High Temperature Superconducting Magnetic Levitation

1.8 Critical current densities Ë 11

The coherence lengths휉of the HTSC materials have strong anisotropy. The con-
ductivity along the chains (b-axis) is more than twice that in thea-axis direction which
is perpendicular to the chains. [19] This results in large anisotropy of the coherence
lengths and the values of the superconducting gap at the same critical temperature.

1.8 Critical current densities

The critical current densityJc(A/m^2 ) of a superconductor is the transport current
which destroys the Cooper pairs and the superconducting state. However, in real
applications of type II superconductors, the critical current densitiesJcrefers to the
value starting the flux flow, which is several orders of magnitude lower than the value
which destroys the Cooper pairs.
The critical current densityJcwhich destroys the Cooper pairs, is determined by
the magnetic fieldHwhich is produced by the critical current density. If a currentI
flows in the axial direction of a superconducting cylinder wire of radiusR, the wire
causes a circular magnetic fieldH 0 around it. This field decreases with radiusrwhich
from the wire outside surface into the center, and could be expressed as

H 0 = I

2 휋r

. (1.31)

If the currentIproduces a magnetic fieldH 0 which is higher thanHc, the supercon-
ducting state will be destroyed. Thus,Icis intuitively defined as the value ofH 0 =Hc
in the type I superconductors, i.e.

Ic= 2 휋RHc(T). (1.32)

In fact, since the magnetic flux is expelled from the inside of a superconducting
wire, the current densityJcannot be uniform. The currentIonly flows in the surface
layer at the penetration depth휆L. The total currentIover the cross section of the
superconducting wire is expressed as

I= 2 휋R휆J, (1.33)

whereJis the current density and the quantity 2휋R휆is the effective cross secti-
on area of the surface layer. Thus, the highest intrinsic current, which destroys
Cooper pairs and superconductivity of a superconductor, can be calculated using the
thermodynamic critical fieldHc, i.e.

Hc=휆J. (1.34)

If the values ofHcand휆of a type II superconductor are 0.1 T and 100 nm, the critical
current densityJcis 10^8 A/cm^2.