Magnetic
Shielding Improving the Current-Carrying Capability
of Superconducting Films
Y.A. Genenko, H. Rauh
Institut
für Materialwissenschaft, Technische Universität Darmstadt
Critical currents in superconducting films are limited
by extended weak-links formed by grain boundaries, twin boundaries or other
two-dimensional defects which often exhibit properties typical for Josephson
junctions and which represent locations where magnetic vortices may enter
first, thus giving rise to the onset of energy dissipation. A promising way to
improve the current-carrying capability of homogeneous superconductor strips
without extended defects and also to reduce ac losses in them is magnetic
shielding. The presence of bulk magnets of high permeability may lead to a substantial
current redistribution and, concomitantly, to an enhancement of the total
critical current by some orders of magnitude. How magnetic shielding effects
real films with extended defects is, however, still an open question.
Here we study current distributions in the Meissner
state of a long, butt-joint Josephson junction between films located inside an
open magnetic cavity. We compare the current patterns, calculated for various
distances to the adjacent bulk magnets, both with those in an isolated
Josephson junction and those in magnetically shielded films without a junction.
The density of the supercurrent across the Josephson
junction is given by the relation
with the Josephson critical current density jC, the
coordinate x indicating positions
along the junction. The phase difference j(x) of the superconductor order parameter
across the junction herein is governed by the nonlinear equation
where lJ denotes the Josephson penetration depth and jm(x) means the transport current
distribution in the (isolated or shielded) Meissner state of the film without
the junction.
Employing specific forms of jm(x)
corresponding to various shielding geometries, we solve the constitutive
equation for the phase difference numerically. Of all the even solutions
satisfying the boundary conditions j ’(0) = 0 and j ’(L) = 0 and pertaining to the flux-free
Meissner state of the Josephson junction of half-length L, we choose the one which furnishes the maximum total current,
that is the critical current in this state.
The current distribution over a long, isolated
Josephson junction exhibits current peaks near the edges of the junction. The
average current density is seen to decrease fast with increasing length of the
junction (Fig. 1).
Fig. 1. Variation of the current
density in a long, isolated Josephson junction of half-length L=35lJ , the coordinate along the junction, x, being given in units of lJ.
In order to study the effect of magnetic shielding on
a butt-joint Josephson junction between thick superconducting films, we refer
to the configuration of a superconductor strip placed orthogonally between two
flat, bulk magnets for which the Meissner current distribution jm(x) is known from previous work. The
current distribution over a long, shielded Josephson junction in the strip
again shows current peaks near the edges of the junction, their height however
diminishing and the average current density simultaneously increasing when the
distance between the centre of the junction and the adjacent magnets is reduced
(Fig. 2).
Fig. 2. Variation of the current
density in a long, shielded Josephson junction of half-length L=35lJ, the coordinate
along the junction, x, and the distance between the centre of the junction and
the adjacent magnets, a, being given
in units of L.
We establish that magnetic shielding tends to
homogenize the current distributions in weak-links - with almost uniform
distributions for virtually direct superconductor/magnet contact - thereby
enhancing the total critical current by possibly several times.
Poster presented at the European Conference for Applied
Superconductivity, Copenhagen (2001)
Fachgebiet Theoretische Grundlagen der Materialentwicklung,
Institut für Materialwissenschaft / Letzte Änderung:24.2.2002 / Elena Genenko