HAL Id: jpa-00217720
https://hal.archives-ouvertes.fr/jpa-00217720
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
ON THE MECHANISM OF THE CURRENT
INDUCED TRANSITION S
→ N IN THE TYPE II
SUPERCONDUCTING WIRES
B. Makiej, A. Sikora, E. Trojnar
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplPment au
no
8,
Tome 39, aotit 1978, page
C6-623
ON
THE MECHANISM OF THE CURRENT INDUCED T R A N S I T I O N S*
N1N THE TYPE
I 1
SUPERCONDUCTING WIRESB. Makiej, A. Sikora and E. Trojnar
I n s t i t u t e f o r Low Temperature and Structure Research, PoZish Academy of Scz^ences 53-529 Wroclaw, Prochnika 95, Poland
RLsum6.- Deux modZles : 1'4tat d'ancrage de flux et 1'Qtat de mouvement de flux sont prbsentbs. Les rgsultats expgrimentaux sur la distribution de l'induction magndtique dans la ligne conductrice sont compargs aux prgdictions thdoriques.
Abstract.- Two models : the flux pinning state and flux flow state are presented. Experimental re- sults of the magnetic induction distribution in the current-carrying wire and the theoretical pre- dictions have been compared.
The purpose of this work is to investigate the nature of the current induced transition of the type I1 superconducting cylinder from the supercon-
ducting to the dissipative state and to compare theoretical predictions on the magnetic induction distribution in a superconducting wire with the ex- perimental results obtained by the bismuth probe me- thod /I/. The present discussion related to the be- haviour of the long, isotropic, type I1 superconduc-
ting cylinder of the radius a carrying the transport current I in the zero applied magnetic field. When the temperature of the sample is constant and the current I is lower than the therehold current It there dominates a flux pinning state in which the Lorentz forces are compensated by the pinning forces. These latter, according to our assumption, are pro- portional to the "magnetic pressure" or to magnetic energy density. The equation expressing the assump- tion is following :
a 1.7 x
BI
=-
BH,
2 (1)
where J denotes transport current density, B = VH
magnetic induction, H
-
magnetic field intensity. Under the simplifying assumption that the permeabi- lity !.I is independent of the distance y from the cy-face can be regarded as independent of y. In this case the solution of the differential equation (3) relevant at least near the surface is
where the constants a,B have to be chosen according to the initial ~ondition of the experiment. One can see from the relation (4) and figure 1 that in the state of flux pinning there is a steep decrease of the magnetic induction with diminishingy. Despite the simplifying assumptionsmade, rather good con- formity with the experimental data can be reached when we disregard the middle part of the sample
(r <
1.4
mm) where magnetic induction observed isprobably due to the flux frozen in 121.
When electric current is higher than the threshold current I and stationary flux flow has
t
been fully established, quite different situations will be encountered. In that case Lorentz forces will be compensated by the viscous flow forces. Be- cause of regular flux flow in the whole volume of the sample we can treat these viscous forces as in- dependent of y. Therefore, the equation for B(y) is now expressed in the form
linder axis we get from the relation (I) 1 dB2 + B2 cos2 r)
_
,
--
2 dy Y
lcurl B x
BI
= aB2, (2)whereadenotes constant, or in the general case of Where and @ denote
helical current flow (2) This leads to the solution of the differential equa-
1 dB2
'
B
cos24
= aB2, tion (5) in the form :- - +
2 dy
Y
( 3 )where B cos $ denotes the azimuthal component of the
IB(~) I
=/
2F y-
9 ( 6 )C
magnetic induction. 2 cos2
4
+ 1 y 2 c0s24
In the part of the sample being near the sample sur- where constant C must fulfil the condition C > 0 as
I
24 46 <B D 08 l b 24 drsfonce from the centre of the sample[mm]
Fig. 1 : Distribution of the magnetic induction in the cylindrical sample at the flux pinning state.
-
experimental curve,-
theoretical curve(4)
Bfy) must diminish by p O . Followingly, the real M-
lues of B(y) are limited to the range yo 6 y ,< a where 2P C = 0.
2 cos2 f$
+
I yo 2 cos2 f$As we see from figure 2 the experimental da- ta can be approximated by the theoretical ones ob- tained from the relation (6) with the appropriately chosen constants F and C.
a,stance from the centre of the sample [mtn]
It is worth noting that the special case C = 0 provides B(y) function of the similar form as the function which could be obtained from the pap& 131.
Taking into account qualitative agreement between the theoretical predictiors, bases on the t w ~
demonstrated models, and the experimental results one can hope that we come across very promissing way for elucidation of the mechanism of the current in- duced transition from the superconducting to the normal state.
References
/I/ Sikora, A., Makiej, B., Trojnar, E., Phys. Let.
2 7
(I
968) 175/2/ Makiej, B., Golab, S., Sikora, A., Trojnar, E. and Zacharko, W., Cryogenics
fi
(1976) 537 131 Nicholson, J.E., Sikora, P.T. and Carrol, K.J.,in Proc. 13th Intern. Conf. Low Temp. Phys., Boulder, 1972, Plenum Press, New York
-
London Vol. 3 (1974) 192Fig. 2 : Distribution of the magnetic induction in the sample at the flux flow state.
