Numerical extension of the power law Jc(B) to zero field in thin superconducting films

Numerical simulations of the current and field distribution in thin superconducting films are carried out for a given material law Jc(B) and as a function of the applied field H, taking the sample's self-field into account. The dependence of the critical current density on the applied field Jc(H) is computed for comparison with experiment, considering the geometry of transport measurements. We show that extrapolating the high field power law Jc \propto B^{-\alpha} to the lowest fields results in a finite critical current at zero applied field Jc(H=0), despite the singularity of Jc(B). Moreover, particular features of the experiment, such as a low field plateau in Jc(H), are reproduced and found to be determined by the self-field.