Order parameter and magnetic field of the distorted vortex lattice and their application to flux pinning in type II superconductors. II. Curved flux lines

From the Ginzburg--Landau equations, the order parameter, local magnetic field, supervelocity, and elastic energy are derived for an arbitrarily distorted lattice of curved or straight flux lines. Exact solutions are given for small strains and for fields close to the upper critical field H/sub c2/. These solutions are generalized to large strains and arbitrary inductions. The general expressions approximately reproduce all previous results. They apply even to isolated and to crossed flux lines and to flux line loops. As a first application of the distorted-lattice solutions the pinning force density exerted by a small inclusion on the flux line elements is calculated. It turns out that the force may be concentrated on a flux line section of length smaller than even the coherence length. The response of the flux line lattice to such localized forces requires treatment by a nonlocal theory of elasticity and is much larger than expected so far