1.8　Critical current densities

The critical current density Jc （A/m2）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 densities Jc refers 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 density Jc which destroys the Cooper pairs, is determined by the magnetic field H which is produced by the critical current density. If a current I flows in the axial direction of a superconducting cylinder wire of radius R, the wire causes a circular magnetic field H0 around it.This field decreases with radius r which from the wire outside surface into the centre, and could be expressed as

If the current I produces a magnetic field H0 which is higher than Hc , the super conducting state will be destroyed. Thus, Ic is intuitively defined as the value of H0=Hc in the type I superconductors, i.e.

In fact, since magnetic flux is expelled from the inside of a superconducting wire, the current density J cannot be uniform. The current I only flows in the surface layer at the penetration depth λL .The total current I over the cross section of the superconducting wire is expressed as

where J is the current density and the quantity 2πRλis the effective cross sec tion area of the surface layer.Thus, the highest intrinsic current, which destroysCooper pairs and superconductivity of a superconductor, can be calculated using the thermodynamic critical field Hc ，i.e.

If the values of Hc andλof a type II superconductors are 0.1 T and 100 nm, the critical current density Jc is 108A/cm2.

The Ginzburg-Landau critical current density is expressed as20

According to the Eq.（1. 6.3）and（1.9.6），

Since the current of a type I superconductor is concentrated within the penetration depth of the surface, the critical current of a type I superconductor wire is directly proportional to the outer circumference of superconducting wire. For a type II superconductor which works in a mixed state between Hc1 and Hc2 for practical applications, the distribution of the superconducting current is more complicated.

For HTSC with planar structure, the critical current densities are smaller when the external field is applied perpendicular to the c-axis than when applied parallel to the axis20.