Amount of flux lines 'pinned' in type II superconductor

[Yakone]

a type II superconductor may not exhibit complete exclusion of magnetic field due to quantum vortices. It is my understanding that the magnetic field present will affect the number of vortices or fluxons present, but what is the relationship between magnetic field, and number of vortices in a type II superconductor (zero-field cooled), or am I completely missing the mark?

 

[M Quack]

Graphically, you can imagine that the magnetic fields lines of the external field are "bundled" into quantized packets inside the superconductor.

The density of vortices is then such that the macroscopic flux is the same as outside of the SC, N*(flux quantum)/(macroscopic area)=B_ext, where N is the number and N/(macroscopic area) is the density of vortices.

In the absence of defects and pinning centers, the vortices may form ordered lattice. In most materials these are hexagonal, but square ones also occur. These lattices can be observed with decoration experiments, neutron scattering or electron microscopy. From the lattice parameters you can calculate the density.