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

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 (similar to 10 grains wide) critical current is reduced, sometimes to zero, over long lengths. For a typical conductor, 1 cm wide with 50 mu m grain size, fluctuations in critical current of less than 10% are expected for kilometre lengths.