An approximate closed-form expression for the electron-scattering-induced interaction between magnetic flux lines and grain boundaries

An approximate closed-form result for the interaction of an isolated magnetic flux line in a type-II superconductor with a grain boundary, due to the scattering of electrons by the boundary, is presented here. The grain boundary need not be infinitely thin, but can include a distribution of scattering centers nearby. The resulting expressions are more suitable for computer simulations of flux pinning and their interpretation is more physically transparent than previous results; they are used here to discuss pinning by nonideal boundaries.