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

A program for the rigorous calculation of the volume pinning force exerted by-imperfections on the flux line lattice in type II superconductors is outlined. As one step of this program, the order parameter, local magnetic field, supervelocity, and elastic energy of the distorted lattice of still parallel flux lines are calculated from the Ginzburg-Landau theory. These general solutions provide a transformation of the Ginzburg-Landau free energy functional of an imperfect material into a mere function of the flux line positions, and thus allow a definition of elastic and pinning force densities which for the first time apply also to large inductions. First, exact solutions for small strains and for fields close toH_c2 are derived. Then, approximate solutions are presented applying to larger strains and to arbitrary inductions. The forces on each flux line exerted by a small needle-shaped inclusion parallel to the flux lines are calculated.