Pinning forces and hysteresis in type II superconductors

Flux lines in type II superconductors experience pinning forces due to material defects. Under critical-current conditions it is assumed that the forces are proportional to |H|n, where H is the local magnetic field and n is an arbitrary constant. On this basis, the magnetic flux distribution in an infinite superconducting slab is calculated as a function of time, when a sinusoidal magnetic field, Ho=Hm sin¿t, is applied parallel to the slab surface. Hence, the instantaneous rate at which flux penetrates into the superconductor is evaluated. The results lead to the hysteresis loop of the material, which implies power dissipation proportional to Hm3¿n for n ¿1. It is shown that the Bean-London and Kim-Anderson models of hysteresis in type II superconductors appear as special cases of the above theory.