Scaling of percolative current flow to long lengths in biaxially textured conductors

Abstract
A random mixture of conducting and non-conducting sites or bonds on a two-dimensional lattice is used to model textured polycrystalline superconducting conductors in which high currents are carried only by low-angle grain boundaries. We calculate the frequency with which unfavourable configurations will significantly decrease current flow. For realistic distributions, in very narrow conductors (~10 grains wide) critical current is reduced, sometimes to zero, over long lengths. For a typical conductor, 1 cm wide with 50 µm grain size, fluctuations in critical current of less than 10% are expected for kilometre lengths.