The pinning of flux lines in superconductors by randomly-spaced pinning centres

Abstract

A simple theory is developed to explain the pinning of a vortex array by a large number of widely spaced pinning centres. By making certain simplifying assumptions, which do not alter the qualitative conclusions, it is possible to obtain analytic expressions for most of the parameters that have been measured on such a system. These include the critical current density, the voltage-current (V-I) characteristics, noise voltages and flux creep. It is shown that there is no regime in which the pinning is proportional to the square of the basic interaction, and also that it is impossible to reconcile the theory with all the experimental results. It is concluded that no theory based on non-interacting pinning centres in an elastic vortex lattice is tenable.