Current-Induced Resistive State
In this section we discuss the electric and magnetic phenomena in superconductors caused directly by a transport current and by the magnetic field associated with this current, in the absence of an external magnetic field. The dimensions of the supercondu
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In this section we discuss the electric and magnetic phenomena in superconductors caused directly by a transport current and by the magnetic field associated with this current, in the absence of an external magnetic field. The dimensions of the superconductor are generally assumed to be large compared to the coherence length and penetration depth.
14.1 Wire Geometry The destruction of superconductivity by an electric current in a cylindrical type-I superconductor with circular cross section was treated theoretically by LONDON [3.5,14.1] 40 years ago. We consider a wire of radius Ro' Electrical resistance will appear in the wire as soon as the current-generated magnetic field at the circumference of the wire exceeds the critical field, i.e., for currents exceeding the critical value IC = cRoHc/2
(14.1)
The breakdown of superconductivity in a current-carrying conductor at the current value at which the current-induced magnetic field reaches Hc is often referred to as Silsbee's rule. According to London's theory, for currents larger than Ic the superconducting wire splits up into a stationary, cylindrically symmetric mixture of normal and superconducting domains. The configuration proposed by LONDON is shown in Fig.14.1. It consists of a core of alternate layers of normal and superconducting phase arranged in conical shapes along the cylinder axis. This core region of alternate layers extends outward to the radius R1 < Ro' In the normal layers of the core the magnetic field is equal to Hc' The transport-current density along the wire is
R. P. Huebener, Magnetic Flux Structures in Superconductors © Springer-Verlag Berlin Heidelberg 2001
212
t
I
N
-4Rl~
---i J
Ro
f--
cIa 't'lT -r -ar (rH(j) )
= -,,-
Fig.14.1. Intermediate-state structure of a wire in the current induced resistive state according to LONDON
c Hc 't'lT r
= -,,- -
(14.2)
where r is the radial coordinate and H(j) the azimuthal field component. The spatially averaged magnetic field in the core is anE H - J Hc = a nE -c4'lTr
(14.3)
where an is the normal-state conductivity and E the electric field. The average field increases from H = 0 for r = 0 to H = Hc for r = R1. From (14.3) we obtain Rl
(14.4)
cHc/4'lTanE
The outer shell between the radii Rl and Ro consists of normal phase with H > Hc' At the critical current Ic the intermediate state is established such that the core region extends to the surface of the wire (R 1 = Ro)' As the current is increased above Ic the radius Rl of the intermediate-state core shrinks, causing a rise in electrical resistance according to R/Rn =
i {I
+ [1 -
(Ic/I)2]~}
(14.5)
Here Rn is the normal-state resistance. From (14.5) at I = Ic we expect the electric resistance to jump discontinuously from zero to 50% of its normal value and to gradually approach Rn as I is increased further. Since the time of London's paper the destruction of superconductivity by a transport
213
current has been studied experimentally from the restoration of electrical resistance in superconducting wires [2.5]. Typical exp
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