Statistical theory of pinning on point defects

Abstract

The statistical treatment of pinning on point defects is given including the correlations of the number of defects in neighbouring volumes (the interaction of these volumes with the fluxoid is taken as the elementary interaction causing the pinning). For higher defect densities, the agreement with the experiments on niobium is better than with the previous theory. This method of correlations seemed suitable for study the effect of “cutting-off” the small elementary interactions and for the replacement of the Gauss distribution function by the Poisson distribution function for the number of defects in the elementary volumes. Both these efforts give negative results with respect to the experiments; so far we are therefore not able to explain quantitatively the large increase of the pinning force at small defect densities and small magnetic fields, as well as its decrease to zero always for fields smaller thanH _c2 . The attractive interaction between the flux lines in type II superconductors with small Ginzburg-Landau parameter could give a qualitative explanation of the enhancement of the pinning at small defect densities.