was a l s o immersed i n He IIp.

superconduct i n g w i r e

a d j u s t . p l u g h e a t e r b a k e l i t e c o v e r

I

1

!&

- superconductino w i r e a d j u s t . p l u g f o r

c o d u i t l e n g t h FRP h o l d e r

c o o l i n g channel thermometer h e a t e r

bake1 i t e cover

F i g . 1 - Schematic e x p e r i m e n t a l arrangement

Four d i f f e r e n t c o n f i g u r a t i o n s o f t h e sample l i s t e d i n T a b l e I were t e s t e d . The amount of Y i n t h e t a b l e expresses t h e p a c k i n g f a c t o r o f t h e s u p e r c o n d u c t i n g w i r e i n t h e c o u n d u i t , i . e . Y(%) = A w / ( A c + A w ) x 100, where & and Ac a r e c r o s s - s e c t i o n a l areas of superconducting w i r e and o f t h e e f f e c t i v e space f o r t h e c o o l a n t r e s p e c t i v e l y . A, was c a l c u l a t e d from t h e measured steady peak h e a t - f l u x d e n s i t y Q ( =qA/Ac) a t which t h e s u p e r f l u i d i t y i s l o s t , on t h e assumption t h a t

W(T) L - ~ / ~ . ~ , where L i s t h e hydro- dynamical l e n g t h and W(T) i s a f u n c t i o n o f temperature /7/.

I " " " I

T a b l e 1. Sample parameters

Sample No. 1 2 3 4

F i g . 2 - An example o f temperature

and v o l t a g e changes

The n u c l e u s o f t h e normal s t a t e i n t h e s u p e r c o n d u c t i n g w i r e was i n i t i a t e d b y p u t t i n g a p u l s e c l u r r e n t w i t h a d u r a t i o n o f 5 msec i n t o a h e a t e r w h i c h was n o n - i n d u c t i v e l y wound on t h e s u p e r c o n d u c t i n g w i r e . Both v o l t a g e changes across thermometers and across taps connected t o t h e s u p e r c o n d u c t i n g w i r e were d i s p l a y e d o n a m u l t i - c h a n n e l photo-galvanometer. A l l measurement was made a t 1 . 8 K.

I 1 - RESULTS AND DISCUSSIONS

F i g u r e 2 shows t r a c e s o f t h e temperature and t h e v o l t a g e changes a f t e r a p p l y i n g thermal d i s t u r b a n c e w i t h t h e c r i t i c a l energy Ed a t which t h e quench i n t o normal s t a t e s e t s i n . We can e a s i l y d i s c r i m i n a t e t h e t r a n s i t i o n f r o m He I 1 t o He I b y o b s e r v i n g second r i s e s on t r a c e s (arrows i n F i g . 2 ) . The p r o p a g a t i o n v e l o c i t y o f t h e i n t e r f a c e between He I 1 and He I was c a l c u l a t e d f r o m t h e s e t r a c e s .

A l t h o u g h v A must be equal t o t h e v e l o c i t y vp i n t h e s t e a d y s t a t e i f we d e a l w i t h i n f i n i t e l y l o n g c a b l e - i n - c o n d u i t , t h e r e a r e d i f f e r e n c e s i n t h e i r v e l o c i t i e s w i t h i n a c e r t a i n t r a n s i t i o n d i s t a n c e f r o m an o r i g i n o f quench. I n t h e case o f Sample 1, 2 and 3 w i t h s m a l l Y, v X i s n e a r l y t h e same as vp as shown i n F i g . 3. F o r t h e l a r g e r Y i n Sample 4, t h e A i n t e r f a c e propagates f a s t e r t h a n vp.

Now we w i l l i n t r o d u c e a b r i e f c r i t e r i o n f o r t h e optimum volume o f c o o l a n t t o a c h i e v e t h e h i g h o v e r a l l c u r r e n t d e n s i t y <j> . The c o n d i t i o n o f v~

vp o r v~ > vp a t a c e r t a i n Y o f a c a b l e - i n - c o n d u i t g i v e s a s t a n d a r d o f t h e p r o p e r q u a n t i t y o f permeated He IIp.

Thus, t h e t u r n i n g p o i n t f r o m t h e c o n d i t i o n v i = vp met i n Sample 1, 2 and 3 t o t h e c o n d i t i o n v~ > v p i n t h e Sample 4 g i v e s t h e o p t i m a l p a c k i n g f a c t o r Yc. T h i s c r i t e r i o n does n o t d e t e r m i n e whether t h e superconductor i n a c o n d u i t quenches o r n o t , b u t s i g - n i f i e s t h a t p r e c e d i n g c o l l a p s e o f t h e s u p e r f l u i d i t y a c c e l e r a t e s t h e p r o p a g a t i o n o f t h e normal f r o n t a t Y > Yc f o r t h e d e f i c i e n c y o f t h e c o o l a n t ( F i g . 3 ) .

F i g . 3 - P r o p a g a t i o n v e l o c i t y vs. c u r r e n t F i g . 4 - C r i t i c a l energy and p r o p a g a t i o n

v e l o c i t y vs. c u r r e n t

CI-518 J O U R N A L DE PHYSIQUE

The minimum p r o p a g a t i n g c u r r e n t Im a t which vp i s z e r o i s small except f o r Sample 1 w h i c h has e x c e s s i v e l y l a r g e space F o r t h e c o o l a n t , e.q. Imp

22 A f o r Samples 2, 3 and 4, and 40 A f o r Sample 1 a t 6 - 7 T. While t h e r e c o v e r y c u r r e n t Ir i s l e s s than 10 A above 5 T i r r e s p e c t i v e o f t h e b a t h temperature. Thus, i t i s n o t a d v i s a b l e t o o p e r a t e t h e superconducting magnet o f t h e c a b l e - i n - c o n d u i t a t Imp much l e s s I , because b o t h c u r r e n t s a r e i n h e r e n t l y small i n t h e i n t e r n a l l y c o o l e d superconducting c a b l e .

I n a d d i t i o n , t h e v a l u e o f Yc appears t o be t o o small t o o b t a i n t h e h i g h o v e r a l l c u r - r e n t d e n s i t y i.e., < j >

Y c . I / A w = 1 6 ~ f m m ~ a t H 5 7 . 5 T and I = I m p .

On t h e o t h e r hand, we have known i n t h i s s t u d y t h a t l a r g e amount o f He I 1 o r s m a l l Y i n c r e a s e s Ed c o n s i d e r a b l y and decreases p r o p a g a t i o n v e l o c i t i e s as shown i n F i g . 4.

Therefore, i n an a c t u a l He IIp c o o l e d c a b l e - i n - c o n d u i t composed o f N w i r e s , we can advantageously e s t i m a t e Ed o f component w i r e s : t h e s t a b i l i t y o f each w i r e i s n o t predominated b y t h e s u b d i v i d e d area Ac which surrounds each w i r e on t h e average and f u l f i 11s t h e c r i t e r i o n Yc, b u t t h e t o t a l c r o s s - s e c t i o n A,T (

N . Ac) i n common should be t a k e n account as t h e e f f e c t i v e h e a t s i n k area because t h e t r a n s i e n t h e a t f l u x d i f f u s e s o v e r t h e wide range owing t o l a r g e t h e r m a l - c o n d u c t i v i t y o f He 11. I f l o c a l - i z e d d i s t u r b a n c e s a r e a t an a l l o w a b l e l e v e l l e s s than Ed enhanced by e f f e c t i v e l y reduced Y i n the a c t u a l cable, we may p r a c t i c a l l y o p e r a t e t h e magnet a t h i g h e r c u r r e n t than N.1, a l t h o u g h t h e c a b l e i s s t i l l accompanied w i t h t h e p o s s i b i l i t y o f t h e normal p r o p a g a t i g n . Of course, t h e s t a b i l i t y Ed i s n o t increased u n l i m i t e d l y b y i n c r e a s i n g A c ~ o r N. The p r o p e r s i z e o f He IIp c o o l e d c a b l e - i n - c o n d u i t must be determined from t h e d i f f u s i o n l e n g t h o f t r a n s i e n t h e a t f l u x /8/.

The c l e a r e f f e c t o f t h e channel l e n g t h L on t h e s t a b i l i z a t i o n c h a r a c t e r i s t i c s was n o t observed w i t h t h e e x c e p t i o n t h a t t h e l o n g e r t h e channel i s , t h e h i g h e r t h e temperature of t h e superconducting w i r e r i s e s d u r i n g quenching /9/. The r e s e a r c h on t h e e f f e c t o f L on t h e s t a b i l i t y i s b e i n g c a r r i e d o u t .

T h i s work i s supported by t h e G r a n t - i n - A i d f o r F u s i o n Research, The M i n i s t r y of Education.

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KOBAYASHI H. and YASUK~CHI K., Advances i n Cryogenic E n g i n e e r i n g 2 (1982) 451.

VAN SCIVER S.W., Advances i n Cryogenic E n g i n e e r i n g 27 (1982) 375.

MORPURGO M., Workshop on t h e S t a b i l i t y of Superconductors i n He I and He 11, Saclay, France, I I F / I I R B u l l e t i n (1982) 209.

SEYFERT P. LAFFERRANDERIE J. and CALUDET G., Cryogenics 22 (1982) 401.

MEURIS C. TURCK B. SEYFERT P. and CLAUDET G., Workshop on t h e S t a b i l i t y o f Superconductors i n He I and He 11, Saclay, France, I I F / I I R B u l l e t i n (1982) 215.

CHUANG C. KAMIOKA Y. and FREDERKING T.H.K., Advances i n Cryogenic E n g i n e e r i n g 27 (1982) 493.

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BON MARDION G. CLAUDET G. and SEYFERT P., Cryogenics 19 (1979) 45.

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KOBAYASHI H. YASUK~CHI K. and FUSE K., Workshop on t h e S t a b i l i t y o f

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