Vortex lattice in 3D-collective pinning theory for type II superconductor

A modification on the theory of collective pinning Larkin et al. (1979) is made by considering the presence of dislocations lines on the vortex lattice besides the elastic interaction among the vortices. The total energy of the vortex lattice-material defects systems, W_T, is minimized with respect to V_c, the correlation volume. By numerical simulation the pinning force density, F_p, is obtained from the equations of the minimisation process as a function of b=B/B_c2. So the calculated F_p can be compared to the experimental results for Nb46.5 wt.%Ti for several optimization levels. It is also concluded that even in better optimizated materials with a high density of strong defects, it is necessary to take the elasticity of the vortex lattice into consideration.