PINNING FORCE DENSITY IN STRONGLY PINNED SUPERCONDUCTORS

Pinning force density in strongly pinned superconductors is theoretically estimated in terms of the coherent potential approximation in which the Labusch parameter is assumed as a single parameter representing the strength of interference among individual pinning potentials through the elasticity of the fluxoid lattice. From the statistical average the pinning force density is shown to have a nonzero value only when the elementary pinning force is larger than some threshold value. At the same time the threshold value is also obtained as a function of the elementary pinning force. When the solution of the pinning force density is obtained consistently, the threshold value is found to be always smaller than the elementary pinning force. This means that the pinning loss is of the hysteresis type, as is well recognized. The obtained pinning force density obeys the linear summation and qualitatively agrees with many experimental results on strongly pinned superconductors. The theoretical result is compared quantitatively with the experimental result on the pinning force density in superconducting Nb-Ta with normal Nb2N precipitates as strong pinning centers.