The statistical summation of weak flux-line pins in type II superconductors

A random array of flux-line-pinning defects is shown to produce instabilities in the flux-line lattice and a significant bulk pinning-force density even if the pins individually fail to satisfy the threshold criterion. A simplified model defect-flux-line interaction is used to obtain approximate expressions for the critical pinning-force densityF _c.The theory predicts that in materials with a dilute array of weak pinsF _cdepends only weakly on magnetic field except within narrow peaks near the upper and lower critical fields. The width of the peaks increases as the pins are made denser or stronger. A broad, dome-shaped peak inF _cand scaling-law behavior, both of which are usually associated with large-F _cmaterials, is the strong-pinning limit of this theory. This limit may be reached either by making the pins very strong or very dense. The results forF _cagree at least qualitatively with a number of experimental observations.