The elastic Green's function for the pinned flux-line lattice in a type II superconductor

The elastic Green's function for the pinned flux-line lattice in the critical state is defined and evaluated in the coherent potential approximation. The presence of pinning sites contributes an additional restoring force, which must be calculated within a complete theory of the critical state, but which can be measured. Results are given for the dependence of the Green's function on the density of strong flux-line pins, and a criterion is derived for the applicability of the dilute-limit approximation. This criterion is never satisfied near the upper and lower critical fields. Assuming that the pins all interact sufficiently strongly with the flux-line lattice to exceed the threshold criterion, we find that the Green's function decreases (the flux-line lattice becomes more rigid) with increasing pin density.Research sponsored by the Division of Materials Science, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.